CHAPTER 11 INVENTORY THEORY

Basic Functions Revenue Costs To protect the production process from changes in the environment RM Stock FG Stock Sales of FG Manufacturing RM Arrivals WIP Revenue Costs

Why is it Important? Pervades the business world Necessary for any company dealing with physical products Manufacturing Wholesalers Retailers Total value (in US) is more than $1000,000,000,000 25% associates with storing cost Hence, reducing a little bit, can enhance company’s competitiveness

Basic Questions in Inventory Control How much should we stock? Two extreme answers to this question: A lot This ensures that we never run out An easy way of managing Stock Expensive in inventory costs, cheap in management costs None/very Little Known as JIT A difficult way of managing stock Cheap in inventory costs, expensive in management costs When should we order?

Types of Inventory Policies Depends on demand and lead time the number of units that will need to be withdrawn from inventory Deterministic Models Stochastic Models

Types of Inventory Costs Purchasing Costs Holding costs Ordering costs Stock out costs Not considered here Annual Inventory Cost=Purchasing Costs+Holding Costs+Ordering Costs

Holding Costs Storage Costs Labor Overheads (Heating, Lighting, Security) Money Tied up (Loss of Interest, Opportunity Cost) Obsolescence Costs Stock Deterioration (Lose Money If Product Deteriorates) Theft/insurance

Ordering Costs Clerical/labor Costs of Processing Orders Inspection and Return of Poor Quality Products Transport Costs Handling Costs

Deterministic Assumptions Demand is known and constant Lead time is known and constant Order quantity does not depend on price Order quantity arrives all at once when needed Planned shortages are not allowed

Basic Model Q Inventory level time

Inventory Control Notation A=ordering cost c=unit purchasing cost H=IC=holding cost per unit per unit of time Q=ordering quantity A=annual demand T=cycle time

Annual Holding Cost H(Q/2) Annual holding cost = (holding cost per unit)(Average inventory H(Q/2) where Q/2 is the average (constant) inventory level Annual Holding Cost Holding Cost Curve Order Quantity

Annual Order Cost Annual order cost = A(D/Q) where (D/Q) is the number of orders per year Total Annual Ordering Cost Annual Order Cost Order Quantity

Total Annual Cost Curve Annual holding cost Annual ordering cost Q

Optimal Policy TC = IC(Q/2) + A(D/Q) The function that we want to minimize by choosing an appropriate value of Q Differentiating total cost with respect to Q and equating to zero :Q* = (2DA/IC)1/2 Total annual cost associated with the EOQ (2DAIC) 1/2