Jeniel Z. Pascual Chapter 6: Inventory Control Models (Part 2) 1 Time between placing an order and its receipt is called lead time (L) Reorder Point Graphs 400 3 days 400 12 days • When the EOQ assumptions are met, it is possible to schedule orders to arrive so that stockouts are completely avoided! • If the demand or the lead time is uncertain, the exact demand during the lead time (ROP in the EOQ situation) will not be known with certainty! • Therefore, to prevent stockouts, it is necessary to carry additional inventory called safety stock. 2 Use of Safety Stock (1 of 4) • If demand or the lead time are uncertain, the exact ROP will not be known with certainty! • To prevent stockouts, it is necessary to carry additional inventory called safety stock. • Can be implemented by adjusting the Reorder Point (ROP) ROP = (Average demand during lead time) + Safety stock ROP = (Average demand during lead time) + SS where SS = safety stock 3 Use of Safety Stock (2 of 4) • When demand is unusually high during the lead time, you dip into the safety stock instead of encountering a stockout! • The main safety stock stockouts demand is expected. purpose of is to avoid when the higher than 4 Use of Safety Stock (3 of 4) • Objective is to choose a safety stock amount the minimises total holding and stockout costs • If variation in demand and holding and stockout costs are known, payoff/cost tables could be used to determine safety stock • More general approach is to choose a desired service level based on satisfying customer demand 5 Use of Safety Stock (4 of 4) • Set safety stock to achieve a desired service level Service level = 1 − Probability of a stockout or Probability of a stockout = 1 − Service level 6 Safety Stock with the Normal Distribution ROP = (Average demand during lead time) + ZσdLT where Z = number of standard deviations for a given service level σdLT = standard deviation of demand during the lead time Thus Safety stock = ZσdLT 7 Sample Problem The Hinsdale Company carries a variety of electronic inventory items, and these are typically identified by SKU. One particular item, SKU A3378, has a demand that is normally distributed during the lead time, with a mean of 350 units and a standard deviation of 10. Hinsdale wants to follow a policy that results in stockouts occurring only 5% of the time on any order. How much safety stock should be maintained and what is the reorder point? 8 Hinsdale Company --- Safety Stock and the Normal Distribution • Item A3378 has normally distributed demand during lead time Mean = 350 units, standard deviation = 10 • Stockouts should occur only 5% of the time μ = Mean demand = 350 σdLT = Standard deviation = 10 X= Mean demand + Safety stock SS= Safety stock = X − μ = Zσ Z X 9 Finding Z: 10 Hinsdale Company From Appendix A we find Z = 1.65 X SS ROP = (Average demand during lead time) + ZdLT = 350 + 1.65(10) = 350 + 16.5 = 366.5 units (or about 367 units) 11 Service Levels, Safety Stock, and Holding Costs • As service levels increase o Safety stock increases at an increasing rate • As safety stock increases o Annual holding costs increase 12 Hinsdale Company Safety Stock for SKU A3378 at Different Service Levels: 13 Calculating Annual Holding Cost with Safety Stock Under standard assumptions of EOQ o Average inventory = Q÷2 o Annual holding cost = (Q÷2)Ch With safety stock where THC = total annual holding cost Q Ch = order quantity = holding cost per unit per year SS = safety stock 14 Hinsdale Company Service Level Versus Annual Holding Costs: 15 Single-Period Inventory Models (News Vendor Problem) Marginal Analysis Marginal profit (MP) is the additional profit achieved if one additional unit is stocked and sold. Marginal loss (ML) is the loss that occurs when an additional unit is stocked but cannot be sold. 16 Single-Period Inventory Models (News Vendor Problem) Marginal Analysis with Discrete Distribution P = probability that demand will be greater than or equal to a given supply (or the probability of selling at least one additional unit) 1 - P = probability that demand will be less than supply (or the probability that one additional unit will not sell) 17 Steps of Marginal Analysis with Discrete Distributions 18 Sample Problem Café du Donut is a popular New Orleans dining spot on the edge of the French Quarter. Its specialty is coffee and doughnuts; it buys the doughnuts fresh daily from a large industrial bakery. The café pays $4 for each carton (containing two dozen doughnuts) delivered each morning. Any cartons not sold at the end of the day are thrown away, for they would not be fresh enough to meet the café’s standards. If a carton of doughnuts is sold, the total revenue is $6. Hence, MP = Marginal profit = $6 - $4 = $2 ML = Marginal loss = $4 19 Café du Donut Example Probability Distribution for Café du Donut 20 Café du Donut Example 21 Café du Donut Example 22 A prudent manager should spend more time managing those items representing the greatest dollar inventory cost because this is where the greatest potential savings are. ABC Analysis (1 of 5) • The purpose is to divide the inventory into three groups (A, B, and C) based on the overall inventory value of the items • Group A items account for the major portion of inventory costs (high price!) o Typically 70% of the dollar value but only 10% of the quantity of items o Great care should be taken in forecasting the demand and developing good inventory management policies for this group! o Mistakes can be expensive! 23 ABC Analysis (2 of 5) • Group B items are more moderately priced o Items represent about 20% of the company’s business in dollars, and about 20% of the items in inventory o Not appropriate to spend as much time developing optimal inventory policies for this group as with the A group since inventory costs are much lower! o Moderate levels of control! 24 ABC Analysis (3 of 5) • Group C items are very low cost but high volume o These items may constitute only 10% of the company’s business in dollars, but they may consist of 70% of the items in inventory. o It is not cost effective to spend a lot of time managing these items! o For the group C items, the company should develop a very simple inventory policy, and this may include a relatively large safety stock. o Since the items cost very little, the holding cost associated with a large safety stock will also be very low. 25 ABC Analysis (4 of 5) • More care should be taken in determining the safety stock with the higher priced group B items. • For the very expensive group A items, the cost of carrying the inventory is so high, it is beneficial to carefully analyse the demand for these so that safety stock is at an appropriate level! • Otherwise, the company may have exceedingly high holding costs for the group A items. 26 ABC Analysis (5 of 5) Summary of ABC Analysis: 27 Material Requirements Planning Dependent Demand Material Structure Tree The Bill of Materials (BOM) identifies the components, their descriptions, and the number required in the production of one unit of the final product. From the BOM, we develop a material structure tree. 28 Material Requirements Planning 29 Material Requirements Planning Gross Materials Requirements Plan 30 MRP Net Materials Requirements Plan 31 Material Requirements Planning Two or More End Products 32 MRP Two or More End Products 33 Just-In-Time Inventory Control With this approach, inventory arrives just in time to be used during the manufacturing process to produce subparts, assemblies, or finished goods. 34 Enterprise Resource Planning A computerized information system that integrates and coordinates the operations of a firm. The benefits of a well-developed ERP system are reduced transaction costs and increased speed and accuracy of information. However, there are drawbacks as well. The software is expensive to buy and costly to customize. 35 Thank You! 36