An industrial company is seeking your help to improve their distribution system. The distribution network consists of: four manufacturing facilities in U.S., Canada, and Mexico, seven major distribution centers (DCs) in New York, San Francisco, Los Angeles, Atlanta, Chicago, Dallas and Washington D.C., as well as 13 smaller regional DCs in cities such as Salt Lake City, Minneapolis, St. Louis, Houston, etc. Note that each major DC supports the distribution of products in its local area as well as one or more regional DCs (except for Washington, D.C. distribution center which does not support any regional DCs). Thus, the major DCs are referred to as "parents" while the regional DCs are referred to as "children".

The company's objective is to have the right amount of inventory at the right locations and at the right times. While shortages will result in poor customer service, holding too much inventory will result in high inventory carrying costs. Determining the appropriate safety stock levels at each of the 20 major and regional DCs is the key to achieving the company's objective. The company desires to have 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 L ^0.7

This model compensates for the variation in the lead times 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.

This company would like you to help them set appropriate safety stock levels at each of their 20 DCs to improve their 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 average transportation lead times (i.e., procurement lead times are fixed while the transportation lead times are variable). Note that the specified lead times (in 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 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 (a) and (b) and explain the reasons for the poor performance of the Sharp Consulting Associates Model.
4. How could the company further reduce its inventory carrying costs? Please provide a few specific areas for improvement

Table 1: Relevant data for a typical product (the major DCs or "parents" are shaded; the regional DCs or "children" listed under each are supported by that major DC):

	Average Daily Demand (Units)	Standard Deviation of Daily Demand	Average Lead Time (Days)	Standard Deviation of Lead Time
San Francisco	101.83	38.34	5.9	0.46
Salt Lake City	13.12	6.68	6.1	3.20
Seattle	35.27	16.40	6.3	2.40
Washington, DC	63.28	29.08	5.7	1.14
New York	251.10	87.76	7	2.50
Puerto Rico	15.72	8.25	7.5	2.60
Chicago	204.26	76.18	5.4	0.84
St Louis	15.41	10.91	4.3	1.60
Indianapolis	81.02	34.16	4.3	1.90
Minneapolis	18.67	9.38	4.9	2.30
Detroit	25.88	13.90	5.9	1.70
Atlanta	245.33	121.19	5.2	0.95
Tampa	64.16	30.80	5.1	1.60
Dallas	289.04	185.11	3.9	0.17
Denver	27.78	15.13	6.1	1.80
Kansas City	27.44	14.50	5.2	2.70
Houston	28.20	16.25	4.8	4.60
Los Angeles	165.48	56.00	5.7	1.10
Phoenix	19.27	9.95	7.1	3.90
Hawaii	13.77	6.93	10.5	2.10