[SCENARIO]
Family: F3 (Shared Resources and Capacity)
Archetype: retail_f3_volumetric_constraint
Scenario ID: retail_f3_volumetric_constraint_v1

[BUSINESS DESCRIPTION]
Business narrative:
One product -- typically a bulky premium item -- uses much more storage volume per unit than the others. Storage capacity at each location becomes tight primarily because of this product, forcing the retailer to choose between stocking bulky high-margin units and smaller items. All demand remains local and exogenous, with no transshipment or backorders.

Structure cues:
- The overall structure and shared storage framework match retail_f3_storage_bottleneck.
- Shelf life: Each product has a shelf life in periods. Inventory must be tracked by REMAINING LIFE.

  VARIABLE DEFINITION: I[p,l,t,r] = inventory at START of period t with r periods remaining.
  Convention: r=1 is OLDEST (sell first FIFO), r=shelf_life[p] is FRESHEST.

  KEY EQUATIONS - implement EXACTLY as written, do NOT add or remove terms:

  (1) Fresh inflow: I[p,l,t,SL] = Q[p,t] * demand_share[l]
      - This is ONLY the inflow from production. Do NOT subtract sales here!
      - Q is total production, demand_share distributes it to locations.

  (2) Aging: I[p,l,t+1,r] = I[p,l,t,r+1] - sales[p,l,t,r+1] for r=1..SL-1
      - Inventory tomorrow with r remaining = inventory today with r+1 remaining - sales

  (3) Waste: W[p,l,t] = I[p,l,t,1] - sales[p,l,t,1]
      - Items with r=1 that aren't sold become waste

  (4) Sales availability: sales[p,l,t,r] <= I[p,l,t,r]
      - Can only sell what you have in inventory

  (5) Inventory holding cost: charged on (I[p,l,t,r] - sales[p,l,t,r]) for r >= 2
      - Charge on END-of-period inventory (after sales), exclude expiring items (r=1)
- Storage capacity: sum over products of (cold_usage[p] * total_inventory[p,l,t]) <= cold_capacity[l]. Product-specific storage usage parameters in the JSON are much larger for the premium product than for other SKUs.
- Inventory cannot be negative and is updated based on previous stock, local production, sales, and waste.
- There is no transshipment, lead times are zero, and substitution behavior follows the JSON graph with standard semantics.
- The objective is to minimize total cost (aggregating purchasing, holding, waste, and lost sales) under capacity constraints that make the volumetrically heavy premium product particularly expensive in terms of space.

[DATA SCHEMA]
{
  "name": str,                          # scenario identifier
  "periods": int,                       # number of time periods
  "products": [str, ...],               # list of product IDs
  "locations": [str, ...],              # list of location IDs

  "shelf_life": {p: int},               # shelf life in periods per product
  "lead_time": {p: int},                # order lead time per product (0 = same-period arrival)

  "demand_curve": {p: [float, ...]},    # demand per product per period (0-indexed list)
  "demand_share": {l: float},           # fraction of total demand at each location

  "production_cap": {p: [float, ...]},  # max production per product per period (0-indexed list)
  "cold_capacity": {l: float},          # storage capacity per location
  "cold_usage": {p: float},             # storage units per unit of product

  "labor_cap": {l: [float, ...]},       # labor hours per location per period (0-indexed list)
  "labor_usage": {p: float},            # labor hours per unit sold
  "return_rate": {p: float},            # fraction of sales returned next period

  "costs": {
    "purchasing": {p: float},           # cost per unit ordered
    "inventory": {p: float},            # holding cost per unit per period
    "waste": {p: float},                # cost per unit expired
    "lost_sales": {p: float},           # penalty per unit of unmet demand
    "fixed_order": float,               # fixed cost per order placed
    "transshipment": float              # cost per unit transshipped
  },

  "constraints": {
    "moq": float,                       # minimum order quantity (0 = no MOQ)
    "pack_size": int,                   # order must be multiple of this (1 = no constraint)
    "budget_per_period": float|null,    # max purchasing cost per period
    "waste_limit_pct": float|null       # max waste as fraction of total demand
  },

  "network": {
    "sub_edges": [[p_from, p_to], ...], # substitution: p_from's demand can be served by p_to
    "trans_edges": [[l_from, l_to], ...]# transshipment: can ship from l_from to l_to
  }
}

[DATA ACCESS]
- The variable `data` is pre-loaded. Do NOT use file I/O.
- Lists are 0-indexed (period t in model uses index [t-1] in data arrays)

CRITICAL - Network edges require tuple conversion for Gurobi:
  sub_edges = [tuple(e) for e in data.get('network', {}).get('sub_edges', [])]
  trans_edges = [tuple(e) for e in data.get('network', {}).get('trans_edges', [])]

[OUTPUT FORMAT]
- Import: import gurobipy as gp; from gurobipy import GRB
- Set Gurobi params: m.Params.OutputFlag = 0; m.Params.Threads = 1; m.Params.Seed = 0
- Print at end:
  print(f"status: {{m.Status}}")
  if m.Status == 2:
      print(f"objective: {{m.ObjVal}}")
- Output ONLY executable Python code. No markdown, no explanations.

[TASK]
Write a GurobiPy script that models and solves this optimization problem.

[SCENARIO]
Family: F3 (Shared Resources and Capacity)
Archetype: retail_f3_volumetric_constraint
Scenario ID: retail_f3_volumetric_constraint_v1

[BUSINESS DESCRIPTION]
Business narrative:
One product -- typically a bulky premium item -- uses much more storage volume per unit than the others. Storage capacity at each location becomes tight primarily because of this product, forcing the retailer to choose between stocking bulky high-margin units and smaller items. All demand remains local and exogenous, with no transshipment or backorders.

Structure cues:
- The overall structure and shared storage framework match retail_f3_storage_bottleneck.
- Shelf life: Each product has a shelf life in periods. Inventory must be tracked by REMAINING LIFE.

  VARIABLE DEFINITION: I[p,l,t,r] = inventory at START of period t with r periods remaining.
  Convention: r=1 is OLDEST (sell first FIFO), r=shelf_life[p] is FRESHEST.

  KEY EQUATIONS - implement EXACTLY as written, do NOT add or remove terms:

  (1) Fresh inflow: I[p,l,t,SL] = Q[p,t] * demand_share[l]
      - This is ONLY the inflow from production. Do NOT subtract sales here!
      - Q is total production, demand_share distributes it to locations.

  (2) Aging: I[p,l,t+1,r] = I[p,l,t,r+1] - sales[p,l,t,r+1] for r=1..SL-1
      - Inventory tomorrow with r remaining = inventory today with r+1 remaining - sales

  (3) Waste: W[p,l,t] = I[p,l,t,1] - sales[p,l,t,1]
      - Items with r=1 that aren't sold become waste

  (4) Sales availability: sales[p,l,t,r] <= I[p,l,t,r]
      - Can only sell what you have in inventory

  (5) Inventory holding cost: charged on (I[p,l,t,r] - sales[p,l,t,r]) for r >= 2
      - Charge on END-of-period inventory (after sales), exclude expiring items (r=1)
- Storage capacity: sum over products of (cold_usage[p] * total_inventory[p,l,t]) <= cold_capacity[l]. Product-specific storage usage parameters in the JSON are much larger for the premium product than for other SKUs.
- Inventory cannot be negative and is updated based on previous stock, local production, sales, and waste.
- There is no transshipment, lead times are zero, and substitution behavior follows the JSON graph with standard semantics.
- The objective is to minimize total cost (aggregating purchasing, holding, waste, and lost sales) under capacity constraints that make the volumetrically heavy premium product particularly expensive in terms of space.

[DATA]
The following JSON contains all instance data. Parse it directly in your code.

```json
{
  "name": "retail_f3_volumetric_constraint_v1",
  "description": "Standard seasonal retail scenario.",
  "periods": 20,
  "products": [
    "SKU_Basic",
    "SKU_Premium",
    "SKU_ShortLife"
  ],
  "locations": [
    "DC1",
    "DC2",
    "DC3",
    "DC4",
    "DC5"
  ],
  "shelf_life": {
    "SKU_Basic": 10,
    "SKU_Premium": 8,
    "SKU_ShortLife": 4
  },
  "lead_time": {
    "SKU_Basic": 0,
    "SKU_Premium": 0,
    "SKU_ShortLife": 0
  },
  "cold_capacity": {
    "DC1": 4408.72627642685,
    "DC2": 3667.439800340886,
    "DC3": 3140.886796114431,
    "DC4": 3377.991537212454,
    "DC5": 2597.040290953764
  },
  "cold_usage": {
    "SKU_Basic": 1.0,
    "SKU_Premium": 15.0,
    "SKU_ShortLife": 1.2
  },
  "production_cap": {
    "SKU_Basic": [
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800
    ],
    "SKU_Premium": [
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400
    ],
    "SKU_ShortLife": [
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500
    ]
  },
  "labor_cap": {
    "DC1": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC2": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC3": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC4": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC5": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ]
  },
  "labor_usage": {
    "SKU_Basic": 0.0,
    "SKU_Premium": 0.0,
    "SKU_ShortLife": 0.0
  },
  "return_rate": {
    "SKU_Basic": 0.0,
    "SKU_Premium": 0.0,
    "SKU_ShortLife": 0.0
  },
  "demand_curve": {
    "SKU_Basic": [
      294,
      271,
      376,
      355,
      492,
      488,
      689,
      879,
      1126,
      1376,
      1222,
      1256,
      1173,
      1021,
      755,
      583,
      425,
      399,
      324,
      299
    ],
    "SKU_Premium": [
      169,
      144,
      159,
      170,
      221,
      257,
      314,
      486,
      469,
      644,
      695,
      628,
      567,
      503,
      307,
      287,
      199,
      158,
      155,
      137
    ],
    "SKU_ShortLife": [
      126,
      129,
      111,
      139,
      167,
      225,
      253,
      373,
      472,
      456,
      530,
      543,
      390,
      319,
      278,
      193,
      165,
      160,
      124,
      115
    ]
  },
  "demand_share": {
    "DC1": 0.25,
    "DC2": 0.2,
    "DC3": 0.2,
    "DC4": 0.2,
    "DC5": 0.15
  },
  "costs": {
    "lost_sales": {
      "SKU_Basic": 50.0,
      "SKU_Premium": 80.0,
      "SKU_ShortLife": 40.0
    },
    "inventory": {
      "SKU_Basic": 1.0,
      "SKU_Premium": 1.5,
      "SKU_ShortLife": 1.0
    },
    "waste": {
      "SKU_Basic": 2.0,
      "SKU_Premium": 3.0,
      "SKU_ShortLife": 2.0
    },
    "fixed_order": 0.0,
    "transshipment": 0.5,
    "purchasing": {
      "SKU_Basic": 10.0,
      "SKU_Premium": 20.0,
      "SKU_ShortLife": 15.0
    }
  },
  "constraints": {
    "moq": 0,
    "pack_size": 1,
    "budget_per_period": null,
    "waste_limit_pct": null
  },
  "network": {
    "sub_edges": [
      [
        "SKU_Basic",
        "SKU_Premium"
      ]
    ],
    "trans_edges": []
  }
}
```

[OUTPUT FORMAT]
- Import: import gurobipy as gp; from gurobipy import GRB; import json
- Set Gurobi params: m.Params.OutputFlag = 0; m.Params.Threads = 1; m.Params.Seed = 0
- Print at end:
  print(f"status: {{m.Status}}")
  if m.Status == 2:
      print(f"objective: {{m.ObjVal}}")
- Output ONLY executable Python code. No markdown, no explanations.

