Inventory Management Short Answers

89. What are some policies that may be based upon the results of an ABC analysis? Some policies include purchasing resources expended on supplier development should be higher for individual A items than for C items, A items should have tighter physical inventory control, and forecasting A items may warrant more care. (Inventory management, moderate) 90. What is cycle counting? Cycle counting is an audit to reconcile inventory with inventory records. (Inventory management, easy) 91. Define shrinkage. Shrinkage is retail inventory that is unaccounted for between receipt and sale. (Inventory management, easy) 92. What are the techniques to control service inventories? Techniques to control service inventories include good personnel selection, training, and discipline; tight control of incoming shipments; and effective control of all goods leaving the facility. (Inventory management, moderate) 93. When is a good time for cycle-counting personnel to audit a particular item? In deciding when to verify inventory through cycle counting, the important considerations are (a) the verification takes place according to a formal schedule, and (b) inventory records of particularly important items are verified more often, those of less important items, less often. As the text suggests, the schedule can be weekly, monthly, or any other criteria, such as when an item goes to zero or when the item is to be ordered. (Inventory management, moderate) 94. What is meant by EOQ being suitable for independent demand? EOQ is suitable for items that are independent of one another. This means that ordering one particular SKU (e.g., baseball bats at K-Mart) does not affect demand for a different SKU (e.g., women’s sandals). When items are dependent, such as tires on a car being made at GM, independent ordering with EOQ is not optimal. From a statistical point of view, EOQ is a reasonable system for independent demand because it is an averaging technique. It averages demands over a year. The independent demand situation assumes that each demand is random from a population that represents the demands over some time period (say over the past year). (Inventory models, moderate) 95. List the typical components that constitute inventory holding or carrying costs. Typical components of inventory holding or carrying costs include housing costs, material handling costs, labor cost from extra handling, investment costs, pilferage, scrap, and obsolescence. (Inventory models, moderate) 96. Describe the costs associated with ordering and maintaining inventory. Costs that are associated with ordering and maintaining inventory include initial purchase cost of the item, holding cost (insurance, space, heat, light, security, warehouse personnel, etc.), obsolescence or deterioration cost (particularly important in perishable goods or in a product that is undergoing rapid technological evolution), and ordering or setup cost (cost of forms, clerical processing, etc., or cost of machine setup). (Inventory models, moderate) 97. List the typical cost components that constitute ordering costs in inventory systems. Typical components of ordering costs include cost of supplies, forms, order processing, clerical support, and so forth. (Inventory models, moderate) 98. Compare the assumptions of the production order quantity model to those of the basic EOQ model. All are the same, except the assumption that receipt of inventory is instantaneous, which holds for EOQ, but not POQ. (Inventory models for independent demand, moderate) 99. In some inventory models, the optimal behavior occurs where ordering costs and carrying costs are equal to one another. Provide an example of a model where this "rule" does not hold; explain how the model's results are optimal anyway. This rule will not hold in all instances of quantity discount models. In order to take advantage of a discount, it may be cheaper to order a quantity that is not an EOQ. The goal in quantity discount models is to minimize the sum of ordering, carrying, and purchase costs. (Inventory models for independent demand, moderate) 100. What are the assumptions of the EOQ model? The more important assumptions of the basic EOQ model are demand is known and constant over time, the lead time, that is, the time between the placement of the order and the receipt of the goods, is known and constant, the receipt of the inventory is instantaneous; i.e., the goods arrive in a single batch, at one instant in time, quantity discounts are not possible, the only variable costs are the cost of setting up or placing an order and the cost of holding or storing inventory over time, and if orders are placed at the right time, stockouts or shortages can be completely avoided. (Inventory models for independent demand, moderate) 101. How sensitive is the EOQ to variations in demand or costs? The EOQ is relatively