3.2 FORMULATING THE MODEL
3.2.1 Input parameters
The input parameters used in this study are classified into four main categories including general, component purchasing, transportation and storage. These categories and their associated parameters are illustrated subsequently.
General input parameters
The following parameters cover those parameters which are related to demand, opening costs of plants and DCs, bill of material, backlogging and so on.
Demand for product i in customer e in period t
Fixed cost of opening and operating plant p in period t Fixed cost of opening and operating DC w in period t
Cost of closing plant p in period t Cost of closing DC w in period t
Unit production cost in regular-time (in the first period of plant opening) for product i in plant p in period t
Unit production cost in overtime (in the first period of plant opening) for product i in plant p in period t
Unit production cost in regular-time (from the second period onward) for product i in plant p in period t
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Unit production cost in overtime (from the second period onward) for product i in plant p in period t
Unit cost of outsourcing product i by plant p in period t Unit holding cost of component c in plant p in period t Unit holding cost of product i in plant p in period t
Cost of backlogging product i in customer e in period t
Quantity of component c used to produce one unit of product i Maximum holding capacity of component c in plant p in period t ̅ Maximum holding capacity of product i in plant p in period t
Maximum allowed backlog for product i in customer e in period t
Maximum capacity for regular-time production of product i in plant p in period t ̅ Maximum capacity for overtime production of product i in plant p in period t
Maximum allowed outsourcing quantity of product i in plant p in period t
Component purchasing
The parameters listed under this category are related to the procurement of components from suppliers. This category covers parameters from purchasing cost of components to the capacity of suppliers for supplying the components to the plants. The suppliers may offer quantity discount for their components. Three intervals were considered for quantity discount that suppliers offer to the manufacturer. The highest price in this case is related to the lowest quantity range which refers to the quantity less than the lower quantity break-point and the lowest price is related to the order quantities larger than the upper quantity break-point. For instance, a supplier may consider its highest price for quantities less than the lower quantity break-point of 200 units of order and lowest price for orders over the upper quantity break- point of 1000 units. In this case, if the manufacturer orders less than 200 units, which falls into the first pricing interval, the price will be the highest. However, if the order quantity is over 1000 units the price will be the lowest and similarly if the order quantity is between the two quantity break-points, then the price will be somewhere between the lowest and highest price. The purchasing cost for quantities less than the lower quantity break-point is referred as the base purchasing cost.
Base purchasing cost (highest rate at lowest quantity range) for the acquisition of component c from supplier s for plant p in period t
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Quantity discount multiplier for purchasing component c from supplier s for plant p in period t
Lower quantity break-point for component c offered by supplier s to plant p in period
t
Upper quantity break-point for component c offered by supplier s to plant p in period
t
Lower discount rate (for medium quantity range) for purchasing component c from supplier s for plant p in period t
Higher discount rate (for large quantity range) for purchasing component c from supplier s for plant p in period t
Minimum allowed purchase quantity of component c from supplier s for plant p in period t
Maximum capacity of supplier s for component c to supply plant p in period t Minimum purchase quantity from supplier s during the planning horizon
Transportation
This category addresses parameters associated with the shipment of finished products from plants to DCs/warehouses, transportation of finished products from DCs to customers and direct transportation of finished products from plants to customers.
Unit transportation cost for the shipment of product i from plant p to DC w by logistics provider l using transport mode m in period t
̅
Unit transportation cost for the shipment of product i from DC w to customer e by logistics provider l using transport mode m in period t
̿
Unit transportation cost for the shipment of product i from plant p to customer e by logistics provider l using transport mode m in period t
Minimum allowed shipment quantity of product i from plant p to DC w by logistics
provider l using mode m in period t
Maximum allowed shipment quantity of product i from plant p to DC w by
logistics provider l using mode m in period t
̅ Minimum allowed shipment quantity of product i from DC w to customer e by
logistics provider l using mode m in period t
̅ Maximum allowed shipment quantity of product i from DC w to customer e by
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̿ Minimum allowed shipment quantity of product i from plant p to customer e by
logistics provider l using mode m in period t
̿ Maximum allowed shipment quantity of product i from plant p to customer e by
logistics provider l using mode m in period t
̅ Minimum allowed shipment quantity delegated to logistics provider l during the planning horizon
Parameters related to the storage of finished products
Following parameters are related to the capacity of DCs/warehouses.
Unit storage cost for holding product i in self-owned DC w in period t Unit storage cost for holding product i in rental warehouse w in period t
Storage multiplier for holding product i in self-owned DC and/or rental warehouse w in period t
Maximum capacity of self-owned DC w for storing product i in period t ̅ Maximum capacity of rental warehouse w for storing product i in period t
Storage multiplier defined above is due to the storage cost difference between a self-owned distribution centre and its neighbourhood warehouse.