[TASK]
Write a GurobiPy script that:
1. Parses the JSON data above (use json.loads on the string)
2. Models and solves the optimization problem
3. Prints status and objective value

Standard seasonal retail scenario.


[SCENARIO]
Family: F3 (Shared Resources and Capacity)
Archetype: retail_f3_volumetric_constraint
Scenario ID: retail_f3_volumetric_constraint_v2

[BUSINESS DESCRIPTION]
Business narrative:
One product -- typically a bulky premium item -- uses much more storage volume per unit than the others. Storage capacity at each location becomes tight primarily because of this product, forcing the retailer to choose between stocking bulky high-margin units and smaller items. All demand remains local and exogenous, with no transshipment or backorders.

Structure cues:
- The overall structure and shared storage framework match retail_f3_storage_bottleneck.
- Shelf life: Each product has a shelf life in periods. Inventory must be tracked by REMAINING LIFE.

  VARIABLE DEFINITION: I[p,l,t,r] = inventory at START of period t with r periods remaining.
  Convention: r=1 is OLDEST (sell first FIFO), r=shelf_life[p] is FRESHEST.

  KEY EQUATIONS - implement EXACTLY as written, do NOT add or remove terms:

  (1) Fresh inflow: I[p,l,t,SL] = Q[p,t] * demand_share[l]
      - This is ONLY the inflow from production. Do NOT subtract sales here!
      - Q is total production, demand_share distributes it to locations.

  (2) Aging: I[p,l,t+1,r] = I[p,l,t,r+1] - sales[p,l,t,r+1] for r=1..SL-1
      - Inventory tomorrow with r remaining = inventory today with r+1 remaining - sales

  (3) Waste: W[p,l,t] = I[p,l,t,1] - sales[p,l,t,1]
      - Items with r=1 that aren't sold become waste

  (4) Sales availability: sales[p,l,t,r] <= I[p,l,t,r]
      - Can only sell what you have in inventory

  (5) Inventory holding cost: charged on (I[p,l,t,r] - sales[p,l,t,r]) for r >= 2
      - Charge on END-of-period inventory (after sales), exclude expiring items (r=1)
- Storage capacity: sum over products of (cold_usage[p] * total_inventory[p,l,t]) <= cold_capacity[l]. Product-specific storage usage parameters in the JSON are much larger for the premium product than for other SKUs.
- Inventory cannot be negative and is updated based on previous stock, local production, sales, and waste.
- There is no transshipment, lead times are zero, and substitution behavior follows the JSON graph with standard semantics.
- The objective is to minimize total cost (aggregating purchasing, holding, waste, and lost sales) under capacity constraints that make the volumetrically heavy premium product particularly expensive in terms of space.

[DATA SCHEMA]
{
  "name": str,                          # scenario identifier
  "periods": int,                       # number of time periods
  "products": [str, ...],               # list of product IDs
  "locations": [str, ...],              # list of location IDs

  "shelf_life": {p: int},               # shelf life in periods per product
  "lead_time": {p: int},                # order lead time per product (0 = same-period arrival)

  "demand_curve": {p: [float, ...]},    # demand per product per period (0-indexed list)
  "demand_share": {l: float},           # fraction of total demand at each location

  "production_cap": {p: [float, ...]},  # max production per product per period (0-indexed list)
  "cold_capacity": {l: float},          # storage capacity per location
  "cold_usage": {p: float},             # storage units per unit of product

  "labor_cap": {l: [float, ...]},       # labor hours per location per period (0-indexed list)
  "labor_usage": {p: float},            # labor hours per unit sold
  "return_rate": {p: float},            # fraction of sales returned next period

  "costs": {
    "purchasing": {p: float},           # cost per unit ordered
    "inventory": {p: float},            # holding cost per unit per period
    "waste": {p: float},                # cost per unit expired
    "lost_sales": {p: float},           # penalty per unit of unmet demand
    "fixed_order": float,               # fixed cost per order placed
    "transshipment": float              # cost per unit transshipped
  },

  "constraints": {
    "moq": float,                       # minimum order quantity (0 = no MOQ)
    "pack_size": int,                   # order must be multiple of this (1 = no constraint)
    "budget_per_period": float|null,    # max purchasing cost per period
    "waste_limit_pct": float|null       # max waste as fraction of total demand
  },

  "network": {
    "sub_edges": [[p_from, p_to], ...], # substitution: p_from's demand can be served by p_to
    "trans_edges": [[l_from, l_to], ...]# transshipment: can ship from l_from to l_to
  }
}

[DATA ACCESS]
- The variable `data` is pre-loaded. Do NOT use file I/O.
- Lists are 0-indexed (period t in model uses index [t-1] in data arrays)

CRITICAL - Network edges require tuple conversion for Gurobi:
  sub_edges = [tuple(e) for e in data.get('network', {}).get('sub_edges', [])]
  trans_edges = [tuple(e) for e in data.get('network', {}).get('trans_edges', [])]

[OUTPUT FORMAT]
- Import: import gurobipy as gp; from gurobipy import GRB
- Set Gurobi params: m.Params.OutputFlag = 0; m.Params.Threads = 1; m.Params.Seed = 0
- Print at end:
  print(f"status: {{m.Status}}")
  if m.Status == 2:
      print(f"objective: {{m.ObjVal}}")
- Output ONLY executable Python code. No markdown, no explanations.

[TASK]
Write a GurobiPy script that models and solves this optimization problem.

[SCENARIO]
Family: F3 (Shared Resources and Capacity)
Archetype: retail_f3_volumetric_constraint
Scenario ID: retail_f3_volumetric_constraint_v2

[BUSINESS DESCRIPTION]
Business narrative:
One product -- typically a bulky premium item -- uses much more storage volume per unit than the others. Storage capacity at each location becomes tight primarily because of this product, forcing the retailer to choose between stocking bulky high-margin units and smaller items. All demand remains local and exogenous, with no transshipment or backorders.

Structure cues:
- The overall structure and shared storage framework match retail_f3_storage_bottleneck.
- Shelf life: Each product has a shelf life in periods. Inventory must be tracked by REMAINING LIFE.

  VARIABLE DEFINITION: I[p,l,t,r] = inventory at START of period t with r periods remaining.
  Convention: r=1 is OLDEST (sell first FIFO), r=shelf_life[p] is FRESHEST.

  KEY EQUATIONS - implement EXACTLY as written, do NOT add or remove terms:

  (1) Fresh inflow: I[p,l,t,SL] = Q[p,t] * demand_share[l]
      - This is ONLY the inflow from production. Do NOT subtract sales here!
      - Q is total production, demand_share distributes it to locations.

  (2) Aging: I[p,l,t+1,r] = I[p,l,t,r+1] - sales[p,l,t,r+1] for r=1..SL-1
      - Inventory tomorrow with r remaining = inventory today with r+1 remaining - sales

  (3) Waste: W[p,l,t] = I[p,l,t,1] - sales[p,l,t,1]
      - Items with r=1 that aren't sold become waste

  (4) Sales availability: sales[p,l,t,r] <= I[p,l,t,r]
      - Can only sell what you have in inventory

  (5) Inventory holding cost: charged on (I[p,l,t,r] - sales[p,l,t,r]) for r >= 2
      - Charge on END-of-period inventory (after sales), exclude expiring items (r=1)
- Storage capacity: sum over products of (cold_usage[p] * total_inventory[p,l,t]) <= cold_capacity[l]. Product-specific storage usage parameters in the JSON are much larger for the premium product than for other SKUs.
- Inventory cannot be negative and is updated based on previous stock, local production, sales, and waste.
- There is no transshipment, lead times are zero, and substitution behavior follows the JSON graph with standard semantics.
- The objective is to minimize total cost (aggregating purchasing, holding, waste, and lost sales) under capacity constraints that make the volumetrically heavy premium product particularly expensive in terms of space.

