ops mgt 18_Inventory Management_w-o-solutions-1

# Tc d c in order now to find the optimal quantity we

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So what is the total cost? TC = D C + + In order now to find the optimal quantity we need to optimize the total cost with respect to the decision variable (the variable we control) Which one is the decision variable? D Q S Q 2 H

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What is the main insight from EOQ? There is a tradeoff between holding costs and ordering costs Order Quantity (Q*) Cost Total cost Holding costs Ordering costs
Economic Order Quantity - EOQ Q* = 2SD H Example: Assume a car dealer that faces demand for 5,000 cars per year, and that it costs \$15,000 to have the cars shipped to the dealership. Holding cost is estimated at \$500 per car per year. How many times should the dealer order, and what should be the order size?

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Receive order Time Inventory Order Quantity Q Place order Lead Time If delivery is not instantaneous, but there is a lead time L:
ROP = LxD Receive order Time Inventory Order Quantity Q Place order Lead Time Reorder Point (ROP) If demand is known exactly, place an order when inventory equals demand during lead time. D: demand per period L: Lead time in periods Q: When shall we order? A: When inventory = ROP Q: How much shall we order? A: Q = EOQ

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Example (continued)… What if the lead time to receive cars is 10 days? (when should you place your order?) Since D is given in years, first convert: 10 days = 10/365yrs
Time Time Inventory Inventory Level Level Order Order Quantity Quantity But demand is rarely predictable! Demand??? Receive order Place order Lead Time ROP = ???

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X Inventory at time of receipt Receive Receive order Time Time Inventory Inventory Level Level Order Order Quantity Quantity Place order order Lead Time Lead Time Actual Demand < Expected Demand ROP Lead Time Demand
Stockout Point Unfilled demand Receiv e Receiv e ord er Ti me Inventory Ord er Ord er Quanti ty Quanti ty Pla ce Pla ce ord er ord er Lead Time Lead Time If Actual Demand > Expected, we Stock Out

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ROP = Expected Demand Average Time Inventory Level Level Order Order Quantity If ROP = expected demand, service level is 50%. Inventory left 50% of the time, stock outs 50% of the time.
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