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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**Relevant Costs**• Holding Costs - Costs proportional to the quantity of inventory held.**Relevant Costs (continued)**• Ordering Cost (or Production Cost). Can include both fixed and variable components. slope = c K**Relevant Costs (continued)**• Penalty or Shortage Costs. All costs that accrue when insufficient stock is available to meet demand.**Simple EOQ Model**• Assumptions: 1. Demand is fixed at l 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 unittime.**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?**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.**All-unit Discount**• Compute EOQs for all discounts • Find realizable EOQ values • Compare cost of realizable EOQ with cost at breakpoints**Incremental Discount**• Cost structure:**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**Average Annual Cost Function for Incremental Discount**Schedule**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%**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 EOQ’s.