[DATA]
The following JSON contains all instance data. Parse it directly in your code.

```json
{
  "name": "retail_f3_volumetric_constraint_v2",
  "description": "Standard seasonal retail scenario.",
  "periods": 20,
  "products": [
    "SKU_Basic",
    "SKU_Premium",
    "SKU_ShortLife"
  ],
  "locations": [
    "DC1",
    "DC2",
    "DC3",
    "DC4",
    "DC5"
  ],
  "shelf_life": {
    "SKU_Basic": 10,
    "SKU_Premium": 8,
    "SKU_ShortLife": 4
  },
  "lead_time": {
    "SKU_Basic": 0,
    "SKU_Premium": 0,
    "SKU_ShortLife": 0
  },
  "cold_capacity": {
    "DC1": 3406.179071113192,
    "DC2": 3048.861714569209,
    "DC3": 2894.369002627237,
    "DC4": 2568.1215645149905,
    "DC5": 2303.0678179461047
  },
  "cold_usage": {
    "SKU_Basic": 1.0,
    "SKU_Premium": 15.0,
    "SKU_ShortLife": 1.2
  },
  "production_cap": {
    "SKU_Basic": [
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800
    ],
    "SKU_Premium": [
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400
    ],
    "SKU_ShortLife": [
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500
    ]
  },
  "labor_cap": {
    "DC1": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC2": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC3": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC4": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC5": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ]
  },
  "labor_usage": {
    "SKU_Basic": 0.0,
    "SKU_Premium": 0.0,
    "SKU_ShortLife": 0.0
  },
  "return_rate": {
    "SKU_Basic": 0.0,
    "SKU_Premium": 0.0,
    "SKU_ShortLife": 0.0
  },
  "demand_curve": {
    "SKU_Basic": [
      284,
      278,
      357,
      319,
      475,
      614,
      814,
      839,
      996,
      1344,
      1288,
      1246,
      969,
      899,
      804,
      493,
      445,
      314,
      333,
      319
    ],
    "SKU_Premium": [
      137,
      140,
      163,
      183,
      248,
      278,
      360,
      390,
      495,
      665,
      737,
      543,
      500,
      429,
      342,
      271,
      227,
      189,
      149,
      153
    ],
    "SKU_ShortLife": [
      108,
      130,
      119,
      146,
      194,
      212,
      296,
      373,
      473,
      471,
      579,
      491,
      403,
      317,
      257,
      219,
      160,
      145,
      127,
      135
    ]
  },
  "demand_share": {
    "DC1": 0.25,
    "DC2": 0.2,
    "DC3": 0.2,
    "DC4": 0.2,
    "DC5": 0.15
  },
  "costs": {
    "lost_sales": {
      "SKU_Basic": 50.0,
      "SKU_Premium": 80.0,
      "SKU_ShortLife": 40.0
    },
    "inventory": {
      "SKU_Basic": 1.0,
      "SKU_Premium": 1.5,
      "SKU_ShortLife": 1.0
    },
    "waste": {
      "SKU_Basic": 2.0,
      "SKU_Premium": 3.0,
      "SKU_ShortLife": 2.0
    },
    "fixed_order": 0.0,
    "transshipment": 0.5,
    "purchasing": {
      "SKU_Basic": 10.0,
      "SKU_Premium": 20.0,
      "SKU_ShortLife": 15.0
    }
  },
  "constraints": {
    "moq": 0,
    "pack_size": 1,
    "budget_per_period": null,
    "waste_limit_pct": null
  },
  "network": {
    "sub_edges": [
      [
        "SKU_Basic",
        "SKU_Premium"
      ]
    ],
    "trans_edges": []
  }
}
```

[OUTPUT FORMAT]
- Import: import gurobipy as gp; from gurobipy import GRB; import json
- Set Gurobi params: m.Params.OutputFlag = 0; m.Params.Threads = 1; m.Params.Seed = 0
- Print at end:
  print(f"status: {{m.Status}}")
  if m.Status == 2:
      print(f"objective: {{m.ObjVal}}")
- Output ONLY executable Python code. No markdown, no explanations.

[TASK]
Write a GurobiPy script that:
1. Parses the JSON data above (use json.loads on the string)
2. Models and solves the optimization problem
3. Prints status and objective value

Standard seasonal retail scenario.


[SCENARIO]
Family: F3 (Shared Resources and Capacity)
Archetype: retail_f3_volumetric_constraint
Scenario ID: retail_f3_volumetric_constraint_v3

[BUSINESS DESCRIPTION]
Business narrative:
One product -- typically a bulky premium item -- uses much more storage volume per unit than the others. Storage capacity at each location becomes tight primarily because of this product, forcing the retailer to choose between stocking bulky high-margin units and smaller items. All demand remains local and exogenous, with no transshipment or backorders.

Structure cues:
- The overall structure and shared storage framework match retail_f3_storage_bottleneck.
- Shelf life: Each product has a shelf life in periods. Inventory must be tracked by REMAINING LIFE.

  VARIABLE DEFINITION: I[p,l,t,r] = inventory at START of period t with r periods remaining.
  Convention: r=1 is OLDEST (sell first FIFO), r=shelf_life[p] is FRESHEST.

  KEY EQUATIONS - implement EXACTLY as written, do NOT add or remove terms:

  (1) Fresh inflow: I[p,l,t,SL] = Q[p,t] * demand_share[l]
      - This is ONLY the inflow from production. Do NOT subtract sales here!
      - Q is total production, demand_share distributes it to locations.

  (2) Aging: I[p,l,t+1,r] = I[p,l,t,r+1] - sales[p,l,t,r+1] for r=1..SL-1
      - Inventory tomorrow with r remaining = inventory today with r+1 remaining - sales

  (3) Waste: W[p,l,t] = I[p,l,t,1] - sales[p,l,t,1]
      - Items with r=1 that aren't sold become waste

  (4) Sales availability: sales[p,l,t,r] <= I[p,l,t,r]
      - Can only sell what you have in inventory

  (5) Inventory holding cost: charged on (I[p,l,t,r] - sales[p,l,t,r]) for r >= 2
      - Charge on END-of-period inventory (after sales), exclude expiring items (r=1)
- Storage capacity: sum over products of (cold_usage[p] * total_inventory[p,l,t]) <= cold_capacity[l]. Product-specific storage usage parameters in the JSON are much larger for the premium product than for other SKUs.
- Inventory cannot be negative and is updated based on previous stock, local production, sales, and waste.
- There is no transshipment, lead times are zero, and substitution behavior follows the JSON graph with standard semantics.
- The objective is to minimize total cost (aggregating purchasing, holding, waste, and lost sales) under capacity constraints that make the volumetrically heavy premium product particularly expensive in terms of space.

[DATA SCHEMA]
{
  "name": str,                          # scenario identifier
  "periods": int,                       # number of time periods
  "products": [str, ...],               # list of product IDs
  "locations": [str, ...],              # list of location IDs

  "shelf_life": {p: int},               # shelf life in periods per product
  "lead_time": {p: int},                # order lead time per product (0 = same-period arrival)

  "demand_curve": {p: [float, ...]},    # demand per product per period (0-indexed list)
  "demand_share": {l: float},           # fraction of total demand at each location

  "production_cap": {p: [float, ...]},  # max production per product per period (0-indexed list)
  "cold_capacity": {l: float},          # storage capacity per location
  "cold_usage": {p: float},             # storage units per unit of product

  "labor_cap": {l: [float, ...]},       # labor hours per location per period (0-indexed list)
  "labor_usage": {p: float},            # labor hours per unit sold
  "return_rate": {p: float},            # fraction of sales returned next period

  "costs": {
    "purchasing": {p: float},           # cost per unit ordered
    "inventory": {p: float},            # holding cost per unit per period
    "waste": {p: float},                # cost per unit expired
    "lost_sales": {p: float},           # penalty per unit of unmet demand
    "fixed_order": float,               # fixed cost per order placed
    "transshipment": float              # cost per unit transshipped
  },

  "constraints": {
    "moq": float,                       # minimum order quantity (0 = no MOQ)
    "pack_size": int,                   # order must be multiple of this (1 = no constraint)
    "budget_per_period": float|null,    # max purchasing cost per period
    "waste_limit_pct": float|null       # max waste as fraction of total demand
  },

  "network": {
    "sub_edges": [[p_from, p_to], ...], # substitution: p_from's demand can be served by p_to
    "trans_edges": [[l_from, l_to], ...]# transshipment: can ship from l_from to l_to
  }
}

[DATA ACCESS]
- The variable `data` is pre-loaded. Do NOT use file I/O.
- Lists are 0-indexed (period t in model uses index [t-1] in data arrays)

CRITICAL - Network edges require tuple conversion for Gurobi:
  sub_edges = [tuple(e) for e in data.get('network', {}).get('sub_edges', [])]
  trans_edges = [tuple(e) for e in data.get('network', {}).get('trans_edges', [])]

[OUTPUT FORMAT]
- Import: import gurobipy as gp; from gurobipy import GRB
- Set Gurobi params: m.Params.OutputFlag = 0; m.Params.Threads = 1; m.Params.Seed = 0
- Print at end:
  print(f"status: {{m.Status}}")
  if m.Status == 2:
      print(f"objective: {{m.ObjVal}}")
- Output ONLY executable Python code. No markdown, no explanations.

[TASK]
Write a GurobiPy script that models and solves this optimization problem.

[SCENARIO]
Family: F3 (Shared Resources and Capacity)
Archetype: retail_f3_volumetric_constraint
Scenario ID: retail_f3_volumetric_constraint_v3

[BUSINESS DESCRIPTION]
Business narrative:
One product -- typically a bulky premium item -- uses much more storage volume per unit than the others. Storage capacity at each location becomes tight primarily because of this product, forcing the retailer to choose between stocking bulky high-margin units and smaller items. All demand remains local and exogenous, with no transshipment or backorders.

Structure cues:
- The overall structure and shared storage framework match retail_f3_storage_bottleneck.
- Shelf life: Each product has a shelf life in periods. Inventory must be tracked by REMAINING LIFE.

  VARIABLE DEFINITION: I[p,l,t,r] = inventory at START of period t with r periods remaining.
  Convention: r=1 is OLDEST (sell first FIFO), r=shelf_life[p] is FRESHEST.

  KEY EQUATIONS - implement EXACTLY as written, do NOT add or remove terms:

  (1) Fresh inflow: I[p,l,t,SL] = Q[p,t] * demand_share[l]
      - This is ONLY the inflow from production. Do NOT subtract sales here!
      - Q is total production, demand_share distributes it to locations.

  (2) Aging: I[p,l,t+1,r] = I[p,l,t,r+1] - sales[p,l,t,r+1] for r=1..SL-1
      - Inventory tomorrow with r remaining = inventory today with r+1 remaining - sales

  (3) Waste: W[p,l,t] = I[p,l,t,1] - sales[p,l,t,1]
      - Items with r=1 that aren't sold become waste

  (4) Sales availability: sales[p,l,t,r] <= I[p,l,t,r]
      - Can only sell what you have in inventory

  (5) Inventory holding cost: charged on (I[p,l,t,r] - sales[p,l,t,r]) for r >= 2
      - Charge on END-of-period inventory (after sales), exclude expiring items (r=1)
- Storage capacity: sum over products of (cold_usage[p] * total_inventory[p,l,t]) <= cold_capacity[l]. Product-specific storage usage parameters in the JSON are much larger for the premium product than for other SKUs.
- Inventory cannot be negative and is updated based on previous stock, local production, sales, and waste.
- There is no transshipment, lead times are zero, and substitution behavior follows the JSON graph with standard semantics.
- The objective is to minimize total cost (aggregating purchasing, holding, waste, and lost sales) under capacity constraints that make the volumetrically heavy premium product particularly expensive in terms of space.

