***Please read the question and restrictions.Available solutions not correct.

*there are 3 extra constraint in here

Mathematical model like

min

s.t

constraint 1

constraint 2

constraint 3

.... sign constraint

V DODD OOOO (30 points) The SCM company plans to open a new single plant among Plants Warehouses Markets four potential location options as can be seen in figure presented right. Five warehouses act as intermediaries between plants and markets each of which has a known demand that needs to be satisfied. It is assumed that only direct deliveries are possible between plants and warehouses, and between warehouses and markets. The demands of each market are as follows: 100, 200, 300, 400 and 500 consecutively. The rest of the data are presented in Tables 1 to 3. There are some restrictions * no need to satisfy the whole demand of Market 2, however, for each unmet demand a penalty cost of 10 TL has to be confronted. Figure 1 Representation of the supply chain network *Note that demand of Markets 1, 3, 4 and 5 have to be still fully satisfied. The demand of Market 1 can be satisfied from at most one Warehouse. No such restriction exists on the other Markets. *Warehouse 5 cannot serve Markets 2 and 5, simultaneously. Question is to develop a mathematical model to identify plant locations and quantities shipped that minimize the total fixed and variable costs. Define parameters and decision variables explicitly.) 1) Table 1 Potential plant capacities and corresponding fixed costs in TL Potential plant Capacity Fixed cost of opening potential plant 1600 10000 1700 20000 3 1800 30000 1900 40000 Table 2 Cost of shipping one unit from potential plant p to warehouse w in TL Warehouses 1 2 3 Potential Plant 1 100 105 100 135 Potential Plant 2 105 115 105 115 Potential Plant 3 110 125 120 145 Potential Plant 4 135 115 135 Table 3 Cost of shipping one unit from warehouse w to market m in TL Markets 1 2 3 Warehouse 1 60 105 100 135 Warehouse 2 105 115 165 125 Warehouse 3 70 125 120 145 Warehouse 4 115 155 145 175 Warehouses 105 115 105 115 - 5 90 80 70 150 115 5 60 90 75 150 180