1 1 Practice Final John H. Vande Vate Fall, 2005

2 2 Question 1 In class we described how a model that holds inventory of incoming supplies to buffer the supply chain from variations in customer demand.

3 3 Question 1 Under the model, the supplier normally ships the same quantity every day. When inventory rises to S, the model recommends curtailing shipments until it falls to Q and when inventory falls to 0, the model recommends expediting shipments or sending an unusually large shipment to bring inventory levels back up to q.

4 4 Question 1 Consider the special case in which: a. there is no inventory holding cost (h = 0) b. because of space limitations, the maximum inventory level S for the part cannot exceed a given level M c. the fixed costs of expediting and curtailing shipments are equal (K = L > 0) d. There are no variable costs for expediting and curtailing shipments (k = l = 0)

5 5 Question 1 What is the optimal strategy in this special case? S = Q = q =

6 6 Answer S = M Q = q = M/2 Reasoning: Inventory is free, so we are only concerned with running into the bounds 0 and M, which we want to do as infrequently as possible. Since there are no variable costs to expedite and curtail, when we do expedite, we should expedite as much as we can to prevent having to expedite or curtail again. Symmetry leads us to Q = q = M/2

7 7 Question 2 We argued in class that, under a periodic review regime, increasing the frequency of shipments generally reduces total inventory and expediting costs. We made this argument assuming that the costs of increasing frequency were negligible.

8 8 Question 2 Suppose –inventory carrying costs are h = $100 per item per year –ordering costs are c = $1,000 per shipment –Demand over time is relatively constant at D = 200,000 per year –The average lead time is 4 weeks with a standard deviation of 2 days. If we intend to hold safety stock constant regardless of the frequency of orders, how frequently should we order?

9 9 Solution The lead time information is a red herring. It’s irrelevant as we have decided to hold safety stock constant. This becomes a simple EOQ type problem with n, the number of times to order as the variable. The total cost formula is hD/2n + cn The solution is n = SQRT(hD/2c)

10 Question 3 We receive a shipment from our supplier once each week. The lead time for those shipments is 4 weeks with a standard deviation of 2 days. Demand each day is normally distributed with mean 100 and standard deviation 10. How much safety stock should we hold to ensure that the chances of stocking out before a shipment (not the annual chances of stocking out) are only 2%?

11 Solution Calculate the variance in demand during the lead time plus the order period. This is (T+E[L])  D 2 +D 2  L 2 Careful with the units. Let’s work in days T = 7 days E[L] = 28 days D = 100 units/day  D 2 = 100 units 2 /day  L 2 = 4 days 2

12 Solution So the variance is (T+E[L])  D 2 +D 2  L 2 35*100+40,000 = 43,500 And the standard deviation is about units We want to carry just over 2 standard deviations or about 417 items

13 Question 4 We ship products from Asia to Europe for sale to customers and are interested in strategies that reduce the “avoidable” costs of supply. A.Under a periodic review regime, which of the following strategies will help reduce pipeline (in-transit) inventories? i.Increasing frequency ii.Improving forecast accuracy iii.Reducing the safety lead-time iv.Moving our source for the products closer to Europe v.Changing to a faster mode of transportation

14 Question 4 B. Under a periodic review regime, which of the following strategies will help reduce cycle inventories (on-hand inventory excluding safety stock)? i.Increasing frequency ii.Improving forecast accuracy iii.Reducing the safety lead-time iv.Moving our source for the products closer to Europe v.Changing to a faster mode of transportation

15 Question 4 C. Under a periodic review regime, which of the following strategies will allow us to reduce safety stock without compromising product availability? i.Increasing frequency ii.Improving forecast accuracy iii.Reducing the safety lead-time iv.Moving our source for the products closer to Europe v.Changing to a faster mode of transportation

16 Solution A.Under a periodic review regime, which of the following strategies will help reduce pipeline (in-transit) inventories? i.Increasing frequency ii.Improving forecast accuracy iii.Reducing the safety lead-time iv.Moving our source for the products closer to Europe v.Changing to a faster mode of transportation

17 Question 4 B. Under a periodic review regime, which of the following strategies will help reduce cycle inventories (on-hand inventory excluding safety stock)? i.Increasing frequency ii.Improving forecast accuracy iii.Reducing the safety lead-time iv.Moving our source for the products closer to Europe v.Changing to a faster mode of transportation Only the first of these is direct. The rest are secondary effects achieved through improved forecast accuracy. We might argue that these only affected safety stock

18 Question 4 C. Under a periodic review regime, which of the following strategies will allow us to reduce safety stock without compromising product availability? i.Increasing frequency ii.Improving forecast accuracy iii.Reducing the safety lead-time iv.Moving our source for the products closer to Europe v.Changing to a faster mode of transportation We strongly suspect increasing frequency will reduce safety stock, but it is not always evident because we face the reduced risks more often.