[DATA]
The following JSON contains all instance data. Parse it directly in your code.

```json
{
  "name": "retail_f3_volumetric_constraint_v3",
  "description": "Standard seasonal retail scenario.",
  "periods": 20,
  "products": [
    "SKU_Basic",
    "SKU_Premium",
    "SKU_ShortLife"
  ],
  "locations": [
    "DC1",
    "DC2",
    "DC3",
    "DC4",
    "DC5"
  ],
  "shelf_life": {
    "SKU_Basic": 10,
    "SKU_Premium": 8,
    "SKU_ShortLife": 4
  },
  "lead_time": {
    "SKU_Basic": 0,
    "SKU_Premium": 0,
    "SKU_ShortLife": 0
  },
  "cold_capacity": {
    "DC1": 3908.8086755208647,
    "DC2": 3666.698399375343,
    "DC3": 3350.9437816388095,
    "DC4": 3187.328873088867,
    "DC5": 2699.649372855567
  },
  "cold_usage": {
    "SKU_Basic": 1.0,
    "SKU_Premium": 15.0,
    "SKU_ShortLife": 1.2
  },
  "production_cap": {
    "SKU_Basic": [
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800
    ],
    "SKU_Premium": [
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400
    ],
    "SKU_ShortLife": [
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500
    ]
  },
  "labor_cap": {
    "DC1": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC2": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC3": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC4": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC5": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ]
  },
  "labor_usage": {
    "SKU_Basic": 0.0,
    "SKU_Premium": 0.0,
    "SKU_ShortLife": 0.0
  },
  "return_rate": {
    "SKU_Basic": 0.0,
    "SKU_Premium": 0.0,
    "SKU_ShortLife": 0.0
  },
  "demand_curve": {
    "SKU_Basic": [
      316,
      294,
      306,
      414,
      380,
      495,
      621,
      1035,
      981,
      1161,
      1304,
      1330,
      1181,
      885,
      631,
      582,
      450,
      409,
      334,
      317
    ],
    "SKU_Premium": [
      131,
      165,
      142,
      196,
      199,
      272,
      308,
      510,
      545,
      714,
      612,
      563,
      504,
      402,
      348,
      257,
      200,
      204,
      166,
      153
    ],
    "SKU_ShortLife": [
      106,
      113,
      142,
      143,
      167,
      214,
      244,
      336,
      495,
      519,
      581,
      466,
      375,
      415,
      295,
      199,
      190,
      151,
      119,
      109
    ]
  },
  "demand_share": {
    "DC1": 0.25,
    "DC2": 0.2,
    "DC3": 0.2,
    "DC4": 0.2,
    "DC5": 0.15
  },
  "costs": {
    "lost_sales": {
      "SKU_Basic": 50.0,
      "SKU_Premium": 80.0,
      "SKU_ShortLife": 40.0
    },
    "inventory": {
      "SKU_Basic": 1.0,
      "SKU_Premium": 1.5,
      "SKU_ShortLife": 1.0
    },
    "waste": {
      "SKU_Basic": 2.0,
      "SKU_Premium": 3.0,
      "SKU_ShortLife": 2.0
    },
    "fixed_order": 0.0,
    "transshipment": 0.5,
    "purchasing": {
      "SKU_Basic": 10.0,
      "SKU_Premium": 20.0,
      "SKU_ShortLife": 15.0
    }
  },
  "constraints": {
    "moq": 0,
    "pack_size": 1,
    "budget_per_period": null,
    "waste_limit_pct": null
  },
  "network": {
    "sub_edges": [
      [
        "SKU_Basic",
        "SKU_Premium"
      ]
    ],
    "trans_edges": []
  }
}
```

[OUTPUT FORMAT]
- Import: import gurobipy as gp; from gurobipy import GRB; import json
- Set Gurobi params: m.Params.OutputFlag = 0; m.Params.Threads = 1; m.Params.Seed = 0
- Print at end:
  print(f"status: {{m.Status}}")
  if m.Status == 2:
      print(f"objective: {{m.ObjVal}}")
- Output ONLY executable Python code. No markdown, no explanations.

[TASK]
Write a GurobiPy script that:
1. Parses the JSON data above (use json.loads on the string)
2. Models and solves the optimization problem
3. Prints status and objective value

Standard seasonal retail scenario.


[SCENARIO]
Family: F3 (Shared Resources and Capacity)
Archetype: retail_f3_volumetric_constraint
Scenario ID: retail_f3_volumetric_constraint_v4

[BUSINESS DESCRIPTION]
Business narrative:
One product -- typically a bulky premium item -- uses much more storage volume per unit than the others. Storage capacity at each location becomes tight primarily because of this product, forcing the retailer to choose between stocking bulky high-margin units and smaller items. All demand remains local and exogenous, with no transshipment or backorders.

Structure cues:
- The overall structure and shared storage framework match retail_f3_storage_bottleneck.
- Shelf life: Each product has a shelf life in periods. Inventory must be tracked by REMAINING LIFE.

  VARIABLE DEFINITION: I[p,l,t,r] = inventory at START of period t with r periods remaining.
  Convention: r=1 is OLDEST (sell first FIFO), r=shelf_life[p] is FRESHEST.

  KEY EQUATIONS - implement EXACTLY as written, do NOT add or remove terms:

  (1) Fresh inflow: I[p,l,t,SL] = Q[p,t] * demand_share[l]
      - This is ONLY the inflow from production. Do NOT subtract sales here!
      - Q is total production, demand_share distributes it to locations.

  (2) Aging: I[p,l,t+1,r] = I[p,l,t,r+1] - sales[p,l,t,r+1] for r=1..SL-1
      - Inventory tomorrow with r remaining = inventory today with r+1 remaining - sales

  (3) Waste: W[p,l,t] = I[p,l,t,1] - sales[p,l,t,1]
      - Items with r=1 that aren't sold become waste

  (4) Sales availability: sales[p,l,t,r] <= I[p,l,t,r]
      - Can only sell what you have in inventory

  (5) Inventory holding cost: charged on (I[p,l,t,r] - sales[p,l,t,r]) for r >= 2
      - Charge on END-of-period inventory (after sales), exclude expiring items (r=1)
- Storage capacity: sum over products of (cold_usage[p] * total_inventory[p,l,t]) <= cold_capacity[l]. Product-specific storage usage parameters in the JSON are much larger for the premium product than for other SKUs.
- Inventory cannot be negative and is updated based on previous stock, local production, sales, and waste.
- There is no transshipment, lead times are zero, and substitution behavior follows the JSON graph with standard semantics.
- The objective is to minimize total cost (aggregating purchasing, holding, waste, and lost sales) under capacity constraints that make the volumetrically heavy premium product particularly expensive in terms of space.

[DATA SCHEMA]
{
  "name": str,                          # scenario identifier
  "periods": int,                       # number of time periods
  "products": [str, ...],               # list of product IDs
  "locations": [str, ...],              # list of location IDs

  "shelf_life": {p: int},               # shelf life in periods per product
  "lead_time": {p: int},                # order lead time per product (0 = same-period arrival)

  "demand_curve": {p: [float, ...]},    # demand per product per period (0-indexed list)
  "demand_share": {l: float},           # fraction of total demand at each location

  "production_cap": {p: [float, ...]},  # max production per product per period (0-indexed list)
  "cold_capacity": {l: float},          # storage capacity per location
  "cold_usage": {p: float},             # storage units per unit of product

  "labor_cap": {l: [float, ...]},       # labor hours per location per period (0-indexed list)
  "labor_usage": {p: float},            # labor hours per unit sold
  "return_rate": {p: float},            # fraction of sales returned next period

  "costs": {
    "purchasing": {p: float},           # cost per unit ordered
    "inventory": {p: float},            # holding cost per unit per period
    "waste": {p: float},                # cost per unit expired
    "lost_sales": {p: float},           # penalty per unit of unmet demand
    "fixed_order": float,               # fixed cost per order placed
    "transshipment": float              # cost per unit transshipped
  },

  "constraints": {
    "moq": float,                       # minimum order quantity (0 = no MOQ)
    "pack_size": int,                   # order must be multiple of this (1 = no constraint)
    "budget_per_period": float|null,    # max purchasing cost per period
    "waste_limit_pct": float|null       # max waste as fraction of total demand
  },

  "network": {
    "sub_edges": [[p_from, p_to], ...], # substitution: p_from's demand can be served by p_to
    "trans_edges": [[l_from, l_to], ...]# transshipment: can ship from l_from to l_to
  }
}

[DATA ACCESS]
- The variable `data` is pre-loaded. Do NOT use file I/O.
- Lists are 0-indexed (period t in model uses index [t-1] in data arrays)

CRITICAL - Network edges require tuple conversion for Gurobi:
  sub_edges = [tuple(e) for e in data.get('network', {}).get('sub_edges', [])]
  trans_edges = [tuple(e) for e in data.get('network', {}).get('trans_edges', [])]

[OUTPUT FORMAT]
- Import: import gurobipy as gp; from gurobipy import GRB
- Set Gurobi params: m.Params.OutputFlag = 0; m.Params.Threads = 1; m.Params.Seed = 0
- Print at end:
  print(f"status: {{m.Status}}")
  if m.Status == 2:
      print(f"objective: {{m.ObjVal}}")
- Output ONLY executable Python code. No markdown, no explanations.

[TASK]
Write a GurobiPy script that models and solves this optimization problem.

[SCENARIO]
Family: F3 (Shared Resources and Capacity)
Archetype: retail_f3_volumetric_constraint
Scenario ID: retail_f3_volumetric_constraint_v4

[BUSINESS DESCRIPTION]
Business narrative:
One product -- typically a bulky premium item -- uses much more storage volume per unit than the others. Storage capacity at each location becomes tight primarily because of this product, forcing the retailer to choose between stocking bulky high-margin units and smaller items. All demand remains local and exogenous, with no transshipment or backorders.

Structure cues:
- The overall structure and shared storage framework match retail_f3_storage_bottleneck.
- Shelf life: Each product has a shelf life in periods. Inventory must be tracked by REMAINING LIFE.

