Lecture Principle of inventory and material management - Lecture 24

Lecture 24 - Order Quantities (Continued). The contents of this chapter include all of the following: Probabilistic models and safety stock, probabilistic demand, other probabilistic models, fixed period system, EOQ consequences, period order quantity model.

Lecture 24 Order Quantities (Continued) 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 • • • • • • Probabilistic Models and Safety Stock Probabilistic Demand Other probabilistic models Fixed period system EOQ consequences Period order quantity model Probabilistic Models and Safety Stock Used when demand is not constant or certain ỵ Use safety stock to achieve a desired service level and avoid stockouts ỵ ROP=dxL+ss Annual stockout costs = the sum of the units short x the probability x the stockout  cost/unit  x the number of orders per year Safety Stock Example ROP = 50 units Orders per year = Stockout cost = $40 per frame Carrying cost = $5 per frame per year Number of Units ROP  30 40 50 60 70 Probability 2 1.0 Safety Stock Example ROP = 50 units Orders per year = Stockout cost = $40 per frame Carrying cost = $5 per frame per year Safety Stock Additional Holding Cost 20 (20)($5) = $100 10 (10)($5) = $ 50 (10)(.1)($40)(6) $ Total Cost Stockout Cost $0 $100 = $240 $290 (10)(.2)($40)(6) + (20)(.1)($40)(6) = $960 $960 A safety stock of 20 frames gives the lowest total cost ROP = 50 + 20 = 70 frames Probabilistic Demand Inventory level Minimum demand during lead time Maximum demand during lead time Mean demand during lead time ROP = 350 + safety stock of 16.5 = 366.5 ROP  Normal distribution probability of demand during lead time Expected demand during lead time (350 kits) Safety stock Lead time Place order Receive order 16.5 units Time 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 Probabilistic Demand Use prescribed service levels to set safety stock  when the cost of stockouts cannot be determined ROP = demand during lead time + ZσdLT where Z = number of standard deviations σdLT = standard deviation of demand during lead time Probabilistic Example Average demand = µ = 350 kits Standard deviation of demand during lead time = σdLT = 10 kits 5% stockout policy (service level = 95%) Using Appendix I, for an area under the curve of 95%, the Z = 1.65 Safety stock = ZσdLT = 1.65(10) = 16.5 kits Reorder point = expected demand during lead time + safety stock = 350 kits + 16.5 kits of safety stock = 366.5 or 367 kits Other Probabilistic Models When data on demand during lead time is not  available, there are other models available When demand is variable and lead time is constant When lead time is variable and demand is constant When both demand and lead time are variable 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 þ Items are independent from one another þ Fixed­Period (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 þ Appropriate in routine situations þ May result in stockouts between periods ỵ May require increased safety stock ỵ EOQAssumptions • • • • Demand is relatively constant and is known The item is produced or purchased in lots or batches  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 24 ... 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... * =  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