Lecture 26 - Order Quantities (Revisited). The contents of this chapter include all of the following: Objectives of inventory management, lot size decision, inventory models, EOQ, robust model, reorder point, production order quantity model, quantity discount model, probabilistic models and safety stock, probabilistic demand, other probabilistic models, fixed period system, EOQ consequences, period order quantity model.
Lecture 26 Order Quantities (Revisited) Books • Introduction to Materials Management, Sixth Edition, J. R. Tony Arnold, P.E., CFPIM, CIRM, Fleming College, Emeritus, Stephen N. Chapman, Ph.D., CFPIM, North Carolina State University, Lloyd M. Clive, P.E., CFPIM, Fleming College • Operations Management for Competitive Advantage, 11th Edition, by Chase, Jacobs, and Aquilano, 2005, N.Y.: McGrawHill/Irwin • Operations Management, 11/E, Jay Heizer, Texas Lutheran University, Barry Render, Graduate School of Business, Rollins College, Prentice Hall Objectives • • • • • • • • • • • • • • Objectives of inventory management Lot size decision Inventory models EOQ Robust model Reorder point Production order quantity model Quantity discount model Probabilistic Models and Safety Stock Probabilistic Demand Other probabilistic models Fixed period system EOQ consequences Period order quantity model Objectives of Inventory Management Determine: • How much should be ordered at one time? • When should an order be placed? LotSize Decision Rules Lotforlot. Order exactly what is needed Fixedorder quantity. Arbitrary Order “n” periods supply. Satisfy demand for a given period of demand Inventory Models for Independent Demand Need to determine when and how much to order Basic economic order quantity ỵ Production order quantity ỵ Quantity discount model ỵ Basic EOQ Model Important assumptions Demand is known, constant, and independent Lead time is known and constant Receipt of inventory is instantaneous and complete Quantity discounts are not possible Only variable costs are setup and holding Stockouts can be completely avoided Inventory Usage Over Time Usage rate Inventory level Order quantity = Q (maximum inventory level) Minimum inventory Time Average inventory on hand Q Minimizing Costs Objective is to minimize total costs Curve for total cost of holding and setup Annual cost Minimum total cost Holding cost curve Setup (or order) cost curve Optimal order quantity (Q*) Order quantity The EOQ ModelAnnual setup cost = Q Q* D S H = Number of pieces per order = Optimal number of pieces per order (EOQ) = Annual demand in units for the inventory item = Setup or ordering cost for each order = Holding or carrying cost per unit per year Annual setup cost = = = (Number of orders placed per year) x (Setup or order cost per order) Annual demand Number of units in each order D (S) Q Setup or order cost per order D S Q The EOQ ModelAnnual setup cost = Q Q* D S H D S Q Q Annual holding cost = H = Number of pieces per order = Optimal number of pieces per order (EOQ) = Annual demand in units for the inventory item = Setup or ordering cost for each order = Holding or carrying cost per unit per year Annual holding cost = (Average inventory level) x (Holding cost per unit per year) Order quantity = = Q (H) (Holding cost per unit per year) FixedPeriod (P) Systems Orders placed at the end of a fixed period ỵ Inventory counted only at end of period ỵ Order brings inventory up to target level ỵ Only relevant costs are ordering and holding ỵ Lead times are known and constant ỵ Items are independent from one another ỵ FixedưPeriod(P)Systems Target quantity (T) Q4 On-hand inventory Q2 Q1 Q3 P P Time P FixedPeriod (P) Example jackets are back ordered It is time to place an order No jackets are in stock Target value = 50 Order amount (Q) = Target (T) - On-hand inventory - Earlier orders not yet received + Back orders Q = 50 - - + = 53 jackets FixedPeriod Systems Inventory is only counted at each review period ỵ May be scheduled at convenient times ỵ Appropriate in routine situations ỵ May result in stockouts between periods ỵ May require increased safety stock ỵ EOQAssumptions ã ã ã ã Demandisrelativelyconstantandisknown Theitemisproducedorpurchasedinlotsorbatches and not continuously Order prep costs & inventorycarrying costs are constant and known Replacement occurs all at once EOQ Consequences Average inventory = EOQ lot size / 2 # of orders per year = Annual demand / lot size Basic EOQ Model • • • • Demand is constant over time Inventory drops at a uniform rate over time When the inventory reaches 0, the new order is placed and received, and the inventory level again jumps to Q units The optimal order quantity will occur at a point where the total setup cost is equal to the total holding cost Basic EOQ: 2AS 2ADS Q* = = ic i Basic EOQ Model (cont.) • Benefit of EOQ model: – • It is a robust model, meaning that it gives satisfactory answers even with substantial variation in the parameters Reorder Points: – – Lead Time the time between the placement and receipt of an order The whentoorder decision is expressed in terms of a reorder point, the inventory level at which an order should be placed Inventory Level Over Time (Basic EOQ Model) Inventory Level Maximum Inventory Level Average Inventory Level Time Production Order Quantity Model • Production Order Quantity Model is useful when: – – – Inventory continuously flows or builds up over a period of time after an order has been placed or when units are produced and sold simultaneously Takes into account the daily production (or inventory flow) rate and the daily demand rate All other EOQ assumptions are valid Production Order Quantity 2ADS Q * = i[1 (AD )] P Inventory Level Over Time (Production Model) Inventory Level Production Portion of Cycle Demand Portion of Cycle Maximum Inventory Level Demand Portion of Cycle Time Period Order Quantities • • • • Calculate or determine EOQ Determine avg. weekly usage Divide EOQ by avg. weekly usage to determine period Order the amount needed during the next period to satisfy demand during that period Practice Question 1. Sarah’s Silk Screening • Sarah’s Silk Screening sells souvenir shirts. Sarah is trying to decide how many to produce for the upcoming naming of the College of Management. The University will allow her to sell the shirts only on one day, the day that the school naming is announced. Sarah will sell the T shirts for $20 each. When the event day is over, she will be allowed to sell the remaining stock to the Bookstore for $4 each. It costs Sarah $8 to make the specialty shirt. She estimates mean demand to be 545, with a standard deviation is 115. How many shirts should she make? Practice Question 2. The Great Southern Automotive Co • • • • • • • • • The Great Southern Automotive Co. buys steering wheels from a supplier. One particular steering wheel has a known and constant demand rate of 2,000 units per year. The fixed cost of ordering is $100 and the inventory holding cost is $2 per unit per year. It takes 2 weeks for an order to arrive. Compute The optimal EOQ The reorder point The average inventory level The time between successive orders The total annual cost If demand was variable with a standard deviation of 4 units per week, and the firm aims for 98% customer satisfaction, what would the reorder point be? End of Lecture 26 ... Probabilistic Demand Risk of a stockout (5% of area of normal curve) Probability of no stockout 95% of the time Mean demand 350 ROP = ? kits Quantity Safety stock z Number of standard deviations... Other Probabilistic Models Both demand? ?and? ?lead time are variable ROP = (average daily demand x average lead time) + ZσdLT σd = standard deviation of demand per day σLT = standard deviation of lead time in days... Demand is known, constant, and independent Lead time is known and constant Receipt of inventory is instantaneous and complete Quantity discounts are not possible Only variable costs are setup and