Change the ordering simulation in Example 12.8 so that the lead time can be 1, 2, 3, or 4 weeks with probabilities 0.5, 0.2, 0.2, and 0.1, respectively. Also, assume that based on previous orders, orders of sizes 350, 0, and 400 are scheduled to arrive at the beginnings of weeks 2, 3, and 4, respectively. Simulate the same (s, S) policies as in the example.
EXAMPLE 12.8 SIMULATING ORDERING POLICIES AT HOME REPAIR
Home Repair is a large hardware retail store that often has to place orders for hammers. The fixed cost for placing an order is $500, independent of the size of the order. The unit cost per hammer is $20. Home Repair estimates that the cost of holding a hammer in inventory for one week is $3. The company defines its inventory position at the beginning of any week as the number of hammers in inventory, plus any that have already been ordered but have not yet arrived, minus any backorders. The company’s ordering policy is an (s, S) policy, a periodic review policy used by many companies. This policy, defined by two numbers s and S, where s
S, specifies that if the inventory position at the beginning of the week is at level x, and x is less than or equal to s, exactly enough hammers are ordered to bring the inventory position up to S; that is, Home Repair orders S x hammers. Otherwise, if the inventory position is greater than s, no order is placed that week. If an order is placed, it arrives after a lead time of one, two, or three weeks with probabilities 0.7, 0.2, and 0.1, respectively. The weekly demand for hammers is uncertain, but it can be described by a normal distribution with mean 300 and standard deviation 75. The company’s policy is to satisfy all demand in the week it occurs. If weekly demand cannot be satisfied completely from on hand inventory, an emergency order is placed at the end of the week for the shortage. This order arrives virtually instantaneously but at a steep cost of $35 per hammer. It is currently the beginning of week 1, and the current inventory of hammers, including any that may have just arrived, is 600. No other orders are on the way. Home Repair wants to simulate several (s, S) policies to see which does best in terms of total cost over the next 48 weeks.9
Objective To use simulation to analyze costs when the company uses an (s, S) ordering policy.