A company produces three types of items. A single machine is used to produce the three items on a cyclical basis. The company has the policy that every item is produced once during each cycle, and it wants to determine the number of production cycles per year that will minimize the sum of holding and setup costs (no shortages are allowed). The following data are given:

P_i= number of units of product i that could be produced per year if the machine were entirely devoted toproducing product i

D_i= annual demand for product i

K_i= cost of setting up production for product i

h_i= cost of holding one unit of product i in inventory for one year

a Suppose there are N cycles per year. Assuming that during each cycle, a fraction 1/N of all demand for each product is met, determine the annual holding cost and the annual setup cost.

b Let q^*_ibe the number of units of product i produced during each cycle. Determine the optimal value of N (call it N*) and q^*_i.

c Let EROQ_ibe the optimal production run size for product i if the cyclical nature of the problem is ignored. Suppose q^*_iis much smaller than EROQ_i. What conclusion could be drawn?

d Under certain circumstances, it might not be desirable to produce every item during each cycle. Which of the following factors would tend to make it undesirable to produce product i during each cycle: (1) Demand is relatively low. (2) The setup cost is relatively high. (3) The holding cost is relatively high.