  VARIABLE DEFINITION: I[p,l,t,r] = inventory at START of period t with r periods remaining.
  Convention: r=1 is OLDEST (sell first FIFO), r=shelf_life[p] is FRESHEST.

  KEY EQUATIONS - implement EXACTLY as written, do NOT add or remove terms:

  (1) Fresh inflow: I[p,l,t,SL] = Q[p,t] * demand_share[l]
      - This is ONLY the inflow from production. Do NOT subtract sales here!
      - Q is total production, demand_share distributes it to locations.

  (2) Aging: I[p,l,t+1,r] = I[p,l,t,r+1] - sales[p,l,t,r+1] for r=1..SL-1
      - Inventory tomorrow with r remaining = inventory today with r+1 remaining - sales

  (3) Waste: W[p,l,t] = I[p,l,t,1] - sales[p,l,t,1]
      - Items with r=1 that aren't sold become waste

  (4) Sales availability: sales[p,l,t,r] <= I[p,l,t,r]
      - Can only sell what you have in inventory

  (5) Inventory holding cost: charged on (I[p,l,t,r] - sales[p,l,t,r]) for r >= 2
      - Charge on END-of-period inventory (after sales), exclude expiring items (r=1)
- Storage capacity: sum over products of (cold_usage[p] * total_inventory[p,l,t]) <= cold_capacity[l]. Product-specific storage usage parameters in the JSON are much larger for the premium product than for other SKUs.
- Inventory cannot be negative and is updated based on previous stock, local production, sales, and waste.
- There is no transshipment, lead times are zero, and substitution behavior follows the JSON graph with standard semantics.
- The objective is to minimize total cost (aggregating purchasing, holding, waste, and lost sales) under capacity constraints that make the volumetrically heavy premium product particularly expensive in terms of space.

[DATA]
The following JSON contains all instance data. Parse it directly in your code.

```json
{
  "name": "retail_f3_volumetric_constraint_v4",
  "description": "Standard seasonal retail scenario.",
  "periods": 20,
  "products": [
    "SKU_Basic",
    "SKU_Premium",
    "SKU_ShortLife"
  ],
  "locations": [
    "DC1",
    "DC2",
    "DC3",
    "DC4",
    "DC5"
  ],
  "shelf_life": {
    "SKU_Basic": 10,
    "SKU_Premium": 8,
    "SKU_ShortLife": 4
  },
  "lead_time": {
    "SKU_Basic": 0,
    "SKU_Premium": 0,
    "SKU_ShortLife": 0
  },
  "cold_capacity": {
    "DC1": 3856.209407179451,
    "DC2": 3798.723085114051,
    "DC3": 2628.0429516606355,
    "DC4": 3092.571454223831,
    "DC5": 2701.5171856724796
  },
  "cold_usage": {
    "SKU_Basic": 1.0,
    "SKU_Premium": 15.0,
    "SKU_ShortLife": 1.2
  },
  "production_cap": {
    "SKU_Basic": [
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800
    ],
    "SKU_Premium": [
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400
    ],
    "SKU_ShortLife": [
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500
    ]
  },
  "labor_cap": {
    "DC1": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC2": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC3": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC4": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC5": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ]
  },
  "labor_usage": {
    "SKU_Basic": 0.0,
    "SKU_Premium": 0.0,
    "SKU_ShortLife": 0.0
  },
  "return_rate": {
    "SKU_Basic": 0.0,
    "SKU_Premium": 0.0,
    "SKU_ShortLife": 0.0
  },
  "demand_curve": {
    "SKU_Basic": [
      322,
      330,
      356,
      373,
      393,
      571,
      615,
      825,
      951,
      1189,
      1367,
      1151,
      1026,
      835,
      737,
      479,
      381,
      352,
      335,
      322
    ],
    "SKU_Premium": [
      143,
      160,
      157,
      158,
      229,
      248,
      345,
      386,
      604,
      710,
      726,
      533,
      481,
      516,
      402,
      255,
      248,
      164,
      165,
      145
    ],
    "SKU_ShortLife": [
      133,
      132,
      131,
      136,
      162,
      194,
      247,
      392,
      378,
      460,
      460,
      553,
      383,
      387,
      303,
      208,
      182,
      145,
      131,
      113
    ]
  },
  "demand_share": {
    "DC1": 0.25,
    "DC2": 0.2,
    "DC3": 0.2,
    "DC4": 0.2,
    "DC5": 0.15
  },
  "costs": {
    "lost_sales": {
      "SKU_Basic": 50.0,
      "SKU_Premium": 80.0,
      "SKU_ShortLife": 40.0
    },
    "inventory": {
      "SKU_Basic": 1.0,
      "SKU_Premium": 1.5,
      "SKU_ShortLife": 1.0
    },
    "waste": {
      "SKU_Basic": 2.0,
      "SKU_Premium": 3.0,
      "SKU_ShortLife": 2.0
    },
    "fixed_order": 0.0,
    "transshipment": 0.5,
    "purchasing": {
      "SKU_Basic": 10.0,
      "SKU_Premium": 20.0,
      "SKU_ShortLife": 15.0
    }
  },
  "constraints": {
    "moq": 0,
    "pack_size": 1,
    "budget_per_period": null,
    "waste_limit_pct": null
  },
  "network": {
    "sub_edges": [
      [
        "SKU_Basic",
        "SKU_Premium"
      ]
    ],
    "trans_edges": []
  }
}
```

[OUTPUT FORMAT]
- Import: import gurobipy as gp; from gurobipy import GRB; import json
- Set Gurobi params: m.Params.OutputFlag = 0; m.Params.Threads = 1; m.Params.Seed = 0
- Print at end:
  print(f"status: {{m.Status}}")
  if m.Status == 2:
      print(f"objective: {{m.ObjVal}}")
- Output ONLY executable Python code. No markdown, no explanations.

[TASK]
Write a GurobiPy script that:
1. Parses the JSON data above (use json.loads on the string)
2. Models and solves the optimization problem
3. Prints status and objective value

Standard seasonal retail scenario.


[SCENARIO]
Family: F4 (Dynamics and Disruptions)
Archetype: retail_f4_demand_surge
Scenario ID: retail_f4_demand_surge_v0

[BUSINESS DESCRIPTION]
Business narrative:
The retailer experiences a single-period viral demand spike where demand suddenly multiplies for all products. Production capacity and other structural elements remain unchanged; only the magnitude of demand in that period is much higher. The retailer must decide whether to build extra inventory in advance or accept lost sales during the surge.

Structure cues:
- The inventory and production structure is the same as in the base scenario.
- Shelf life: Each product has a shelf life in periods. Inventory must be tracked by REMAINING LIFE.

  VARIABLE DEFINITION: I[p,l,t,r] = inventory at START of period t with r periods remaining.
  Convention: r=1 is OLDEST (sell first FIFO), r=shelf_life[p] is FRESHEST.

  KEY EQUATIONS - implement EXACTLY as written, do NOT add or remove terms:

  (1) Fresh inflow: I[p,l,t,SL] = Q[p,t] * demand_share[l]
      - This is ONLY the inflow from production. Do NOT subtract sales here!
      - Q is total production, demand_share distributes it to locations.

  (2) Aging: I[p,l,t+1,r] = I[p,l,t,r+1] - sales[p,l,t,r+1] for r=1..SL-1
      - Inventory tomorrow with r remaining = inventory today with r+1 remaining - sales

  (3) Waste: W[p,l,t] = I[p,l,t,1] - sales[p,l,t,1]
      - Items with r=1 that aren't sold become waste

  (4) Sales availability: sales[p,l,t,r] <= I[p,l,t,r]
      - Can only sell what you have in inventory

  (5) Inventory holding cost: charged on (I[p,l,t,r] - sales[p,l,t,r]) for r >= 2
      - Charge on END-of-period inventory (after sales), exclude expiring items (r=1)
- Storage capacity: sum over products of (cold_usage[p] * total_inventory[p,l,t]) <= cold_capacity[l]. These limits must be respected.
- In the JSON, one mid-horizon period has demand for each product scaled up by a large factor, representing the surge. This period is treated as having much higher exogenous demand.
- Inventory stays non-negative and is updated using previous stock, current production, sales, and waste.
- Substitution behavior is unchanged, there is no transshipment, and lead times remain effectively zero.
- The objective is to minimize total cost (aggregating purchasing, holding, waste, and lost sales), with the demand spike increasing the importance of planning ahead for that particular period.

[DATA SCHEMA]
{
  "name": str,                          # scenario identifier
  "periods": int,                       # number of time periods
  "products": [str, ...],               # list of product IDs
  "locations": [str, ...],              # list of location IDs

  "shelf_life": {p: int},               # shelf life in periods per product
  "lead_time": {p: int},                # order lead time per product (0 = same-period arrival)

  "demand_curve": {p: [float, ...]},    # demand per product per period (0-indexed list)
  "demand_share": {l: float},           # fraction of total demand at each location

  "production_cap": {p: [float, ...]},  # max production per product per period (0-indexed list)
  "cold_capacity": {l: float},          # storage capacity per location
  "cold_usage": {p: float},             # storage units per unit of product

  "labor_cap": {l: [float, ...]},       # labor hours per location per period (0-indexed list)
  "labor_usage": {p: float},            # labor hours per unit sold
  "return_rate": {p: float},            # fraction of sales returned next period

  "costs": {
    "purchasing": {p: float},           # cost per unit ordered
    "inventory": {p: float},            # holding cost per unit per period
    "waste": {p: float},                # cost per unit expired
    "lost_sales": {p: float},           # penalty per unit of unmet demand
    "fixed_order": float,               # fixed cost per order placed
    "transshipment": float              # cost per unit transshipped
  },

  "constraints": {
    "moq": float,                       # minimum order quantity (0 = no MOQ)
    "pack_size": int,                   # order must be multiple of this (1 = no constraint)
    "budget_per_period": float|null,    # max purchasing cost per period
    "waste_limit_pct": float|null       # max waste as fraction of total demand
  },

  "network": {
    "sub_edges": [[p_from, p_to], ...], # substitution: p_from's demand can be served by p_to
    "trans_edges": [[l_from, l_to], ...]# transshipment: can ship from l_from to l_to
  }
}

[DATA ACCESS]
- The variable `data` is pre-loaded. Do NOT use file I/O.
- Lists are 0-indexed (period t in model uses index [t-1] in data arrays)

CRITICAL - Network edges require tuple conversion for Gurobi:
  sub_edges = [tuple(e) for e in data.get('network', {}).get('sub_edges', [])]
  trans_edges = [tuple(e) for e in data.get('network', {}).get('trans_edges', [])]

[OUTPUT FORMAT]
- Import: import gurobipy as gp; from gurobipy import GRB
- Set Gurobi params: m.Params.OutputFlag = 0; m.Params.Threads = 1; m.Params.Seed = 0
- Print at end:
  print(f"status: {{m.Status}}")
  if m.Status == 2:
      print(f"objective: {{m.ObjVal}}")
- Output ONLY executable Python code. No markdown, no explanations.

