Question 5. Saint-Gold is a British company specialized in the production of cei

Question

Question 5. Saint-Gold is a British company specialized in the production of ceiling fans. For the production of the Airmax model, the company needs a special numerical controller. There are four potential suppliers, whose scores, determined using the weighted scoring method, are 6.97, 6.75, 6.31 and 6.92, respectively During the negotiation phase, each supplier has imposed to the company a daily minimum and maximum quantity to be ordered. These values are shown in the second and third columns of the following Table. Write down the supplier selection model to select the highest scoring and suppliers with minimum late delivery percentage Supplier Minimum Maximum supply 1140 900 300 720 supply 3000 3600 3000 4800 Late delivery (96) 3.50 2.80 4.30 2.50 2 3 4

Explanation / Answer

Supplier selection model in this case, is a multi objective linear programming (MOLP) as follows

Decision variables: Binary variable Xi = 1 indicates that supplier i is selected, where i=1,2,3,4

Yi = Quantity supplied by supplier i

Objective1 : Max 6.97X1 + 6.75X2 + 6.31X3 + 6.92X4

Objective 2: Minimize 3.5%*Y1 + 2.8%*Y2 + 4.3%*Y3 + 2.5%*Y4

s.t.

3000*X1 - Y1 >= 0

3600*X2 - Y2 >= 0

3000*X3 - Y3 >= 0

4800*X4 - Y4 > 0

Y1 - 1140*X1 >= 0

Y2 - 900*X2 >= 0

Y3 - 300*X3 >= 0

Y4 - 720*X4 >= 0

X1, X2, X3, X4 = 0,1

Y1, Y2, Y3, Y4 >= 0

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