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
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.