[TASK]
Write a GurobiPy script that models and solves this optimization problem.

[SCENARIO]
Family: F4 (Dynamics and Disruptions)
Archetype: retail_f4_demand_surge
Scenario ID: retail_f4_demand_surge_v0

[BUSINESS DESCRIPTION]
Business narrative:
The retailer experiences a single-period viral demand spike where demand suddenly multiplies for all products. Production capacity and other structural elements remain unchanged; only the magnitude of demand in that period is much higher. The retailer must decide whether to build extra inventory in advance or accept lost sales during the surge.

Structure cues:
- The inventory and production structure is the same as in the base scenario.
- Shelf life: Each product has a shelf life in periods. Inventory must be tracked by REMAINING LIFE.

  VARIABLE DEFINITION: I[p,l,t,r] = inventory at START of period t with r periods remaining.
  Convention: r=1 is OLDEST (sell first FIFO), r=shelf_life[p] is FRESHEST.

  KEY EQUATIONS - implement EXACTLY as written, do NOT add or remove terms:

  (1) Fresh inflow: I[p,l,t,SL] = Q[p,t] * demand_share[l]
      - This is ONLY the inflow from production. Do NOT subtract sales here!
      - Q is total production, demand_share distributes it to locations.

  (2) Aging: I[p,l,t+1,r] = I[p,l,t,r+1] - sales[p,l,t,r+1] for r=1..SL-1
      - Inventory tomorrow with r remaining = inventory today with r+1 remaining - sales

  (3) Waste: W[p,l,t] = I[p,l,t,1] - sales[p,l,t,1]
      - Items with r=1 that aren't sold become waste

  (4) Sales availability: sales[p,l,t,r] <= I[p,l,t,r]
      - Can only sell what you have in inventory

  (5) Inventory holding cost: charged on (I[p,l,t,r] - sales[p,l,t,r]) for r >= 2
      - Charge on END-of-period inventory (after sales), exclude expiring items (r=1)
- Storage capacity: sum over products of (cold_usage[p] * total_inventory[p,l,t]) <= cold_capacity[l]. These limits must be respected.
- In the JSON, one mid-horizon period has demand for each product scaled up by a large factor, representing the surge. This period is treated as having much higher exogenous demand.
- Inventory stays non-negative and is updated using previous stock, current production, sales, and waste.
- Substitution behavior is unchanged, there is no transshipment, and lead times remain effectively zero.
- The objective is to minimize total cost (aggregating purchasing, holding, waste, and lost sales), with the demand spike increasing the importance of planning ahead for that particular period.

[DATA]
The following JSON contains all instance data. Parse it directly in your code.

```json
{
  "name": "retail_f4_demand_surge_v0",
  "description": "Standard seasonal retail scenario.",
  "periods": 20,
  "products": [
    "SKU_Basic",
    "SKU_Premium",
    "SKU_ShortLife"
  ],
  "locations": [
    "DC1",
    "DC2",
    "DC3",
    "DC4",
    "DC5"
  ],
  "shelf_life": {
    "SKU_Basic": 10,
    "SKU_Premium": 8,
    "SKU_ShortLife": 4
  },
  "lead_time": {
    "SKU_Basic": 0,
    "SKU_Premium": 0,
    "SKU_ShortLife": 0
  },
  "cold_capacity": {
    "DC1": 4000,
    "DC2": 3500,
    "DC3": 3000,
    "DC4": 3000,
    "DC5": 2500
  },
  "cold_usage": {
    "SKU_Basic": 1.0,
    "SKU_Premium": 3.0,
    "SKU_ShortLife": 1.2
  },
  "production_cap": {
    "SKU_Basic": [
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800
    ],
    "SKU_Premium": [
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400
    ],
    "SKU_ShortLife": [
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500
    ]
  },
  "labor_cap": {
    "DC1": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC2": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC3": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC4": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC5": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ]
  },
  "labor_usage": {
    "SKU_Basic": 0.0,
    "SKU_Premium": 0.0,
    "SKU_ShortLife": 0.0
  },
  "return_rate": {
    "SKU_Basic": 0.0,
    "SKU_Premium": 0.0,
    "SKU_ShortLife": 0.0
  },
  "demand_curve": {
    "SKU_Basic": [
      303,
      311,
      328,
      365,
      435,
      549,
      711,
      906,
      1100,
      1245,
      1300,
      1245,
      1100,
      906,
      2844,
      549,
      435,
      365,
      328,
      311
    ],
    "SKU_Premium": [
      151,
      155,
      164,
      182,
      217,
      274,
      355,
      453,
      550,
      622,
      650,
      622,
      550,
      453,
      1420,
      274,
      217,
      182,
      164,
      155
    ],
    "SKU_ShortLife": [
      121,
      124,
      131,
      146,
      174,
      219,
      284,
      362,
      440,
      498,
      520,
      498,
      440,
      362,
      1136,
      219,
      174,
      146,
      131,
      124
    ]
  },
  "demand_share": {
    "DC1": 0.25,
    "DC2": 0.2,
    "DC3": 0.2,
    "DC4": 0.2,
    "DC5": 0.15
  },
  "costs": {
    "lost_sales": {
      "SKU_Basic": 50.0,
      "SKU_Premium": 80.0,
      "SKU_ShortLife": 40.0
    },
    "inventory": {
      "SKU_Basic": 1.0,
      "SKU_Premium": 1.5,
      "SKU_ShortLife": 1.0
    },
    "waste": {
      "SKU_Basic": 2.0,
      "SKU_Premium": 3.0,
      "SKU_ShortLife": 2.0
    },
    "fixed_order": 0.0,
    "transshipment": 0.5,
    "purchasing": {
      "SKU_Basic": 10.0,
      "SKU_Premium": 20.0,
      "SKU_ShortLife": 15.0
    }
  },
  "constraints": {
    "moq": 0,
    "pack_size": 1,
    "budget_per_period": null,
    "waste_limit_pct": null
  },
  "network": {
    "sub_edges": [
      [
        "SKU_Basic",
        "SKU_Premium"
      ]
    ],
    "trans_edges": []
  }
}
```

[OUTPUT FORMAT]
- Import: import gurobipy as gp; from gurobipy import GRB; import json
- Set Gurobi params: m.Params.OutputFlag = 0; m.Params.Threads = 1; m.Params.Seed = 0
- Print at end:
  print(f"status: {{m.Status}}")
  if m.Status == 2:
      print(f"objective: {{m.ObjVal}}")
- Output ONLY executable Python code. No markdown, no explanations.

[TASK]
Write a GurobiPy script that:
1. Parses the JSON data above (use json.loads on the string)
2. Models and solves the optimization problem
3. Prints status and objective value

Standard seasonal retail scenario.


[SCENARIO]
Family: F4 (Dynamics and Disruptions)
Archetype: retail_f4_demand_surge
Scenario ID: retail_f4_demand_surge_v1

[BUSINESS DESCRIPTION]
Business narrative:
The retailer experiences a single-period viral demand spike where demand suddenly multiplies for all products. Production capacity and other structural elements remain unchanged; only the magnitude of demand in that period is much higher. The retailer must decide whether to build extra inventory in advance or accept lost sales during the surge.

Structure cues:
- The inventory and production structure is the same as in the base scenario.
- Shelf life: Each product has a shelf life in periods. Inventory must be tracked by REMAINING LIFE.

  VARIABLE DEFINITION: I[p,l,t,r] = inventory at START of period t with r periods remaining.
  Convention: r=1 is OLDEST (sell first FIFO), r=shelf_life[p] is FRESHEST.

  KEY EQUATIONS - implement EXACTLY as written, do NOT add or remove terms:

  (1) Fresh inflow: I[p,l,t,SL] = Q[p,t] * demand_share[l]
      - This is ONLY the inflow from production. Do NOT subtract sales here!
      - Q is total production, demand_share distributes it to locations.

  (2) Aging: I[p,l,t+1,r] = I[p,l,t,r+1] - sales[p,l,t,r+1] for r=1..SL-1
      - Inventory tomorrow with r remaining = inventory today with r+1 remaining - sales

  (3) Waste: W[p,l,t] = I[p,l,t,1] - sales[p,l,t,1]
      - Items with r=1 that aren't sold become waste

  (4) Sales availability: sales[p,l,t,r] <= I[p,l,t,r]
      - Can only sell what you have in inventory

  (5) Inventory holding cost: charged on (I[p,l,t,r] - sales[p,l,t,r]) for r >= 2
      - Charge on END-of-period inventory (after sales), exclude expiring items (r=1)
- Storage capacity: sum over products of (cold_usage[p] * total_inventory[p,l,t]) <= cold_capacity[l]. These limits must be respected.
- In the JSON, one mid-horizon period has demand for each product scaled up by a large factor, representing the surge. This period is treated as having much higher exogenous demand.
- Inventory stays non-negative and is updated using previous stock, current production, sales, and waste.
- Substitution behavior is unchanged, there is no transshipment, and lead times remain effectively zero.
- The objective is to minimize total cost (aggregating purchasing, holding, waste, and lost sales), with the demand spike increasing the importance of planning ahead for that particular period.

