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| Symbol | Description |
|
| Indices |
|
| Product item () |
| Customer/retailer () |
| Factory (manufacturer) () |
| Distributor () |
| Mode of transportation () |
| Number of factories |
| Number of customers/retailers |
| Number of distributors |
| Number of product items |
| Number of ransportation modes |
|
| Input parameters |
|
| Distributor’s cost (fixed) |
| Volume/capacity occupied by product item |
| Weight of product item |
| Max capacity/volume of distributor |
| Production capacity of factory for product item |
| Cost of product item in factory |
| If distributor can supply product item then ; otherwise |
| Time required to prepare the dispatch of product item by distributor |
| Cut-off time of supply of product item to customer/retailer |
| Size of the order for product item placed by customer c |
| Number of transportation units using transportation mode e |
| Capacity of transportation unit using transportation mode e |
| Tonnage of transportation unit using transportation mode e |
| Supply time from factory (manufacturer) a to distributor b by transportation mode e |
| Cost of supplying product item d from factory (manufacturer) a to distributor b by transportation mode e (variable) |
| If factory (manufacturer) a can supply distributor b using transportation mode e, then ; otherwise |
| Cost of supply from factory (manufacturer) a to distributor b by transportation mode e (fixed) |
| Overall cost of supply from distributor b to customer c by transportation mode e |
| Time of supply from distributor b to customer/retailer c by transportation mode e |
| Variable cost of supply of product item d from distributor b to customer/retailer c by transportation mode e |
| If distributor b can supply customer/retailer c by transportation mode e, then ; otherwise |
| Fixed cost of supply from distributor b to customer/retailer c by transportation mode e |
| Overall cost of supply from distributor b to customer/retailer c by transportation mode e |
| Environmental cost of using transportation mode e |
|
| Decision variables |
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| Quantity of a product item d supplied from factory (manufacturer) a to distributor b by transportation mode e to customer/retailer c |
| If supply is from factory (manufacturer) a to distributor b of product d by transportation mode e to customer/retailer , then , otherwise |
| Number of travels from factory (manufacturer) a to distributor b by transportation mode e |
| Quantity of product item d supplied from distributor b to customer c by transportation mode e |
| If supply is from distributor b to customer/retailer c for product d by transportation mode e, then ; otherwise |
| Number of travels from distributor b to customer/retailer c by transportation mode e |
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