Inventory Management.ppt

1、1,Inventory Management,Chapter 12,2,Independent and Dependent Demand,Dependent Demand Used in the production of a final or finished product. Is derived from the number of finished units to be produced. E.g. For Each Car: 4-wheels. Wheels are the dependent demand. Independent Demand Sold to someone.

2、Precise determination of quantity impossible due to randomness. Forecasting the number of units that can be sold.,Focus on management of Independent Demand Items.,3,Types of Inventory,Raw material Components Work-in-progress Finished goods Distribution Inventory Maintenance/repair/operating supply (

3、MRO),4,To meet anticipated demand. To smooth production requirements. To decouple operations. To protect against stockouts. To take advantage of economic lot size. To hedge against price increases or to take advantage of quantity discounts.,Functions of Inventory,5,Objectives of Inventory Control,In

4、ventory Management has two main concerns: Level of Customer Service. Cost of ordering and carrying inventories. Achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds. 2 fundamental decisions: -Timing of Orders -Size of Orders Measures of effective Inv

5、entory Management: Customer Satisfaction. Inventory Turnover = COGS / Average Inventory. Days of Inventory: expected number of days of sales that can be supplied from existing inventory.,i.e. when to order and how much to order.,6,Characteristics of Inventory Systems,Demand - Constant Vs Variable -

6、Known Vs Random Lead time - Known Vs Random Review Time - Continuous Vs Periodic Excess demand - Backordering Vs Lost Sales Changing Inventory,7,Periodic Vs Continuous Review Systems,Periodic Review System Inventory level monitored at constant intervals. Decisions: To order or not. How much to order

7、? Realize economies in processing and shipping. Risk of stockout between review periods. Time and cost of physical count. Continuous Review System Inventory level monitored continuously. Decisions: When to order? How much to order? Shortages can be avoided. Optimal order quantity can be determined.

8、Added cost of record keeping., More appropriate for valuable items,8,Relevant Inventory Costs,Item price (Cost of an item). Holding costs: Variable costs dependent upon the amount of inventory held (e.g.: capital p = production rate; S = ordering / setup cost; D = Annual demand and H = Annual Holdin

9、g cost.,EPQ Equations,21,Example,A toy manufacturer uses 48,000 rubber wheels per year for its popular dump truck series. The firm makes its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $1 per wheel a year. S

10、etup cost for a production run of wheels is $45. The firm operates 240 days per year. Determine the: A.Optimal run size. B.Minimum total annual cost for carrying and setup. C.Cycle time for the optimal run size. D.Run time.,22,Same as the EOQ, except: Unit price depends upon the quantity ordered. Ad

11、justed total cost equation:,Quantity Discount Model,23,Total Costs with Purchasing Cost (PD),24,Quantity Discount Representation,Order Price Quantityper Box 1 to 44$2.00 45 to 69 $1.70 70 or more$1.40,PD $2.00 each,PD $1.70 each,PD $1.40 each,0,45,70,Quantity,Total Cost,TC $1.70 each,TC $2.00 each,T

12、C $1.40 each,25,Quantity Discount Model,The objective is to identify an order quantity that will represent the lowest total cost for the entire set of curves. 2 General Cases: Carrying Cost is constant. Single EOQ. Same for all total cost curves. Carrying Cost is a percentage of the Price. Different

13、 EOQ for different prices. Lower carrying cost means larger EOQ. As unit price decreases, each curve EOQ will be to the right of the next higher curves EOQ.,26,Calculate the EOQ at the lowest price. Determine whether the EOQ is feasible at that price Will the vendor sell that quantity at that price.

14、 If yes, Stop if no, Continue. Check the feasibility of EOQ at the next higher price Continue until you identify a feasible EOQ. Calculate the total costs (including purchase price) for the feasible EOQ model. Calculate the total costs of buying at the minimum quantity allowed for each of the cheape

15、r unit prices. Compare the total cost of each option 500 to 999, 85 cents each; and 1,000 or more, 80 cents each. It costs approximately $30 to prepare an order and receive it, and carrying costs are 40 percent of purchase price per unit on an annual basis. Determine the optimal order quantity and t

16、he total annual cost.,Examples,28,ROP = d(LT),When to Order?,where LT = Lead time (in days or weeks) d = Daily or weekly demand rate,29,An office supply store sells floppy disk sets at a fairly constant rate of 6,000 per year. The accounting dept. states that it costs 8$ to place an order and annual

17、 holding cost are 20% of the purchase price 3$ per unit. It takes 4 days to receive an order. Assuming a 300-day year, find: a) Optimal order size and ROP. b) Annual ordering cost, annual carrying cost. c) How many orders are given a year and what is the time between the orders?,Example,30,What if D

18、emand is Uncertain?,ROP,Time,Quantity on hand,31,Uncertain Demand (Lead Time),Safety Stock Models: Use the same order quantity (EOQ) based on expected (average) annual demand. Determine ROP to satisfy a target Service Level: Probability that demand will not exceed supply during lead time (Lead time

