EOQ History –Interest on capital tied up in wages, material and overhead sets a maximum limit to the quantity of parts which can be profitably manufactured.

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Presentation transcript:

EOQ History –Interest on capital tied up in wages, material and overhead sets a maximum limit to the quantity of parts which can be profitably manufactured at one time; “set-up” costs on the job fix the minimum. Experience has shown one manager a way to determine the economical size of lots. –Early application of mathematical modeling to Scientific Management –Introduced in 1913 by Ford W. Harris, “How Many Parts to Make at Once”

MedEquip Example Small manufacturer of medical diagnostic equipment. Purchases standard steel “racks” into which components are mounted. Metal working shop can produce (and sell) racks more cheaply if they are produced in batches due to wasted time setting up shop. MedEquip doesn’t want to tie up too much precious capital in inventory. Question: how many racks should MedEquip order at once?

EOQ Modeling Assumptions 1. Production is instantaneous – there is no capacity constraint and the entire lot is produced simultaneously. 2. Delivery is immediate – there is no time lag between production and availability to satisfy demand. 3. Demand is deterministic – there is no uncertainty about the quantity or timing of demand. 4. Demand is constant over time – in fact, it can be represented as a straight line, so that if annual demand is 365 units this translates into a daily demand of one unit. 5. A production run incurs a fixed setup cost – regardless of the size of the lot or the status of the factory, the setup cost is constant. 6. Products can be analyzed singly – either there is only a single product or conditions exist that ensure separability of products.

Notation D demand rate (units per year) c unit production cost, not counting setup or inventory costs (dollars per unit) A fixed or setup cost to place an order (dollars) hholding cost (dollars per year); if the holding cost is consists entirely of interest on money tied up in inventory, then h = ic where i is an annual interest rate. Qthe unknown size of the order or lot size decision variable

Inventory vs Time in EOQ Model Q/D2Q/D3Q/D4Q/D Q Inventory Time

MedEquip Example Costs D = 1000 racks per year c = $250 A = $500 (estimated from supplier’s pricing) h = (0.1)($250) + 10 = $35 per unit per year