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Inventory Management

Inventory Management. Chapter 12. 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

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Inventory Management

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  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. • 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 (MRO)

  4. Functions of Inventory • 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.

  5. Objectives of Inventory Control Inventory 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 Inventory 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 -- 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? • 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. • 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 & opportunity costs, storage & insurance, risk of obsolescence). • Expressed either as a percentage of unit price or as a dollar amount per unit. • Ordering & setup costs: • Fixed cost of placing an order (e.g.: clerical accounting & physical handling) or setting up production (e.g.: lost production to change tools & clean equipment). • Expressed as a fixed dollar amount per order regardless of order size. • Shortage costs: • Result when demand exceeds the supply of inventory on-hand. (stock-out) • Lost profit, expediting & back ordering expenses. • Are sometimes difficult to measure, & they may be subjectively estimated.

  9. Why Control Inventory Cost Vs Service • Under-stock: Frequent stock-outs • Lost sales, loss of customer goodwill • Low level of customer service • Over-stock: Excess inventory • Costs of ordering and carrying inventory increase • Objective: Establish an inventory control system to find a balance between cost and service: • When to order? • How much to order?

  10. Ordering Quantity Approaches • Lot-for-lot: • Order exactly what is needed. • Fixed order quantity: • Order a predetermined amount each time. • Min-max system: • When inventory falls to a set minimum level, order up to the predetermined maximum level. • Order enough for n periods: • The order quantity is determined by total demand for the item for the next n-periods. • Periodic review: • At specified intervals, order up to a predetermined target level.

  11. Classification System • Divides on-hand inventory into 3 classes: • A class, B class, C class (very --> moderate --> least: important). • Basis is usually annual $ volume: • $ volume = Annual demand x Unit cost • Class A: 15% -20% of items but 70%- 80% dollar usage. • Class B: 30% -35% of items but 15% -20% dollar usage. • Class C: 50% -60% of items but 5% -10% dollar usage. • Policies based on ABC analysis: • Develop class A suppliers more • Give tighter physical control of A items • Forecast A items more carefully

  12. Example Classify the inventory items as A,B and C based on annual dollar value. 72% of total value and 17% of items: Class A. 25% of value and 33% of items: Class B. 3% of total value and 50% of items: Class C.

  13. Economic-Order Quantity Models • Basic Economic Order Quantity (EOQ). • Economic Production Quantity (EPQ) (EOQ with non-instantaneous delivery). • Quantity Discount Model.

  14. EOQ Model Assumptions • Only one product is involved. • Demand is known & constant - no safety stock is required. • Lead time is known & constant. • No quantity discounts are available. • Ordering (or setup) costs are constant. • All demand is satisfied (no shortages). • The order quantity arrives in a single shipment.

  15. Inventory Level (Cycle) Q Quantity on hand ROP Place Order Receive Order Receive Order Lead Time

  16. EOQ Model Total annual costs = Annual ordering costs + Annual holding costs

  17. EOQ: Total Cost Equations Minimize the TC by ordering the EOQ: D = Annual Demand. H= Annual Inventory Holding/Carrying Cost per Unit. S= Ordering/Setup Cost per order. Length of an Order Cycle (time between orders) = (Q/D) years.

  18. Example • A local distributor for a national tire company expects to sell approximately 9,600 belted radial tires for a certain size and tread design next year. Annual carrying cost is $16 per tire, and ordering cost is $75. The distributor operates 288 days a year. A. What is the EOQ? B. How many times per year does the store order? C. What is the length of an order cycle? D. What is the total annual cost if the EOQ quantity is ordered? • Pidding Manufacturing assembles security monitors. It purchases 3,600 black-and-white cathode ray tubes a year at $65 each. Ordering cost is $31 per order, and annual carrying cost per unit is 20% of the purchase price. Compute the optimal order quantity and the total annual cost of ordering and carrying the inventory.

  19. Economic Production Quantity Model Assumptions: Same as the EOQ except: inventory arrives in increments & is drawn down as it arrives.

  20. EPQ Equations • Adjusted total cost: • Maximum inventory: • Adjusted order quantity: • Cycle Time: Q/d. • Run Time (production phase of the cycle): Q/p. • where, d = demand (usage rate); p = production rate; S = ordering / setup cost; • D = Annual demand and H = Annual Holding cost.

  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. Setup 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. Quantity Discount Model • Same as the EOQ, except: • Unit price depends upon the quantity ordered. • Adjusted total cost equation:

  23. Cost Adding Purchasing costdoesn’t change EOQ TC with PD TC without PD Annual purchasing cost=(PD) 0 Quantity EOQ Total Costs with Purchasing Cost (PD)

  24. Quantity Discount Representation Order Price Quantity per Box 1 to 44 $2.00 45 to 69 $1.70 70 or more $1.40 TC@ $2.00 each Total Cost TC@ $1.70 each TC@ $1.40 each PD @ $2.00 each PD @ $1.70 each PD @ $1.40 each 0 Quantity 45 70

  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 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. Quantity Discount Procedure • 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. • 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 cheaper unit prices. • Compare the total cost of each option & choose the lowest cost alternative.

  27. Examples • The maintenance department of a large hospital uses about 816 cases of liquid cleaner annually. Ordering costs are $12, carrying costs are $4 per case a year, and the new price schedule indicates that orders of less than 50 cases will cost $20 per case, 50 to 79 cases will cost $18 per case, 80 to 99 cases will cost $17 per case, and larger orders will cost $16 per case. Determine the optimal order quantity and the total cost. • Surge Electric uses 4,000 toggle switches a year. Switches are priced as follows: 1 to 499, 90 cents each; 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 the total annual cost.

  28. When to Order? ROP = d(LT) where LT = Lead time (in days or weeks) d = Daily or weekly demand rate

  29. Example 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 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?

  30. What if Demand is Uncertain? Quantity on hand ROP Time

  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 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. Adding Safety Stock • Demand variability. • Lead time variability. • Order-cycle service level: • From a managerial standpoint, determine the acceptable probability that demand during lead time won’t exceed on-hand inventory. • Risk of a stockout: 1 – (service level).

  33. Adjusted Reorder Point Equation R = reorder point d = average daily demand LT = lead time in days z = number of standard deviations associated with desired service level σ= 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)

  34. Example Suppose that the manager of a construction supply house determined 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 that 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 formula. • 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 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 appropriate 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 expected 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 σdLT=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 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.: Given the following information, determine the amount to order.

  41. Single-Period Models • Used for order perishables. • Analysis focus on two costs: Shortage and Excess. Goal is to identify the order quantity, or stocking level, that will minimize the long-run total excess and shortage cost. 2 kinds of problems: • Demand can be approximated using a continuous distribution. • Demand can be approximated using a discrete distribution.

  42. Continuous Stocking Levels: E.g.: Sweet cider is delivered weekly to Cindy’s Cider Bar. Demand varies uniformly between 300 liters and 500 liters 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.: Cindy’s Cider Bar also sells 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. Discrete Stocking Levels: E.g.: Historical records 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 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 economic 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 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 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 cost-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 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. • 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 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 estimates 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 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 ordering 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 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 minimize 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 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 maintain 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 few 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 the 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. 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 is the possibility of stock-out?

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