Warehouse Location In modeling distribution systems, decisions must be made about tradeoffs between transportation costs and...

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Warehouse Location In modeling distribution systems, decisions must be made about tradeoffs between transportation costs and costs for operating distribution centers. As an example, suppose that a manager must decide which of n warehouses to use for meeting the demands of m customers for a good. The decisions to be made are which warehouses to operate and how much to ship from any warehouse to any customer. Let The relevant costs are: fi = Fixed operating cost for warehouse i, ifopened (for example, a cost to lease the warehouse), subject to: cij = Per-unit operating cost at warehouse i plus the transportation cost for shipping from warehouse i to customer j. There are two types of constraints for the model: y = = {1 xij = Amount to be sent from warehouse i to customer j. i) the demand d, of each customer must be filled from the warehouses; and ii) goods can be shipped from a warehouse only if it is opened. The model is: m if warehouse i is opened, if warehouse i is not opened; }=1 71 m Minimize axy + 1=1 /=1 1=1 j=1 xy-ydj 0 () /=1 X1 20 y = 0 = dj or 1 (j = 1, 2,..., n), (i = 1, 2, ..., m), (i = 1,2, ..., m; j = 1, 2, ..., n), (i 1, 2, ..., m). (1) e (2) (3) Warehouse Location In modeling distribution systems, decisions must be made about tradeoffs between transportation costs and costs for operating distribution centers. As an example, suppose that a manager must decide which of n warehouses to use for meeting the demands of m customers for a good. The decisions to be made are which warehouses to operate and how much to ship from any warehouse to any customer. Let The relevant costs are: fi = Fixed operating cost for warehouse i, ifopened (for example, a cost to lease the warehouse), subject to: cij = Per-unit operating cost at warehouse i plus the transportation cost for shipping from warehouse i to customer j. There are two types of constraints for the model: y = = {1 xij = Amount to be sent from warehouse i to customer j. i) the demand d, of each customer must be filled from the warehouses; and ii) goods can be shipped from a warehouse only if it is opened. The model is: m if warehouse i is opened, if warehouse i is not opened; }=1 71 m Minimize axy + 1=1 /=1 1=1 j=1 xy-ydj 0 () /=1 X1 20 y = 0 = dj or 1 (j = 1, 2,..., n), (i = 1, 2, ..., m), (i = 1,2, ..., m; j = 1, 2, ..., n), (i 1, 2, ..., m). (1) e (2) (3)