Lecture10 (1) - ISyE 1101 Foundations of Industrial and...

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. . ISyE 1101: Foundations of Industrial and Systems Engineering Lecture 10: Inventory Models Prof. J. G. Carlsson Department of Industrial and Systems Engineering, University of Minnesota November 7, 2013 J. G. Carlsson, U of MN ISyE Lecture 10: Inventory Models November 7, 2013 1 / 55
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Administrivia PS7 due Friday before COB Forum? J. G. Carlsson, U of MN ISyE Lecture 10: Inventory Models November 7, 2013 1 / 55
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Today Inventory models: EOQ Model EOQ with shortages EOQ with lead times EOQ with quantity discounts Multi-item capacitated EOQ POQ Model Po2 Model Periodic review model J. G. Carlsson, U of MN ISyE Lecture 10: Inventory Models November 7, 2013 2 / 55
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Suggested reading Hillier & Lieberman, Chapter 18, “Inventory Theory” Muckstadt, J. A., and Sapra, Amar. Principles of Inventory Management: When You Are Down to Four, Order More . Springer, 2010. [available online at https://www.lib.umn.edu], Chapter 2, “EOQ Model” J. G. Carlsson, U of MN ISyE Lecture 10: Inventory Models November 7, 2013 3 / 55
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Introduction Inventory problems deal with stocking an item to meet fluctuations in demand Keeping too much of an item increases costs of capital and storage; stocking too little disrupts production and sales Our basic objective is to come up with an inventory policy that answers two questions: . 1 How much should we order? . 2 When should we order? J. G. Carlsson, U of MN ISyE Lecture 10: Inventory Models November 7, 2013 4 / 55
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Cost components The basic cost function is given by: Total inventory cost = Production cost + Setup cost + Holding cost + Shortage cost where the above components are defined as follows: Production cost is the price per unit of an inventory item, e.g. $ 500 / TV ; this may be discounted if we produce in bulk (also called purchasing cost ) Setup cost is a fixed charge incurred when an order is placed (also called transaction cost ) Holding cost represents the cost of maintaining inventory in stock Shortage cost is the penalty incurred when stock is out, including potential loss of income, disruption in production, and loss of customer loyalty J. G. Carlsson, U of MN ISyE Lecture 10: Inventory Models November 7, 2013 5 / 55
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The basic EOQ model The simplest inventory model involves constant-rate demand with instantaneous order replenishment (stuff that we order arrives right away) and no shortage (we’re not allowed to run out of stock): a = constant demand rate of the product K = setup cost for ordering one batch c = unit cost for producing or purchasing each unit h = holding cost per unit per unit of time in inventory The units are a : units hour K : $ c : $ unit h : $ unit · hour J. G. Carlsson, U of MN ISyE Lecture 10: Inventory Models November 7, 2013 6 / 55
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The basic EOQ model Let’s assume that we’re going to buy the same quantity of units, Q , at each order Since there are no shortages allowed, we’ll just buy Q units whenever we run out Since demand rate a is constant, if we order Q at time 0, it will take us Q / a hours to sell off all products: Inventory level Q - at Q / a 2 Q / a Time 3 Q / a Q 0 What should Q be?
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