19、service level). Percent of annual demand immediately satisfied (Annual service level or fill-rate). Equals: 1- stock-out risk Safety Stock: Stock that is held in excess of expected demand due to variable demand rate and/or lead time.,32,Demand variability. Lead time variability. Order-cycle service

20、level: From a managerial standpoint, determine the acceptable probability that demand during lead time wont exceed on-hand inventory. Risk of a stockout: 1 (service level).,Adding Safety Stock,33,R = reorder point d = average daily demand LT = lead time in days z = number of standard deviations asso

21、ciated with desired service level = standard deviation of demand during lead time (Assumes that any variability in demand rate or lead time can be adequately described by a normal distribution),Adjusted Reorder Point Equation,34,Example,Suppose that the manager of a construction supply house determi

22、ned from historical records that demand for sand during lead time averages 50 tons. In addition, suppose the manager determined that demand during lead time could be described by a normal distribution that has a mean of 50 tons and a standard deviation of 5 tons. Answer these questions, assuming tha

23、t the manager is willing to accept a stockout risk of no more than 3 percent. A.What value of z is appropriate? B.How much safety stock should be held? C.What reorder point should be used?,35,Reorder Point -Continued,When data on lead time demand is not readily available, cannot use the standard for

24、mula. Use the daily or weekly demand and the length of the lead time to generate lead time demand. If only demand is variable, then use , and the ROP is:,36,If only lead time is variable, then use , and the ROP is: If both demand and lead times variable, then,37,Example,A restaurant uses an average

25、of 50 jars of a special sauce each week. Weekly usage of sauce has a standard deviation of 3 jars. The manager is willing to accept no more than a 10 percent risk of stockout during lead time, which is two weeks. Assume the distribution of usage is normal. A. Which of the above formula is appropriat

26、e for this situation? Why? B. Determine the value of z. C. Determine the ROP.,38,Shortage and Service Level,E.g.: Suppose the standard deviation of lead time demand is known to be 20 units and lead time demand is approximately Normal. For a lead time service level of 90 percent, determine the expect

27、ed number of units short for any order cycle. What lead time service level would an expected shortage of 2 units imply?,39,Given the following information, determine the expected number of units short per year. D=1,000; Q=250; E (n)=2.5.,Given a lead time service level of 90%, D=1,000, Q=250, and dL

28、T=16, determine (a) the annual service level, and (b) the amount of cycle safety stock that would provide an annual service level of .98 (Given: E (z) = 0.048 for 90% lead time service level).,40,Fixed-Order Interval Model,Order groupings can produce savings in ordering and shipping costs. Can have

29、variations in demand, lead time, or in both. Our focus is only on demand variability, with constant lead times.,OI = Order Interval (length of time between orders) Imax = Maximum amount of inventory (also called order-up-to-level point) = Expected demand during protection interval + Safety stock,E.g

30、.: Given the following information, determine the amount to order.,41,Single-Period Models,Goal is to identify the order quantity, or stocking level, that will minimize the long-run total excess and shortage cost.,Used for order perishables. Analysis focus on two costs: Shortage and Excess.,2 kinds

31、of problems: Demand can be approximated using a continuous distribution. Demand can be approximated using a discrete distribution.,42,Continuous Stocking Levels:,Discrete Stocking Levels:,E.g.: Sweet cider is delivered weekly to Cindys Cider Bar. Demand varies uniformly between 300 liters and 500 li

32、ters per week. Cindy pays 20 cents per liter for the cider and charges 80 cents per liter for it. Unsold cider has no salvage value and cannot be carried over into the next week due to spoilage. Find the optimal stocking level and its stockout risk for that quantity.,E.g.: Cindys Cider Bar also sell

33、s a blend of cherry juice and apple cider. Demand for the blend is approximately Normal, with a mean of 200 liters per week and a standard deviation of 10 liters per week. Cs=60 cents per liter, and Ce=20 cents per liter. Find the optimal stocking level for the apple cherry blend.,E.g.: Historical r

34、ecords on the use of spare parts for several large hydraulic presses are to serve as an estimate of usage for spares of a newly installed press. Stockout costs involve downtime expenses and special ordering costs. These average $4,200 per unit short. Spares cost $800 each, and unused parts have zero

35、 salvage. Determine the optimal stocking level.,43,Examples,A large bakery buys flour in 25-pound bags. The bakery uses an average of 4,860 bags a year. Preparing an order and receiving a shipment of flour involves a cost of $4 per order. Annual carrying costs are $30 per bag. A.Determine the econom

36、ic order quantity. B.What is the average number of bags on hand? C.Compute the total cost of ordering and carrying flour. D.If ordering cost were to increase by $1 per order, how much would that affect the minimum total annual ordering and carrying cost?,44,Examples,A large law firm uses an average