insensitive to small changes in demand or setup or carrying costs because the cost curve is relatively flat around the EOQ. For example, if demand increases by 10%, EOQ will increase by approximately 5%. (Inventory models for independent demand, moderate) 102. Does the production model or the standard EOQ model yield a higher EOQ if setup cost and holding costs are the same? Why? The production inventory model will yield a higher EOQ than the standard model, other things equal, because the maximum inventory level (and thus the effective carrying charge) is less. (Inventory models for independent demand, moderate) 103. What happens to total inventory costs (and EOQ) if inventory holding costs per unit increase as inventory increases (that is, increase at an increasing rate)? If per unit holding costs increase with increasing inventory, total inventory cost will increase; EOQ will decrease. (Inventory models for independent demand, moderate) 104. What is a reorder point? A reorder point is the inventory level (point) at which action is taken (an order placed) to replenish the stocked item. (Inventory models for independent demand, easy) 105. Define service level. The service level is the percentage of demand met by available stock; it is the complement of the probability of a stockout. (Probabilistic models with constant lead time, moderate) 106. What happens to the cost of the inventory policy when the service level increases? The cost of the inventory policy increases dramatically with increases in service level. (Probabilistic models with constant lead time, moderate) 107. How would a firm go about determining service level? Service level is a difficult parameter to determine. Basically, the firm uses its subjective judgment to balance the cost of additional inventory against the cost of lost goodwill due to stockouts or shortages. (Probabilistic models with constant lead time, moderate) 108. What is a fixed-period system? It is a system in which inventory orders are made are regular time intervals. (Fixed-period systems, easy) 109. Describe the difference between a fixed-quantity and a fixed-period inventory system? In a fixed-quantity inventory system, when the quantity on hand reaches the reorder point, an order is placed for the specified quantity. In a fixed-period inventory system, an order is placed at the end of the period. The quantity ordered is that needed to bring on-hand inventory up to a specified level. (Fixed-period systems, moderate) PROBLEMS 110. Montegut Manufacturing produces a product for which the annual demand is 10,000. Production averages 100 per day, while demand is 40 per day. Holding costs are $1.00 per unit per year; set-up costs $200.00. If they wish to produce this product in economic batches, what size batch should be used? What is the maximum inventory level? How many order cycles are there per year? How much does management of this good in inventory cost the firm each year? This problem requires economic order quantity, noninstantaneous delivery. Q 2 DS H (1 d / p ) 2 *10000 * 200 1.00(1 40 / 100) 2582 units The maximum inventory level is 1549.2; there are approximately 3.9 cycles per year. (Inventory models for independent demand, moderate) 111. Lead time for one of Montegut Manufacturing's fastest moving products is 4 days. Demand during this period averages 100 units per day. What would be an appropriate re-order point? Re-order point = demand during lead time = 100 units/day * 4 days = 400 units. (Inventory models for independent demand, easy) 112. Your company has compiled the following data on the small set of products that comprise the specialty repair parts division. Perform ABC analysis on the data. Which products do you suggest the firm keep the tightest control over? Explain. SKU Annual Demand Unit Cost R11 250 $250 S22 75 $90 T33 20 $60 U44 150 $150 V55 100 $75 R11 and U44 represent over 80% of the firm's volume in this area. R11 is classified A, U44 is classified B, and all others are C. The tightest controls go to R11, then U44 because of their high percentage of sales volume. Data R11 U44 V55 S22 T33 Volume 250 150 100 75 20 Unit cost $250 $150 $75 $90 $60 Results Dollar % Dollar Cumulative volume volume $-vol % 62500 62.22% 62.22% 22500 22.40% 84.62% 7500 7.47% 92.09% 6750 6.72% 98.81% 1200 1.19% 100.00% Total 100450 (Inventory models for independent demand, moderate) Class A B C C C 113. The annual demand, ordering cost, and the inventory carrying cost rate for a certain item are D = 600 units, S = $20/order and I = 30% of item price. Price is established by the following quantity discount schedule. What should the order quantity be in order to minimize the total annual cost? Quantity Price 1 to 49 $5.00 per unit 50 to 249 $4.50 per unit 250 and up $4.10 per unit Order 250 per order, paying $4.10 per unit. Holding costs are much larger than ordering costs, but