Operations Management
Operations Management Session 24: Inventory Systems Previous Lectures EOQ Model Known demand, multi-periods Newsvendor Model Uncertain demand, but only 1 period The tension between setup cost and inventory holding cost is not relevant. How do we handle uncertain demand and multiple periods? Session 24 Operations Management 2 Today’s Lecture Inventory systems Inventory turns/turnover Briefing on the simulation game Session 24 Operations Management 3 Inventory Level in Real Life Inventory on Hand Order quantity, Q Q Reorder point d1 Amount used during first lead time Safety stock, SS First lead time, LT1 LT2 Time Order 2 placed Order 1 placed Shipment 1 received Session 24 Order 3 placed Operations Management Shipment 2 received 4 Inventory Systems Continuous (perpetual) system: System that keeps track of removals from inventory continuously, thus monitoring current levels of each item. Fixed quantity is ordered when a certain level is reached. Good: (1) Keeps constant count of inventory and (2) fixed order quantity. Bad: (1) Higher record keeping cost; (2) Periodic inventory counting is still require; (3) Time of delivery is random. Session 24 Operations Management 5 Continuous System with Positive Lead-time (ROP,Q) policy Order when the inventory reaches the ROP The order size is always Q What is the optimal Q? How do we decide when to order? Should the reorder point be greater than dL? Session 24 Operations Management 6 Safety Stock Safety Stock: Stock that is held in excess of expected demand due to variable demand rate and/or lead time. An expense of doing business. Necessary to ensure good customer service. Safety stock is determined by demand variability and target service level. Session 24 Operations Management 7 Example Daily demand for a certain product is normally distributed with a mean of 60 and a standard deviation of 7. The source of supply is reliable and maintains a constant lead time of six days. The cost of placing the order is $10 and annual holding costs are $0.50 per unit. There are no stockout costs, and unfilled orders are filled as soon as the order arrives. Assume sales occur over the entire 365 days of the year. Find the order quantity and reorder point to satisfy a 95% probability of not stocking out during the lead time. (Example 17.4, page 562) Session 24 Operations Management 8 Example Let us first ignore the random/uncertainty part. If daily demand is 60 for sure, what is the order quantity and the reorder point? Session 24 Operations Management 9 Example The optimal order quantity is : 2DS 2 * 60 * 365 *10 936 units H 0.50 Average daily demand Leadtime Reorder point : R dL z z value st. dev. of demand over the leadtime Session 24 Operations Management 10 Example Reorder point : R dL z The z-value associated with 0.95 is 1.64. 2 2 6 * 7 17.15 i1 d L The re-order point R is 60(6)+1.64*17.15 = 388 units. To summarize, an order for 936 units is placed whenever the number of units remaining in inventory drops to 388. Session 24 Operations Management 11 Example What happens if demand is not normal? Demand Probability 2 0.02 3 0.05 4 0.09 5 0.14 6 0.2 7 0.17 8 0.15 9 0.1 10 0.05 11 0.03 Session 24 Operations Management 12 Example What is the average on hand inventory level? Session 24 Operations Management 13 Example What if the supplier is able to reduce the leadtime from 6 days to 3 days? Session 24 Operations Management 14 Example What if the cost of placing an order is reduced from $10 to $2.5? Session 24 Operations Management 15 Inventory Level in Real Life Inventory on Hand Target inventory level, TIL Review period RP RP First order quantity, Q1 d1 Amount used during RP+ first lead time Safety stock, SS Q2 First lead time, LT1 LT2 LT3 Time Order 2 placed Order 1 placed Shipment 1 received Session 24 Operations Management Shipment 2 received Order 3 placed Shipment 3 received 16 Inventory Systems Periodic system: Physical count of items made at periodic intervals (weekly, monthly) Good: (1) Economics of scale and (2) Delivery is performed on a known schedule Bad: (1) Lack of control between reviews; (2) Carry extra stock to protect against shortages between reviews; (3) Order quantity is random Session 24 Operations Management 17 Periodic System (Order-up-to,T) policy How do we compute how much to order at every review period? If there was no variability in the system, we would order exactly the amount needed to satisfy demand over the period T+L. Session 24 Operations Management 18 Example Daily demand for a product is 10 units with a standard deviation of 3 units. The review period is 30 days, and the lead time is 14 days. Management has set a policy of satisfying 98 percent of demand from items in stock. At the beginning of this review