Slide 1 Matching Supply with Demand: An Introduction to Operations Management Gérard Cachon ChristianTerwiesch All slides in this file are copyrighted by Gerard Cachon and Christian Terwiesch. Any instructor that adopts Matching Supply with Demand: An Introduction to Operations Management as a required text for their course is free to use and modify these slides as desired. All others must obtain explicit written permission from the authors to use these slides.
Slide 2 Medtronic’s InSync pacemaker supply chain and objectives Supply chain: One distribution center (DC) in Mounds View, MN. About 500 sales territories throughout the country. Consider Susan Magnotto’s territory in Madison, Wisconsin. Objective: Because the gross margins are high, develop a system to minimize inventory investment while maintaining a very high service target, e.g., a 99.9% in-stock probability or a 99.9% fill rate.
Slide 3 InSync demand and inventory at the DC Average monthly demand = 349 units Standard deviation of monthly demand = Average weekly demand = 349/4.33 = 80.6 Standard deviation of weekly demand = (The evaluations for weekly demand assume 4.33 weeks per month and demand is independent across weeks.) Monthly implants (columns) and end of month inventory (line)
Slide 4 InSync demand and inventory in Susan’s territory Total annual demand = 75 units Average daily demand = 0.29 units (75/260), assuming 5 days per week. Poisson demand distribution works better for slow moving items Monthly implants (columns) and end of month inventory (line)
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Slide 7 Order up-to level, S, and, if Normal demand, z = (S – ) / Exp. demand in one period Distribution function table Loss function table Expected backorder In-stock probability Stockout probability Fill rate Expected inventory Pipeline inventory If Normal demand, Lead time, l Demand over lead time + 1,
Slide 8 The optimal in-stock probability is usually quite high Suppose the annual holding cost is 35%, the backorder penalty cost equals the gross margin and inventory is reviewed daily.
Slide 9 Example with mean demand per week = 100 and standard deviation of weekly demand = 75. Inventory over time follows a “saw-tooth” pattern. Period lengths of 1, 2, 4 and 8 weeks result in average inventory of 597, 677, 832 and 1130 respectively:
Slide 10 Tradeoff between inventory holding costs and ordering costs Costs: Ordering costs = $275 per order Holding costs = 25% per year Unit cost = $50 Holding cost per unit per year = 25% x $50 = 12.5 Period length of 4 weeks minimizes costs: This implies the average order quantity is 4 x 100 = 400 units EOQ model: Ordering costs Inventory holding costs Total costs
Slide 11 Better service requires more inventory at an increasing rate More inventory is needed as demand uncertainty increases for any fixed fill rate. The required inventory is more sensitive to the fil rate level as demand uncertainty increases The tradeoff between inventory and fill rate with Normally distributed demand and a mean of 100 over (l+1) periods. The curves differ in the standard deviation of demand over (l+1) periods: 60,50,40,30,20,10 from top to bottom.
Slide 12 Shorten lead times and you will reduce inventory Reducing the lead time reduces expected inventory, especially as the target fill rate increases The impact of lead time on expected inventory for four fill rate targets, 99.9%, 99.5%, 99.0% and 98%, top curve to bottom curve respectively. Demand in one period is Normally distributed with mean 100 and standard deviation 60.
Slide 13 Do not forget about pipeline inventory Reducing the lead time reduces expected inventory and pipeline inventory The impact on pipeline inventory can be even more dramatic that the impact on expected inventory Expected inventory (diamonds) and total inventory (squares), which is expected inventory plus pipeline inventory, with a 99.9% fill rate requirement and demand in one period is Normally distributed with mean 100 and standard deviation 60
Slide 14 Annual inventory turns for Wal-Mart. (Source: 10-K filings)