Question

Question 4 (20 marks) An automotive manufacturing company is planning its manufacturing and stock for the next four months. The table below includes the demand and the variable manufacturing cost for each month. Month 2 3 4 Production demand (units) 100 140 210 180 Variable cost ($/unit) 15 12 10 14 The setup cost for production is $200. In addition, the company can stock just enough supply to meet each month's demand, or it can overstock to meet the demand for two or more successive and consecutive months. In the latter case, a holding cost of $1.20 is charged per overstocked unit per month. The company wants to develop a purchasing plan that will minimize the total costs of manufacturing and holding the item in stock. Formulate the problem as a network model in order to reach the company objective.

Answer 1

10 1.2 This can be formulated as a network model as follows: Months Total Demand (Units) 100 210 180 630 Variable Cost ($/Unit) 15 Production During Month (UNITS) Production Set Ups (Numbers) X1 X3 Closing Inventory(Units) Y1 Y2 Y3 Y4 Holding Cost ($/Unit) 1.2 1.2 1.2 Set Up Costs ($/Set Up) 200 200 200 200 Here the network model would be to minimize = (X1*200+15*P1+1.2*Y1)+(x2*200+12*P2+1.2*Y2)+(x3*200+10*P3+1.2*Y3)+(X4*200+14*P4+1.2*Y4) Contraints here are P1+P2+P3+P4=630 X1, X2,X3,X4 >=0 Y1,92,93,94>=0 Let us solve taking the help of a spread sheet to solve and settle the lowest cost of manufacturing. Month Production Demand Variable Cost Production Set Up Production Beginning Inventory Closing Inventory Holding Cost Set Up Cost variable Cost Set Up Cost Holding Cost Total Plan Cost Units $/Unit Numbers Units Units $/Unit $/set Up $ F=D+E-A G H I=B* D J EC*H K=G*F L=l+J+K 100 200 1500 200 1700 2 140 140 1.2 200 1680 200 1880 210 390 180 1.2 200 3900 200 216 4316 180 180 1.2 O 0 Total 630 630 180 180 4.8 600 7080 600 216 7896 Units 15 100 1.2 0 0 0