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ISEN 315 Spring 2011 Dr. Gary Gaukler

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Inventory Control Deterministic inventory control Stochastic inventory control MRP / Lot sizing / JIT Supply chain management

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Reasons for Holding Inventories

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Relevant Costs Holding Costs - Costs proportional to the quantity of inventory held.

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Relevant Costs (continued) Ordering Cost (or Production Cost). Can include both fixed and variable components. slope = c K

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Relevant Costs (continued) Penalty or Shortage Costs. All costs that accrue when insufficient stock is available to meet demand.

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Simple EOQ Model Assumptions: 1. Demand is fixed at units per unit time. 2. Shortages are not allowed. 3. Orders are received instantaneously. 4. Order quantity is fixed at Q per cycle. 5. Cost structure: a) Fixed and marginal order costs (K + cx) b) Holding cost at h per unit held per unit time.

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Inventory Levels for the EOQ Model

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Cost Equation for the EOQ Model

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The Average Annual Cost Function G(Q)

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Properties of the EOQ Solution

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Example Desk production rate = 200 per month Each desk needs 40 screws Screws cost $0.03 Fixed delivery charges are $100 per order 25% interest rate for holding cost What is the optimal order size?

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Example

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EOQ Cost Function

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Quantity Discount Models All Units Discounts: the discount is applied to ALL of the units in the order. Incremental Discounts: the discount is applied only to the number of units above the breakpoint.

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All-Units Discount Order Cost Function

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Incremental Discount Order Cost Function

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All-unit Discount Compute EOQs for all discounts Find realizable EOQ values Compare cost of realizable EOQ with cost at breakpoints

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All-Units Discount Average Annual Cost

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All-unit Discount Optimality

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Incremental Discount Cost structure:

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Incremental Discount Establish C(Q) curve Determine cost per unit C(Q)/Q Substitute C(Q)/Q into G(Q) Compute G(Q) for each range Pick feasible solution with lowest cost

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Average Annual Cost Function for Incremental Discount Schedule

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Incremental Discount Example Demand 600 bags / year Setup cost for ordering: $8 Unit cost –Up to 500: $0.30 –Up to 1000: first 500 at $0.30, remaining at $0.29 –Over 1000: first 500 at $0.30, next 500 at $0.29, remaining at $0.28 Holding cost: 20%

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Incremental Discount Example

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Properties of the Optimal Solutions For all units discounts, the optimal will occur at the bottom of one of the cost curves or at a breakpoint. One compares the cost at the largest realizable EOQ and all of the breakpoints succeeding it. For incremental discounts, the optimal will always occur at a realizable EOQ value. Compare costs at all realizable EOQs.

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