At the beginning of a period, a company observes its inventory level. An order is placed and received. The period's demand is observed. We are given the following info:
1. A $2 cost is assessed against each unit of inventory on hand at the end of the period.
2. A $3 penalty is assessed against each unit of demand not met on time. Assuming all shortages result in lost sales.
3. Placing an order costs 50c per unit plus a $5 ordering cost.
4. During each period demand is equally likely to equal 1, 2, or 3 units.
The company is considering the following ordering policy: At the end of any period, if the on-hand inventory is 1 unit or less, order sufficient units to bring the on-hand inventory level at the beginning of the next period up to 4 units.
a. What fraction of time will the on-hand inventory level at the end of each period be 0 unit? 1 unit? 2 units? 3 units? 4 units?
b. Determine the average cost per period incurred by the ordering policy.
c. Answer parts (a) and (b) if all shortages are backlogged. Assume that the cost for each unit backlogged is $3.