this is offset by the unit price reduction. The annual total cost is $2,460. The EOQ value for the $4.50 price has an annual cost of $2,700, not much higher than this solution. Data Demand rate, D Setup cost, S Holding cost %, I 600 20 30% Range 1 Minimum quantity Unit Price, P Range 2 1 5 Range 3 50 250 4.5 4.1 Results Q* (Square root formula) Order Quantity Holding cost Setup cost Range 1 Range 2 Range 3 126.491106 133.333333 139.686059 126.491106 133.333333 250 $94.87 $94.87 $90.00 $90.00 $153.75 $48.00 $3,000.00 $2,700.00 $2,460.00 Total cost, Tc $3,189.74 $2,880.00 (Inventory models for independent demand, moderate) $2,661.75 Unit costs 114. Thomas's Bike Shop stocks a high volume item that has a normally distributed demand during the reorder period. The average daily demand is 70 units, the lead time is 4 days, and the standard deviation of demand during the reorder period is 15. a. How much safety stock provides a 95% service level to Thomas? b. What should the reorder point be? a. SS = 1.65 x 15 = 24.75 units or 25 units b. ROP = (70* 4) + 25 = 305 units. (Probabilistic models with constant lead time, moderate) 115. The new office supply discounter, Paper Clips, Etc. (PCE), sells a certain type of ergonomically correct office chair which costs $300. The annual holding cost rate is 40%, annual demand is 900, and the order cost is $20 per order. The lead time is 4 days. Because demand is variable (standard deviation of daily demand is 2.4 chairs), PCE has decided to establish a customer service level of 90%. The store is open 300 days per year. a. What is the optimal order quantity? b. What is the safety stock? c. What is the reorder point? ROP= lead time demand + safety stock = (3 chairs/day * 4) + 1.282 * 2.4 x sqrt(4) = 18 chairs. Data Demand rate, D 900 Setup cost, S 20 Holding cost, H 40.00% Unit Price, P 300 Daily demand rate 3 Lead time in days 4 Results Optimal Order Quantity, Q* Maximum Inventory Average Inventory Number of Setups Holding cost Setup cost 17.32050808 17.32050808 8.660254038 51.96152423 $1,039.23 $1,039.23 Unit costs $270,000.00 Total cost, Tc $272,078.46 (Probabilistic models with constant lead time, moderate) 116. The soft goods department of a large department store sells 175 units per month of a certain large bath towel. The unit cost of a towel to the store is $2.50 and the cost of placing an order has been estimated to be $12.00. The store uses an inventory carrying charge of 27% per year. Determine the optimal order quantity, order frequency, and the annual cost of inventory management. If, through automation of the purchasing process, the ordering cost can be cut to $4.00, what will be the new economic order quantity, order frequency, and annual inventory management cost? Explain these results. At S=$12, EOQ 273, and there are about 8 orders per year. Annual costs of inventory management are $184.44. At S=$4, EOQ falls to 158, and order frequency rises to 13. Annual inventory management costs fall to $106.48. The lower order cost encourages smaller, more frequent orders. Data Demand rate, D Setup cost, S Holding cost, H Unit Price, P Results Optimal Order Quantity, Q* Maximum Inventory Average Inventory Number of Setups 2100 12 27.00% 2.5 273.2520204 273.2520204 136.6260102 7.685213074 Holding cost Setup cost $92.22 $92.22 Unit costs Total cost, Tc $5,250.00 $5,434.45 Data Demand rate, D Setup cost, S Holding cost, H Unit Price, P Results Optimal Order Quantity, Q* Maximum Inventory Average Inventory Number of Setups 2100 4 27.00% 2.5 157.7621275 157.7621275 78.88106377 13.31117951 Holding cost Setup cost $53.24 $53.24 Unit costs Total cost, Tc $5,250.00 $5,356.49 117. Central University uses $123,000 of a particular toner cartridge for laser printers in the student computer labs each year. The purchasing director of the university estimates the ordering cost at $45 and thinks that the university can hold this type of inventory at an annual storage cost of 22% of the purchase price. How many months' supply should the purchasing director order at one time to minimize the total annual cost of purchasing and carrying? First, calculate the EOQ from the data provided. In this problem, the "units" are dollars, and the "price" of each is 1. One month's usage is 123000/12 = $10,250. EOQ = 7094. Month’s usage = 7094/10250 = 0.69, or about three week’s usage. (This is supported by the order frequency of 17 per year). Data Demand rate, D 123000 Setup cost, S 45 Holding cost, H 22.00% Unit Price, P 1 Results Optimal Order Quantity, Q* Maximum Inventory Average Inventory Number of Setups Holding cost Setup cost 7093.530984 7093.530984 3546.765492 17.3397424 $780.29 $780.29 Unit costs $123,000.00 Total cost, Tc $124,560.58 (Inventory models for independent demand, difficult) 118. A printing company estimates that it will require 1,000 reams of a certain type of paper in a given period. The cost