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SCM Test 1 Outline - Inventory Management Why keep...

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Inventory Management Why keep inventory? Fluctuations in demand: Seasonal, economic,variability Lead times and uncertainty in lead times. Supply chain disruptions Economies of scale Opportunity cost of losing sales Inventory comes in three forms: Finished product Unfinished product (work in progress) Raw materials (Just in time) Characteristics of the supply chain: Customer demand, lead time, capacity, throughput, product portfolio, holding costs, service level requirements, depreciation, transportation costs, costs. Single Echelon Inventory Theory Single Period Models (Newsvendor problem) Assumes there is only one period Overage (C o ) for ordering too much Underage (C u ) for ordering too little. Probability density function of demand is known. F(Q)= C u /C o +C u This is the Critical Ratio D min + (D max - D min ) * Critical Ratio = optimal inventory level Overly simplistic because only one ordering period Fixed Cost We are given several demand scenarios with probability of occurring. 1. Pick an order quantity, Q 2. For each order quantity, calculate expected profit (loss) based on demand scenarios 3. Pick order quantity that results in the highest expected profit If overage>underage, order less than mean demand If overage<underage, order more than mean demand Multi Period Models Economic Lot Size Model (EOQ model) Assumptions: Supplier has infinite capacity. Demand is constant at a rate of D items per unit of time Quantities are fixed at Q items per order. Cost: Ordering cost – K , units Inventory holding – h Lead time is zero Initial inventory is zero
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Planning horizon is infinite Average inventory: (Q/2) Average holding cost: h(Q/2) Ordering cost: D/Q*K (D=total demand) During a cycle of T, average cost is: K+ h Q/2 Order quantity that minimizes the average cost is: Q*=sqrt(2KD/ h ) TC=(Dk/Q)+( h Q/2) If we derivate from Q*, and order b Q*, cost will derivate by how much we derivate Q* by. ( b -1) 2 /2 b If we order 10% too much, then change in cost is . 45% EOQ in the presence of quantity discounts Think of h as a function of production cost: h = i C. So, total cost is (DK/Q)+( i C j Q/2)+DC j where DC j is the purchasing cost. Holding cost is i C j Q/2 Assume pricing schedule has specified break points (q0, q1…qr) so that order placed Q is greater than q j , but less than q j-1 , the cost is C j . Biggest drawback of EOQ: Demand is deterministic Continuous Review Policy Assumptions: Demand is normally distributed. (Mean:AVG, Standard Deviation:STD) Fixed(K) and proportional ordering cost Inventory holding cost per item unit of time ( h ) Replenishments from supplier take L periods Demand is lost when not immediately satisfied Require a probability of α for not stocking out during a lead time.
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