An industrial company is seeking your help to improve their distribution system. The distribution network consists of four manufacturing facilities in the U.S., Canada, and Mexico; seven major distribution centers (DCs) in New York, San Francisco, Los Angeles, Atlanta, Chicago, Dallas, and Washington, D.C.; and 13 smaller regional DCs in cities such as Salt Lake City, Minneapolis, St. Louis, Houston, etc. Note that each major DC supports distribution of products in its local area as well as one or more regional DCs, except for the Washington, D.C. distribution center, which does not support any regional DCs. Thus, the major DCs are referred to as parents and the regional DCs are referred to as children. The companys objective is to have the right amount of inventory at the right locations at the right times. While shortages result in poor customer service, holding too much inventory results in high inventory carrying costs. Determining the appropriate safety stock levels at each of the 20 DCs is the key to achieving the companys objective. The company desires a 97% service level. Currently, the company utilizes the following model recommended by Sharp Consulting Associates (a management consulting firm) to set safety stock levels at all its 20 DCs. z x STD x L0.7 The model compensates for the variation in lead time by inflating the z-value to 2, as well as inflating all the lead times, L, by 2 days. Unfortunately, as a result of this approach the company is experiencing high inventory carrying cost as well as poor service levels in particular DCs. The company would like you to help them set appropriate safety stock levels at each of the 20 DCs to improve its performance. Table 1 provides some information regarding a typical product manufactured in Arkansas to give you an opportunity to perform an analysis. The average lead times are calculated by adding the fixed procurement lead times of 3 days to the average transportation lead times (i.e., procurement lead times are fixed while transportation lead times are variable). Note that the specified lead times (Table 1) for major DCs represent the procurement and transportation lead times from the Arkansas manufacturing facility to the major DCs, while the specified lead times for the regional DCs represent the procurement and transportation times from their parents.

1. Calculate the safety stock levels for each of the 20 DCs using the model recommended by Sharp Consulting Associates.

2. Calculate safety stock levels for each of the 20 DCs by utilizing an appropriate model that explicitly considers the variation in lead times.

3. Compare the results obtained in sections (1) and (2) and explain the reasons for the poor performance of the Sharp Consulting Associates model. Table 1

	Average Demand	Standard Deviation of Demand	Average Lead Time	Standard Deviation of Lead Time
San Francisco	151.73	70.93	6.10	0.40
Salt Lake City	8.79	3.34	6.50	3.50
Seattle	49.03	20.50	5.90	2.30
Washington DC	48.73	36.06	5.75	1.10
New York	384.18	150.07	7.20	2.40
Puerto Rico	23.11	11.22	7.25	2.70
Chicago	351.33	88.37	5.25	1.00
St Louis	29.59	11.56	7.23	4.70
Indianapolis	155.56	47.14	4.25	1.75
Minneapolis	33.42	12.66	5.10	2.00
Detroit	18.37	21.68	5.70	1.95
Atlanta	191.36	73.93	5.00	0.70
Tampa	58.39	46.20	5.60	1.20
Dallas	517.38	340.60	3.65	0.25
Denver	30.28	19.52	8.05	6.75
Kansas City	35.67	8.85	4.90	2.50
Houston	22.28	24.38	4.90	4.90
Los Angeles	228.36	95.20	5.75	1.50
Phoenix	20.04	17.51	6.90	3.60
Hawaii	10.60	3.81	10.15	2.30