of carrying one unit in inventory for that period is 50 cents. The company buys the paper from a wholesaler in the same town, sending its own truck to pick up the orders at a fixed cost of $20.00 per trip. Treating this cost as the order cost, what is the optimum number of reams to buy at one time? How many times should lots of this size be bought during this period? What is the minimum cost of maintaining inventory on this item for the period? Of this total cost, how much is carrying cost and how much is ordering cost? This is an EOQ problem, even though the time period is not a year. All that is required is that the demand value and the carrying cost share the same time reference. EOQ 2  1000 20 0.50 283 This will require approximately 3.5 orders per period. Setup costs and carrying costs are each $70.71, and the annual total is $141.42. Data Demand rate, D Setup cost, S Holding cost, H Unit Price, P Daily demand rate Lead time in days 1000 20 0.5 Results Optimal Order Quantity, Q* 282.842712 Maximum Inventory 282.842712 Average Inventory 141.421356 Number of Setups 3.53553391 Holding cost Setup cost $70.71 $70.71 Unit costs Total cost, Tc $0.00 $141.42 (Inventory models for independent demand, moderate) 119. The Rushton Trash Company stocks, among many other products, a certain container, each of which occupies four square feet of warehouse space. The warehouse space currently available for storing this product is limited to 600 square feet. Demand for the product is 15,000 units per year. Holding costs are $4 per container per year; Ordering costs are $5 per order. a. What is the cost-minimizing order quantity decision for Rushton? b. What is the total inventory-related cost of this decision? c. What is the total inventory-related cost of managing the inventory of this product, when the limited amount of warehouse space is taken into account? d. What would the firm be willing to pay for additional warehouse space? The warehouse will hold only 150 containers. The annual cost at Q=150 is 100 x 5 + 75 x 4 = $800. The EOQ is about 194, more than there is room to store. Total cost at Q=194 is $774.60 This cost is $25.40 less than current cost, which reflects the limited storage space. Rushton would consider paying up to $25.40 for a year's rental of enough space to store 44 additional containers. (Inventory models for independent demand, difficult) 120. A firm that makes electronic circuits has been ordering a certain raw material 250 ounces at a time. The firm estimates that carrying cost is 30% per year, and that ordering cost is about $20 per order. The current price of the ingredient is $200 per ounce. The assumptions of the basic EOQ model are thought to apply. For what value of annual demand is their action optimal? This problem reverses the unknown of a standard EOQ problem. D 20 2  250  .3 200 ; solving for D results in D = .3 200 2 20 2 250 93,750 (Inventory models for independent demand, difficult) 121. Given the following data: D=65,000 units per year, S = $120 per setup, P = $5 per unit, and I = 25% per year, calculate the EOQ and calculate annual costs following EOQ behavior. EOQ is 3533 units, for a total cost of $4,415.88 Data Demand rate, D Setup cost, S Holding cost, H Unit Price, P Results Optimal Order Quantity, Q* Maximum Inventory Average Inventory Number of Setups Holding cost Setup cost 65000 120 25.00% 5 3532.704347 3532.704347 1766.352173 18.3995018 $2,207.94 $2,207.94 Unit costs $325,000.00 Total cost, Tc $329,415.88 (Inventory models for independent demand, moderate) 122. A toy manufacturer makes its own wind-up motors, which are then put into its toys. While the toy manufacturing process is continuous, the motors are intermittent flow. Data on the manufacture of the motors appears below. Annual demand (D) = 50,000 units Daily subassembly production rate = 1,000 Setup cost (S) = $85 per batch Daily subassembly usage rate = 200 Carrying cost = $.20 per unit per year a. To minimize cost, how large should each batch of subassemblies be? b. Approximately how many days are required to produce a batch? c. How long is a complete cycle? d. What is the average inventory for this problem? e. What is the total inventory cost (rounded to nearest dollar) of the optimal behavior in this problem? Each batch should be 7,289 units. It will take approximately 7289/ 1000 = 7.3 days to make these units. A complete cycle will last approximately 7289 / 200 = 36 days. Average inventory is 2,915 (not one-half of 9014) and the annual costs will total $1,166.19. Data Demand rate, D Setup cost, S Holding cost, H Daily production rate, p Daily demand rate, d Results Optimal production quantity, Q* Maximum Inventory Average Inventory Number of Setups Holding cost Setup cost 50000 85 0.2 1000 200 7288.69 5830.952 2915.476 6.859943 583.0952 583.0952 Total cost, Tc 1166.19 (Inventory models for independent demand, moderate)