Question

ABCD imports an item whose demands over the next 4 months are 100, 240, 210 and 180 units, respectively. The company can either stock out just enough to fulfill the current month's demand or keep inventory for the succeeding months demand requirements. However, ABCD incurs a holdiong cost of 1.20$ per unit that is held in inventory per month. Furthermore due to fluctuations in dollar exhange rates, ABCD estimates that the unit prices for the next 4 months 15$, 12$, 10$, and 14$ repectively. A fixed order cost of 200$ is incurred each time an order is placed. The company then wants to develop a purchasing plan that will minimize the total cost of ordering, purchasing, and holding an item in stock. Use network model to formulate this problem.

Answer 1

Network model is following

Formulate LP model

Let binary variable Yi = 1, if an order is placed in month i

Xi be the quantity produced in month i

Vi be the inventory in month i

Min 200(Y1+Y2+Y3+Y4)+15X1+12X2+ 10X3+14X4+1.2(V1+V2+V3+V4)

s.t.

1000Yi - Xi >= 0 , for i = {1,2,3,4}

X1 - V1 = 100

X2 - V2 + V1 = 240

X3 - V3 + V2 = 210

X4 - V4 + V3 = 180

All variables >= 0