Ch10 Inventory Models - Lecture Notes Chapter 10 Inventory...

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Lecture Notes Chapter 10 Inventory Models: Deterministic Demand 10.1 Economic Order Quantity (EOQ) Model 10.2 Economic Production Lot Size Model 10.3 Inventory Model with Planned Shortages 10.4 Quantity Discounts for the EOQ Model Inventory Models The study of inventory models is concerned with two basic questions: How much should be ordered each time? When should the reordering occur? The objective is to minimize total variable cost over a specified time period (assumed to be annual in the following review). Inventory Costs Ordering cost – salaries and expenses of processing an order, regardless of the order quantity Holding cost – usually a percentage of the value of the item assessed for keeping an item in inventory (including finance costs, insurance, security costs, taxes, warehouse overhead, and other related variable expenses) Backorder cost – costs associated with being out of stock when an item is demanded (including lost goodwill) Purchase cost – the actual price of the items Other costs Deterministic Models The simplest inventory models assume demand and the other parameters of the prob- lem to be deterministic and constant. The deterministic models covered in this chapter are: Economic order quantity (EOQ) Economic production lot size EOQ with planned shortages EOQ with quantity discounts 1
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10.1 Economic Order Quantity (EOQ) The most basic of the deterministic inventory models is the economic order quantity (EOQ) . The variable costs in this model are annual holding cost and annual ordering cost. For the EOQ, annual holding and ordering costs are equal. Assumptions: Demand is constant throughout the year at D items per year. Ordering cost is $ C o per order. Holding cost is $ C h per item in inventory per year. Purchase cost per unit is constant (no quantity discount). Delivery time (lead time) is constant. Planned shortages are not permitted. General description: 2
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Formulas: Optimal order quantity: Q * = q 2 DC o /C h Number of orders per year: D/Q * Time between orders (cycle time): Q * /D years Total annual cost: [ 1 2 Q * C h ] + [ DC o /Q * ] (holding + ordering) Example (Bart’s Barometer Business). Bart’s Barometer Business is a retail outlet that deals exclusively with weather equipment. Bart is trying to decide on an inventory and reorder policy for home barometers. Barometers cost Bart $50 each and demand is about 500 per year distributed fairly evenly throughout the year. Reordering costs are $80 per order and holding costs are figured at 20% of the cost of the item. BBB is open 300 days a year (6 days a week and closed two weeks in August). Lead time is 60 working days. This is an Economic Order Quantity model. Total Variable Cost = Minimize Total Variable Cost: Optimal Reorder Quantity = Optimal Reorder Point: Number of Orders Per Year Total Annual Variable Cost 3
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10.2 Economic Production Lot Size The economic production lot size model is a variation of the basic EOQ model.
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