37、of 40 packages of copier paper a day. Each package contains 500 sheets. The firm operates 260 days a year. Storage and handling costs for the paper are $1 a year per pack, and it costs approximately $6 to order and receive a shipment of paper. What order size would minimize total annual ordering and

38、 carrying costs? Compute the total annual cost using your order size from part a. Except for rounding, are annual ordering and carrying costs always equal at the EOQ? The office manager is currently using an order size of 400 packages. The partners of the firm expect the office to be managed “in a c

39、ost-efficient manner.” Would you recommend that the office manager use the optimal order size instead of 400 packages? Justify your answer.,45,Examples,A chemical form produces sodium bisulphate in 100-kg bags. Demand for this product is 20 tons per day. The capacity for producing the product is 50

40、tons per day. Setup costs $100, and storage and handling costs are $50 per ton per year. The firm operates 200 days a year. (Note: 1 ton = 1,000 kg) How many bags per run are optimal? What would the average inventory be for this lot size? Determine the approximate length of a production run, in days

41、. About how many runs per year would there be? How much could the company save annually if the setup cost could be reduced to $25 per run?,46,Examples,A company is about to begin production of a new product. The manager of the department that will produce one of the components for the product wants

42、to know how often the machine to be used to produce the item will be available for other work. The machine will produce the item at a rate of 200 units a day. Eighty units will be used daily in assembling the final product. Assembly will take place five days a week, 50 weeks a year. The manager esti

43、mates that it will take almost a full day to get the machine ready for a production run, at a cost of $300. Inventory holding costs will be $10 per unit a year. What run quantity should be used to minimize total annual costs? What is the length of a production run in days? During production, at what

44、 rate will inventory build up? If the manager wants to run another job between runs of this item, and needs a minimum of 10 days per cycle for the other work, will there be enough time.,47,Examples,A mail-order company uses 18,000 boxes a year. Carrying costs are 20 cents per box per year, and order

45、ing costs are $32 per order. The following quantity discount is available. Determine: The optimal order quantity. The number of orders per year.,48,Examples,A jewelry firm buys semi-precious stones to make bracelets and rings. The supplier quotes a price of $8 per stone and quantities of 600 stones

46、or more, $9 per stone for orders of 400 to 599 stones, and $10 per stone for lesser quantities. The jewelry firm operates 200 days per year. Usage rate is 25 stones per day, and ordering cost is $48 per order. A.If carrying cost are $2 per year for each stone, find the order quantity that will minim

47、ize total annual cost. B.If annual carrying cost are 30 percent of unit cost, what is the optimal order size? C.If lead time is six working days, at what point should the company reorder?,49,Examples,The housekeeping department of a motel uses approximately 400 washcloths per day. The actual amount

48、tends to vary with the number of guests on any given night. Usage can be approximated by a normal distribution that has a mean of 400 and a standard deviation of 9 washcloths per day. A linen supply company delivers towels and washcloths with a lead time of three days. If the motel policy is to main

49、tain a stockout risk of 2 percent, what is the minimum number of washcloths that must be on hand at reorder point, and how much of that amount can be considered safety stock? The motel in the preceding example uses approximately 600 bars of soap each day, and this tends not to vary by more than a fe

50、w bars either way. Lead time for soap delivery is normally distributed with a mean of six days and a standard deviation of two days. A service level of 90 percent is desired. Find the ROP.,50,Examples,A distributor of large appliances needs to determine the order quantities and reorder points for th

51、e various products it carries. The following data refers to a specific refrigerator in its product line: Cost to place an order:$100 Holding Cost:20 percent of product cost per year. Cost of refrigerator:$500 each. Annual demand:500 refrigerators. Standard deviation during lead time:10 refrigerators

52、. Lead time:7 days. Consider an even daily demand and a 365-day year. A. What is the economic order quantity? B. If the distributor wants a 97% service probability, what reorder point R should be used? What is the corresponding safety stock? C. If the current reorder point is 26 refrigerators, what

53、is the possibility of stock-out?,51,Examples,A local service station is open 7 days a week, 365 days per year. Sales of 10W40 grade premium oil average 20 cans per day. Inventory holding costs are $0.50 pre can per year. Ordering costs are $10 per order. Lead time is two weeks. Backorders are not pr

54、actical - the motorist drives away. A.Based on these data, choose the appropriate inventory model and calculate the economic order quantity and reorder point. ( Demand is deterministic). B.The boss is concerned about this model because demand really varies. The standard deviation of demand was deter

55、mined from a data sample to be 6.15 cans per day. The manager wants a 99.5% service probability. Determine the new reorder point? Use Qopt from Part-A.,52,Examples,A small copy centre uses five boxes of copy paper a day. Each box contains 10 packages of 500 sheets. Experience suggests that usage can be well approximated by a Normal distribution with a mean of five boxes per day and a standard deviation of one-half box per day. Two days are required to fill an order for paper. Ordering cost