# Handout3 3 .docx - Handout 3: Inventory Control Inventory...

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Handout3: Inventory ControlInventory level is controlled through ordering policy. The ordering policy needs to beoptimized by minimizing costs while fulfilling demands. Each inventory control model has someassumptions and it is important to validate these assumptions when applying a model to a real-lifesystem.1. Economic Order Quantity (EOQ) ModelAssumptions:Production (purchase) is instantaneous.Demand is deterministic and constant over time.A production (purchase) run incurs a fixed setup cost. Regardless of the size of the lot or thestatus of the factory, the setup cost is the same.Backorders are not allowed.Notations:D = demand rate (in units per year)c = unit production (purchase) cost, not counting setup or inventory costs (in dollars perunit)A = fixed setup cost to produce (purchase) a loth = inventory holding cost (in dollars per unit per year); if the holding cost consists entirely ofinterest on money tied up in inventory, then h=ic, where i is the annual interest rateQ = lot size (in units); this is the decision variableInventory behavior of EOQ model in an optimal ordering policy:Total cost per year, which we denote by Y(Q), can be expressed as1
The lot size that minimizes annual cost isThis square root formula is the well-known economic order quantity (EOQ), also referred toas the economic lot size. And, optimal order interval isExample) Consider a shop that produces metal racks. The demand for metal racks is fairly steadyand predictable at D=1,000 units per year. The unit cost of the racks is c=\$250, but themetalworking shop also charges a fixed cost of A=\$500 per order, to cover the cost of shutting downthe shop to set up. The shop estimates its opportunity cost for money at 10 percent per year. It alsoestimates that the floor space required to store a rack costs roughly \$10 per year in annualized costs.2
2. Economic Production Lot (EPL) ModelOne extension of EOQ model is to the case in which replenishment is not instantaneous;instead, there is a finite, but constant and deterministic, production rate. This model is sometimescalled the economic production lot (EPL) model. If we let P represent the production rate (andassume that P > D so that the system has capacity to keep up with demand), then the EPL modelresults in the following lot size to minimize the sum of setup and holding costs:Note that if P=∞, then, this formula reduces to the regular EOQ. Otherwise, it results in alarger lot size to cover for the fact that replenishment items take time to produce. Other variants ofthe basic EOQ include backorders (i.e., orders that are not filled immediately, but have to wait until

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Term
Spring
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Staff