[DATA SCHEMA]
{
  "name": str,                          # scenario identifier
  "periods": int,                       # number of time periods
  "products": [str, ...],               # list of product IDs
  "locations": [str, ...],              # list of location IDs

  "shelf_life": {p: int},               # shelf life in periods per product
  "lead_time": {p: int},                # order lead time per product (0 = same-period arrival)

  "demand_curve": {p: [float, ...]},    # demand per product per period (0-indexed list)
  "demand_share": {l: float},           # fraction of total demand at each location

  "production_cap": {p: [float, ...]},  # max production per product per period (0-indexed list)
  "cold_capacity": {l: float},          # storage capacity per location
  "cold_usage": {p: float},             # storage units per unit of product

  "labor_cap": {l: [float, ...]},       # labor hours per location per period (0-indexed list)
  "labor_usage": {p: float},            # labor hours per unit sold
  "return_rate": {p: float},            # fraction of sales returned next period

  "costs": {
    "purchasing": {p: float},           # cost per unit ordered
    "inventory": {p: float},            # holding cost per unit per period
    "waste": {p: float},                # cost per unit expired
    "lost_sales": {p: float},           # penalty per unit of unmet demand
    "fixed_order": float,               # fixed cost per order placed
    "transshipment": float              # cost per unit transshipped
  },

  "constraints": {
    "moq": float,                       # minimum order quantity (0 = no MOQ)
    "pack_size": int,                   # order must be multiple of this (1 = no constraint)
    "budget_per_period": float|null,    # max purchasing cost per period
    "waste_limit_pct": float|null       # max waste as fraction of total demand
  },

  "network": {
    "sub_edges": [[p_from, p_to], ...], # substitution: p_from's demand can be served by p_to
    "trans_edges": [[l_from, l_to], ...]# transshipment: can ship from l_from to l_to
  }
}

[DATA ACCESS]
- The variable `data` is pre-loaded. Do NOT use file I/O.
- Lists are 0-indexed (period t in model uses index [t-1] in data arrays)

CRITICAL - Network edges require tuple conversion for Gurobi:
  sub_edges = [tuple(e) for e in data.get('network', {}).get('sub_edges', [])]
  trans_edges = [tuple(e) for e in data.get('network', {}).get('trans_edges', [])]

[OUTPUT FORMAT]
- Import: import gurobipy as gp; from gurobipy import GRB
- Set Gurobi params: m.Params.OutputFlag = 0; m.Params.Threads = 1; m.Params.Seed = 0
- Print at end:
  print(f"status: {{m.Status}}")
  if m.Status == 2:
      print(f"objective: {{m.ObjVal}}")
- Output ONLY executable Python code. No markdown, no explanations.

[TASK]
Write a GurobiPy script that models and solves this optimization problem.

[SCENARIO]
Family: F4 (Dynamics and Disruptions)
Archetype: retail_f4_demand_surge
Scenario ID: retail_f4_demand_surge_v1

[BUSINESS DESCRIPTION]
Business narrative:
The retailer experiences a single-period viral demand spike where demand suddenly multiplies for all products. Production capacity and other structural elements remain unchanged; only the magnitude of demand in that period is much higher. The retailer must decide whether to build extra inventory in advance or accept lost sales during the surge.

Structure cues:
- The inventory and production structure is the same as in the base scenario.
- Shelf life: Each product has a shelf life in periods. Inventory must be tracked by REMAINING LIFE.

  VARIABLE DEFINITION: I[p,l,t,r] = inventory at START of period t with r periods remaining.
  Convention: r=1 is OLDEST (sell first FIFO), r=shelf_life[p] is FRESHEST.

  KEY EQUATIONS - implement EXACTLY as written, do NOT add or remove terms:

  (1) Fresh inflow: I[p,l,t,SL] = Q[p,t] * demand_share[l]
      - This is ONLY the inflow from production. Do NOT subtract sales here!
      - Q is total production, demand_share distributes it to locations.

  (2) Aging: I[p,l,t+1,r] = I[p,l,t,r+1] - sales[p,l,t,r+1] for r=1..SL-1
      - Inventory tomorrow with r remaining = inventory today with r+1 remaining - sales

  (3) Waste: W[p,l,t] = I[p,l,t,1] - sales[p,l,t,1]
      - Items with r=1 that aren't sold become waste

  (4) Sales availability: sales[p,l,t,r] <= I[p,l,t,r]
      - Can only sell what you have in inventory

  (5) Inventory holding cost: charged on (I[p,l,t,r] - sales[p,l,t,r]) for r >= 2
      - Charge on END-of-period inventory (after sales), exclude expiring items (r=1)
- Storage capacity: sum over products of (cold_usage[p] * total_inventory[p,l,t]) <= cold_capacity[l]. These limits must be respected.
- In the JSON, one mid-horizon period has demand for each product scaled up by a large factor, representing the surge. This period is treated as having much higher exogenous demand.
- Inventory stays non-negative and is updated using previous stock, current production, sales, and waste.
- Substitution behavior is unchanged, there is no transshipment, and lead times remain effectively zero.
- The objective is to minimize total cost (aggregating purchasing, holding, waste, and lost sales), with the demand spike increasing the importance of planning ahead for that particular period.

[DATA]
The following JSON contains all instance data. Parse it directly in your code.

```json
{
  "name": "retail_f4_demand_surge_v1",
  "description": "Standard seasonal retail scenario.",
  "periods": 20,
  "products": [
    "SKU_Basic",
    "SKU_Premium",
    "SKU_ShortLife"
  ],
  "locations": [
    "DC1",
    "DC2",
    "DC3",
    "DC4",
    "DC5"
  ],
  "shelf_life": {
    "SKU_Basic": 10,
    "SKU_Premium": 8,
    "SKU_ShortLife": 4
  },
  "lead_time": {
    "SKU_Basic": 0,
    "SKU_Premium": 0,
    "SKU_ShortLife": 0
  },
  "cold_capacity": {
    "DC1": 3402.049614362719,
    "DC2": 3601.0137027081646,
    "DC3": 3079.9458330278408,
    "DC4": 3367.5100616585687,
    "DC5": 2373.1356267711126
  },
  "cold_usage": {
    "SKU_Basic": 1.0,
    "SKU_Premium": 3.0,
    "SKU_ShortLife": 1.2
  },
  "production_cap": {
    "SKU_Basic": [
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800
    ],
    "SKU_Premium": [
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400
    ],
    "SKU_ShortLife": [
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500
    ]
  },
  "labor_cap": {
    "DC1": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC2": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC3": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC4": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC5": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ]
  },
  "labor_usage": {
    "SKU_Basic": 0.0,
    "SKU_Premium": 0.0,
    "SKU_ShortLife": 0.0
  },
  "return_rate": {
    "SKU_Basic": 0.0,
    "SKU_Premium": 0.0,
    "SKU_ShortLife": 0.0
  },
  "demand_curve": {
    "SKU_Basic": [
      285,
      348,
      340,
      316,
      395,
      540,
      795,
      1029,
      1254,
      1405,
      1246,
      1095,
      1078,
      795,
      3200,
      623,
      444,
      339,
      340,
      312
    ],
    "SKU_Premium": [
      153,
      156,
      158,
      196,
      232,
      263,
      344,
      492,
      598,
      635,
      675,
      564,
      556,
      388,
      1529,
      249,
      222,
      162,
      176,
      172
    ],
    "SKU_ShortLife": [
      107,
      111,
      129,
      129,
      196,
      223,
      283,
      374,
      505,
      456,
      591,
      464,
      503,
      388,
      1082,
      243,
      158,
      162,
      148,
      128
    ]
  },
  "demand_share": {
    "DC1": 0.25,
    "DC2": 0.2,
    "DC3": 0.2,
    "DC4": 0.2,
    "DC5": 0.15
  },
  "costs": {
    "lost_sales": {
      "SKU_Basic": 50.0,
      "SKU_Premium": 80.0,
      "SKU_ShortLife": 40.0
    },
    "inventory": {
      "SKU_Basic": 1.0,
      "SKU_Premium": 1.5,
      "SKU_ShortLife": 1.0
    },
    "waste": {
      "SKU_Basic": 2.0,
      "SKU_Premium": 3.0,
      "SKU_ShortLife": 2.0
    },
    "fixed_order": 0.0,
    "transshipment": 0.5,
    "purchasing": {
      "SKU_Basic": 10.0,
      "SKU_Premium": 20.0,
      "SKU_ShortLife": 15.0
    }
  },
  "constraints": {
    "moq": 0,
    "pack_size": 1,
    "budget_per_period": null,
    "waste_limit_pct": null
  },
  "network": {
    "sub_edges": [
      [
        "SKU_Basic",
        "SKU_Premium"
      ]
    ],
    "trans_edges": []
  }
}
```

[OUTPUT FORMAT]
- Import: import gurobipy as gp; from gurobipy import GRB; import json
- Set Gurobi params: m.Params.OutputFlag = 0; m.Params.Threads = 1; m.Params.Seed = 0
- Print at end:
  print(f"status: {{m.Status}}")
  if m.Status == 2:
      print(f"objective: {{m.ObjVal}}")
- Output ONLY executable Python code. No markdown, no explanations.

[TASK]
Write a GurobiPy script that:
1. Parses the JSON data above (use json.loads on the string)
2. Models and solves the optimization problem
3. Prints status and objective value

Standard seasonal retail scenario.


[SCENARIO]
Family: F4 (Dynamics and Disruptions)
Archetype: retail_f4_demand_surge
Scenario ID: retail_f4_demand_surge_v2

[BUSINESS DESCRIPTION]
Business narrative:
The retailer experiences a single-period viral demand spike where demand suddenly multiplies for all products. Production capacity and other structural elements remain unchanged; only the magnitude of demand in that period is much higher. The retailer must decide whether to build extra inventory in advance or accept lost sales during the surge.

Structure cues:
- The inventory and production structure is the same as in the base scenario.
- Shelf life: Each product has a shelf life in periods. Inventory must be tracked by REMAINING LIFE.

  VARIABLE DEFINITION: I[p,l,t,r] = inventory at START of period t with r periods remaining.
  Convention: r=1 is OLDEST (sell first FIFO), r=shelf_life[p] is FRESHEST.

  KEY EQUATIONS - implement EXACTLY as written, do NOT add or remove terms:

  (1) Fresh inflow: I[p,l,t,SL] = Q[p,t] * demand_share[l]
      - This is ONLY the inflow from production. Do NOT subtract sales here!
      - Q is total production, demand_share distributes it to locations.