period, there are 150 units in inventory. How many units should be ordered? (Example 17.5, page 563) Session 24 Operations Management 19 Example Let us first ignore the random/uncertainty part. If daily demand is 10 for sure, what is the orderup-to level? d(T+L) Session 24 Operations Management 20 The Safety Stock Level and Order Quantity Safety stock = z*(st. dev. of demand over review and lead time) q = d(T+L) + zσ - I Part in light blue is the target inventory level. q = Quantity to be ordered T = number of days between reviews L = lead time d = forecast avg. daily demand z = z-value for a specified service level σ = st. dev. of demand over review and lead time I = current inventory level Session 24 Operations Management 21 Example Formula: q = d(T+L) + z*σ - I d = 10; T = 30; L = 14; I = 150 We must calculate z and σ. The z value for 0.98 is 2.05. T L i 1 d2 (T L) d2 (30 14)(32 ) 19.90 The quantity to order is: q = 10(30+14)+2.05*19.90-150 = 331 units to ensure 98% probability of not stocking out over the review period. Session 24 Operations Management 22 Example What is the average on hand inventory level? Session 24 Operations Management 23 Inventory Level T L T-L Safety stock, SS Time Session 24 Operations Management 24 Inventory Level 6+20 20 6 6 3 7 Safety stock, SS Session 24 Operations Management 25 Inventory Level 20 6 6 3 Safety stock, SS Session 24 7 3 Operations Management 26 Inventory Level 20 6 3 Safety stock, SS Session 24 7 3 Operations Management 27 Inventory Level dT dL L Safety stock, SS Session 24 T-L L Operations Management 28 Example What if the supplier is able to reduce the leadtime from 14 days to 7 days? Session 24 Operations Management 29 Example What if the review period is reduced from 30 days to 15 days? What is the main trade-off that determines T, the review cycle? Session 24 Operations Management 30 Inventory Turn Inventory Turn = (Annual) Cost of goods sold/Average inventory value = [(Annual) Sales quantity * Unit Cost] / (Average inventory quantity * Unit Cost) = (Annual) Sales quantity / Average inventory quantity = Throughput Rate / Average WIP = 1 / Throughput Time Session 24 Operations Management 31 Inventory Turn Continuous System Inventory turn = D / (Q/2 + SS) Periodic System Inventory turn = D / (DT/2 + SS) Session 24 Operations Management 32 Comparison: Continuous Review vs Periodic Continuous review inventory system: The order quantity Q is constant (i.e., the same amount is ordered every time), and an order is placed every time the inventory drops to the reorder level R. The time between orders is variable. Periodic review inventory system: There is a target inventory level, and an order is placed every T time units. The size of the order is variable, and equals the target inventory level minus the inventory currently on hand. The time between orders is constant. Session 24 Operations Management 33 The Simulation Game: First Run Monitoring utilization rate Buy machines when the utilization rate is high Forecasting and planning Occasional information updating and monitoring Session 24 Operations Management 34 The Simulation Game: First Run Monitoring utilization rate It is very hard to play catch-up game What the cause of peak rate? Noise? Underlying demand? What is the right utilization rate for the desired leadtime? Forecasting and planning Capacity requirement Capacity requirement with 85% target utilization rate Spreadsheet waiting time calculation for leadtime Session 24 Operations Management 35 The Simulation Game: First Run Do we want to delay the purchase? Do we want to sell the machines in the end? Do we want to change the queue priority? Session 24 Operations Management 36 The Simulation Game: Second Run Preparing Testing Centrifuging Decisions: 1. Three pricing contract type (7 day, 1 day, and half day) 2. The number of machines at each station. (Start with 1.) 3. The inventory policy (reorder point, reorder quantity) 4. The priority at the testing queue (FIFO, initial, or final). Session 24 Operations Management 37 The Simulation Game: Second Run Observation period for the second simulation game starts at 7:00 pm, 4/15/09 (Wed.). Second Simulation Game Starts at 4/16/09 7:00pm (Thurs.) The simulator stops running at 7 pm on 4/23/09 7:00pm (Thurs.) 50% is your standing against the other teams in this class. 50% is a 2 page write-up. Session 24 Operations Management 38 Next Class Supply Chain Coordination Article reading: "Back to the Future: Benetton Transforms it’s Global network" MIT Sloan management Review, Fall 2001. Beer Game Please download the game before class at http://scm.bus.umich.edu/BeerNet/Beerwin32.exe Bring laptops to the class next time Session 24 Operations Management 39
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