(Canadian Tire inventory control, Section 1.2) Daily demand for paint brushes at a particular store follows the demand distribution:

The stock level is reviewed in the evening every four days and when warranted an order is placed at the central warehouse to augment stock. Orders arrive two days later (a two day lead time) and are available to meet demand on the morning of the third day following the review. For example, an order placed Sunday evening can be used to meet demand on Wednesday. Demand not satisfed from stock on hand is never filled. Management imposes a penalty to account for this.

a. Find a reodering policy that minimizes expected total ordering, holding and shortage costs under the assumption that the fixed cost for placing an order is $0.20, the daily per unit holding cost is $0.01 and the per unit penalty cost for unfilled orders is $0.50. Assume a planning horizon of 84 days and assign a value of $0.70 for each unit on hand at the end of this period.

b. Investigate the sensitivity of the optimal policy to the penalty cost.

c. Investigate the sensitivity of the expected total cost to the review period. In particular what is the effect of reviewing the inventory level every 7 days instead. (Hint: Write a system equation which describes the system state every review period as a function of the system state at the previous review period and the daily demand at each day between reviews. Note further that the two day demand can be found by computing the convolution of the above demand distribution with itself. Of course, solving this problem involves writing a computer program.)