  (2) Aging: I[p,l,t+1,r] = I[p,l,t,r+1] - sales[p,l,t,r+1] for r=1..SL-1
      - Inventory tomorrow with r remaining = inventory today with r+1 remaining - sales

  (3) Waste: W[p,l,t] = I[p,l,t,1] - sales[p,l,t,1]
      - Items with r=1 that aren't sold become waste

  (4) Sales availability: sales[p,l,t,r] <= I[p,l,t,r]
      - Can only sell what you have in inventory

  (5) Inventory holding cost: charged on (I[p,l,t,r] - sales[p,l,t,r]) for r >= 2
      - Charge on END-of-period inventory (after sales), exclude expiring items (r=1)
- Storage capacity: sum over products of (cold_usage[p] * total_inventory[p,l,t]) <= cold_capacity[l]. These limits must be respected.
- In the JSON, one mid-horizon period has demand for each product scaled up by a large factor, representing the surge. This period is treated as having much higher exogenous demand.
- Inventory stays non-negative and is updated using previous stock, current production, sales, and waste.
- Substitution behavior is unchanged, there is no transshipment, and lead times remain effectively zero.
- The objective is to minimize total cost (aggregating purchasing, holding, waste, and lost sales), with the demand spike increasing the importance of planning ahead for that particular period.

[DATA SCHEMA]
{
  "name": str,                          # scenario identifier
  "periods": int,                       # number of time periods
  "products": [str, ...],               # list of product IDs
  "locations": [str, ...],              # list of location IDs

  "shelf_life": {p: int},               # shelf life in periods per product
  "lead_time": {p: int},                # order lead time per product (0 = same-period arrival)

  "demand_curve": {p: [float, ...]},    # demand per product per period (0-indexed list)
  "demand_share": {l: float},           # fraction of total demand at each location

  "production_cap": {p: [float, ...]},  # max production per product per period (0-indexed list)
  "cold_capacity": {l: float},          # storage capacity per location
  "cold_usage": {p: float},             # storage units per unit of product

  "labor_cap": {l: [float, ...]},       # labor hours per location per period (0-indexed list)
  "labor_usage": {p: float},            # labor hours per unit sold
  "return_rate": {p: float},            # fraction of sales returned next period

  "costs": {
    "purchasing": {p: float},           # cost per unit ordered
    "inventory": {p: float},            # holding cost per unit per period
    "waste": {p: float},                # cost per unit expired
    "lost_sales": {p: float},           # penalty per unit of unmet demand
    "fixed_order": float,               # fixed cost per order placed
    "transshipment": float              # cost per unit transshipped
  },

  "constraints": {
    "moq": float,                       # minimum order quantity (0 = no MOQ)
    "pack_size": int,                   # order must be multiple of this (1 = no constraint)
    "budget_per_period": float|null,    # max purchasing cost per period
    "waste_limit_pct": float|null       # max waste as fraction of total demand
  },

  "network": {
    "sub_edges": [[p_from, p_to], ...], # substitution: p_from's demand can be served by p_to
    "trans_edges": [[l_from, l_to], ...]# transshipment: can ship from l_from to l_to
  }
}

[DATA ACCESS]
- The variable `data` is pre-loaded. Do NOT use file I/O.
- Lists are 0-indexed (period t in model uses index [t-1] in data arrays)

CRITICAL - Network edges require tuple conversion for Gurobi:
  sub_edges = [tuple(e) for e in data.get('network', {}).get('sub_edges', [])]
  trans_edges = [tuple(e) for e in data.get('network', {}).get('trans_edges', [])]

[OUTPUT FORMAT]
- Import: import gurobipy as gp; from gurobipy import GRB
- Set Gurobi params: m.Params.OutputFlag = 0; m.Params.Threads = 1; m.Params.Seed = 0
- Print at end:
  print(f"status: {{m.Status}}")
  if m.Status == 2:
      print(f"objective: {{m.ObjVal}}")
- Output ONLY executable Python code. No markdown, no explanations.

[TASK]
Write a GurobiPy script that models and solves this optimization problem.

[SCENARIO]
Family: F4 (Dynamics and Disruptions)
Archetype: retail_f4_demand_surge
Scenario ID: retail_f4_demand_surge_v2

[BUSINESS DESCRIPTION]
Business narrative:
The retailer experiences a single-period viral demand spike where demand suddenly multiplies for all products. Production capacity and other structural elements remain unchanged; only the magnitude of demand in that period is much higher. The retailer must decide whether to build extra inventory in advance or accept lost sales during the surge.

Structure cues:
- The inventory and production structure is the same as in the base scenario.
- Shelf life: Each product has a shelf life in periods. Inventory must be tracked by REMAINING LIFE.

  VARIABLE DEFINITION: I[p,l,t,r] = inventory at START of period t with r periods remaining.
  Convention: r=1 is OLDEST (sell first FIFO), r=shelf_life[p] is FRESHEST.

  KEY EQUATIONS - implement EXACTLY as written, do NOT add or remove terms:

  (1) Fresh inflow: I[p,l,t,SL] = Q[p,t] * demand_share[l]
      - This is ONLY the inflow from production. Do NOT subtract sales here!
      - Q is total production, demand_share distributes it to locations.

  (2) Aging: I[p,l,t+1,r] = I[p,l,t,r+1] - sales[p,l,t,r+1] for r=1..SL-1
      - Inventory tomorrow with r remaining = inventory today with r+1 remaining - sales

  (3) Waste: W[p,l,t] = I[p,l,t,1] - sales[p,l,t,1]
      - Items with r=1 that aren't sold become waste

  (4) Sales availability: sales[p,l,t,r] <= I[p,l,t,r]
      - Can only sell what you have in inventory

  (5) Inventory holding cost: charged on (I[p,l,t,r] - sales[p,l,t,r]) for r >= 2
      - Charge on END-of-period inventory (after sales), exclude expiring items (r=1)
- Storage capacity: sum over products of (cold_usage[p] * total_inventory[p,l,t]) <= cold_capacity[l]. These limits must be respected.
- In the JSON, one mid-horizon period has demand for each product scaled up by a large factor, representing the surge. This period is treated as having much higher exogenous demand.
- Inventory stays non-negative and is updated using previous stock, current production, sales, and waste.
- Substitution behavior is unchanged, there is no transshipment, and lead times remain effectively zero.
- The objective is to minimize total cost (aggregating purchasing, holding, waste, and lost sales), with the demand spike increasing the importance of planning ahead for that particular period.

[DATA]
The following JSON contains all instance data. Parse it directly in your code.

```json
{
  "name": "retail_f4_demand_surge_v2",
  "description": "Standard seasonal retail scenario.",
  "periods": 20,
  "products": [
    "SKU_Basic",
    "SKU_Premium",
    "SKU_ShortLife"
  ],
  "locations": [
    "DC1",
    "DC2",
    "DC3",
    "DC4",
    "DC5"
  ],
  "shelf_life": {
    "SKU_Basic": 10,
    "SKU_Premium": 8,
    "SKU_ShortLife": 4
  },
  "lead_time": {
    "SKU_Basic": 0,
    "SKU_Premium": 0,
    "SKU_ShortLife": 0
  },
  "cold_capacity": {
    "DC1": 3819.945865685423,
    "DC2": 3609.9362252451174,
    "DC3": 3185.7109811662085,
    "DC4": 3387.014925133641,
    "DC5": 2300.786190660187
  },
  "cold_usage": {
    "SKU_Basic": 1.0,
    "SKU_Premium": 3.0,
    "SKU_ShortLife": 1.2
  },
  "production_cap": {
    "SKU_Basic": [
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800,
      800
    ],
    "SKU_Premium": [
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400,
      400
    ],
    "SKU_ShortLife": [
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500,
      500
    ]
  },
  "labor_cap": {
    "DC1": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC2": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC3": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC4": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ],
    "DC5": [
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0,
      99999.0
    ]
  },
  "labor_usage": {
    "SKU_Basic": 0.0,
    "SKU_Premium": 0.0,
    "SKU_ShortLife": 0.0
  },
  "return_rate": {
    "SKU_Basic": 0.0,
    "SKU_Premium": 0.0,
    "SKU_ShortLife": 0.0
  },
  "demand_curve": {
    "SKU_Basic": [
      297,
      306,
      348,
      417,
      416,
      526,
      645,
      871,
      1162,
      1062,
      1275,
      1416,
      1228,
      796,
      3191,
      580,
      493,
      366,
      358,
      351
    ],
    "SKU_Premium": [
      171,
      138,
      150,
      170,
      233,
      301,
      324,
      406,
      537,
      663,
      711,
      550,
      495,
      398,
      1267,
      252,
      190,
      169,
      173,
      176
    ],
    "SKU_ShortLife": [
      118,
      131,
      135,
      152,
      174,
      208,
      286,
      326,
      434,
      443,
      551,
      484,
      475,
      340,
      1222,
      193,
      154,
      155,
      121,
      108
    ]
  },
  "demand_share": {
    "DC1": 0.25,
    "DC2": 0.2,
    "DC3": 0.2,
    "DC4": 0.2,
    "DC5": 0.15
  },
  "costs": {
    "lost_sales": {
      "SKU_Basic": 50.0,
      "SKU_Premium": 80.0,
      "SKU_ShortLife": 40.0
    },
    "inventory": {
      "SKU_Basic": 1.0,
      "SKU_Premium": 1.5,
      "SKU_ShortLife": 1.0
    },
    "waste": {
      "SKU_Basic": 2.0,
      "SKU_Premium": 3.0,
      "SKU_ShortLife": 2.0
    },
    "fixed_order": 0.0,
    "transshipment": 0.5,
    "purchasing": {
      "SKU_Basic": 10.0,
      "SKU_Premium": 20.0,
      "SKU_ShortLife": 15.0
    }
  },
  "constraints": {
    "moq": 0,
    "pack_size": 1,
    "budget_per_period": null,
    "waste_limit_pct": null
  },
  "network": {
    "sub_edges": [
      [
        "SKU_Basic",
        "SKU_Premium"
      ]
    ],
    "trans_edges": []
  }
}
```

[OUTPUT FORMAT]
- Import: import gurobipy as gp; from gurobipy import GRB; import json
- Set Gurobi params: m.Params.OutputFlag = 0; m.Params.Threads = 1; m.Params.Seed = 0
- Print at end:
  print(f"status: {{m.Status}}")
  if m.Status == 2:
      print(f"objective: {{m.ObjVal}}")
- Output ONLY executable Python code. No markdown, no explanations.

[TASK]
Write a GurobiPy script that:
1. Parses the JSON data above (use json.loads on the string)
2. Models and solves the optimization problem
3. Prints status and objective value

Standard seasonal retail scenario.