Inventory Management Answers Part 3

123. Louisiana Specialty Foods can produce their famous Natchitoches (pronounced naka-tish – honest!) meat pies at a rate of 1650 cases of 48 pies each per day. The firm distributes the pies to regional stores and restaurants at a steady rate of 250 cases per day. The cost of setup, cleanup, idle time in transition from other products to pies, etc., is $320. Annual holding costs are $11.50 per case. Assume 250 days per year. a. Determine the optimum production run. b. Determine the number of production runs per year. c. Determine total inventory-related (setup and carrying) costs per year. d. Determine maximum inventory. The optimum production run is 2,025 cases. The number of production runs will be 62500/2025 = 30.87. Total inventory management costs are $19,756.09, and maximum inventory is 1,718 (not 2,025) cases. Data Demand rate, D 62500 Setup cost, S 320 Holding cost, H 11.5 Daily production rate, p 1650 Daily demand rate, d 250 Results Optimal production quantity, Q* Maximum Inventory Average Inventory Number of Setups Holding cost Setup cost 2024.692 1717.921 858.9604 30.86889 9878.044 9878.044 Total cost, Tc 19756.09 (Inventory models for independent demand, moderate) 124. Holstein Computing manufactures an inexpensive audio card (Audio Max) for assembly into several models of its microcomputers. The annual demand for this part is 100,000 units. The annual inventory carrying cost is $5 per unit and the cost of preparing an order and making production setup for the order is $750. The company operates 250 days per year. The machine used to manufacture this part has a production rate of 2000 units per day. a. Calculate the optimum lot size. b. How many lots are produced in a year? c. What is the annual cost of preparing the orders and making the setups for Audio Max? d. What is the average inventory for Audio Max? Problem requires the production order quantity model. The optimum lot size is 6,124; this lot size will be repeated 16.33 times per year. The total inventory management cost will be $24,494.90, and average inventory will be 2,449.49 units. Data Demand rate, D 100000 Setup cost, S 750 Holding cost, H 5 Daily production rate, p 2000 Daily demand rate, d 400 Results Optimal production quantity, Q* Maximum Inventory Average Inventory Number of Setups Holding cost Setup cost 6123.724 4898.979 2449.49 16.32993 12247.45 12247.45 Total cost, Tc 24494.9 (Inventory models for independent demand, moderate) 125. Huckaby Motor Services, Inc., rebuilds small electrical items such as motors, alternators, and transformers, all using a certain type of copper wire. The firm's demand for this wire is approximately normal, averaging 20 spools per week, with a standard deviation of 6 spools per week. Cost per spool is $24; ordering costs are $25 per order; inventory handling cost is $4.00 per spool per year. Acquisition lead time is four weeks. The company works 50, 5-day weeks per year. a. What is the optimal size of an order, if minimization of inventory system cost is the objective? b. What are the safety stock and reorder point if the desired service level is 90%? EOQ 2  20  50 25 112 spools; SS 4 and ROP=20  4 + 16 = 96 spools. Data Demand rate, D Setup cost, S Holding cost, H Unit Price, P Daily demand rate Lead time in days Results Optimal Order Quantity, Q* Maximum Inventory Average Inventory Number of Setups Holding cost Setup cost 1.29  64 15.48 spools; 1000 25 4 24 4 20 111.803399 111.803399 55.9016994 8.94427191 $223.61 $223.61 Unit costs $24,000.00 Total cost, Tc $24,447.21 (Probabilistic models with constant lead time, moderate) 126. Demand for ice cream at the Ouachita Dairy can be approximated by a normal distribution with a mean of 47 gallons per day and a standard deviation of 8 gallons per day. The new management desires a service level of 95%. Lead time is four days; the dairy is open seven days a week. What reorder point would be consistent with the desired service level? SS = 1.65  8  4 = 26.4 gallons; and ROP = 47* 4 + 26.4 = 214.4 gallons. (Probabilistic models with constant lead time, moderate) 127. The Winfield Distributing Company has maintained an 80% service level policy for inventory of string trimmers. Mean demand during the reorder period is 170 trimmers, and the standard deviation is 60 trimmers. The annual cost of carrying one trimmer in inventory is $6. The area sales people have recently told Winfield's management that they could expect a $400 improvement in profit (based on current figures of cost per trimmer) if the service level were increased to 99%. Is it worthwhile for Winfield to make this change? This is solved with a cost comparison: total costs status quo compared to total costs at higher service, as amended by the increased profit. First calculate their safety stock. SS = 0.84  60 = 50.4 trimmers at $6 each, this safety stock policy costs about $302.40. At a service level of 99%, the safety stock rises to 2.33  60 = 139.8, which will cost $838.80. The added cost is $536.40, which is more than the added profit, so Winfield should not increase its service level. (Probabilistic models with constant lead time, moderate) 128. Daily demand for a product is normally distributed with a mean of 150 units and a standard deviation of 15 units. The firm currently uses a reorder point system, and seeks a 75% service level during the lead time of 6 days. a. What safety stock is appropriate for the firm? b. What is the reorder point? SS = 0.67  15  6 = 26.6; ROP = 150  6 + 26.6 = 926.6 (Probabilistic models with constant lead time, moderate) 129. Daily demand for a product is normally distributed with a mean of 200 units and a standard deviation of 2 units. The firm currently uses a reorder point system, with a lead time of 4 days. a. What safety stock provides a 50% service level? b. What safety stock provides a 90% service level? c. What safety stock provides a 99% service level? Standard deviation during lead time is 20  4 = 40 units. Z is 0 for 50% service level, 1.29 for 90%, and 2.33 for 99%. The resulting safety stocks are 0, 51.6, and 93.2. (Probabilistic models with constant lead time, moderate) 130. Clement Bait and Tackle has been buying a chemical water conditioner for its bait (to help keep its baitfish alive) in an optimal fashion using EOQ analysis. The supplier has now offered Clement a discount of $0.50 off all units if the firm will make its purchases quarterly. Current data for the problem are: D=1800 units per year; S = $6.00, I = 15% per year; P = $25. a. What is the EOQ at the current behavior? b. What is the annual total cost of continuing their current EOQ-based behavior? c. What is the annual total cost, if they accept the proposed discount? d. At the cheaper of the two total costs, are carrying costs equal to ordering costs? Explain. (a) Approximately 85 units (b) $45,424.26 (c) Placing orders on a quarterly basis implies four order per year. Therefore, D/Q = 4, Q=D/4 = 1800/4 = 450. Therefore, consider whether placing an order of 450 with a 50 cent reduction is worthwhile. Their cost would be $45,242.50. Therefore order quarterly. (d) They are not; accepting the discount requires an order quantity that is not EOQ. Purchasing 85 units at a time led to setup costs and holding costs of 212.13 each. With the discount, setup costs are $40 while holding costs are $1,102.50. Data Demand rate, D Setup cost, S Holding cost %, I 1800 10 20% Range 1 Minimum quantity Unit Price, P Range 2 1 25 450 24.5 Results Q* (Square root formula) Order Quantity Holding cost Setup cost Unit costs Range 1 Range 2 84.8528137 85.7142857 84.8528137 450 $212.13 $212.13 $1,102.50 $40.00 $45,000.00 $44,100.00 Total cost, Tc $45,424.26 $45,242.50 (Inventory models for independent demand, moderate) 131. The annual demand for an item is 10,000 units. The cost to process an order is $75 and the annual inventory holding cost is 20% of item cost. What is the optimal order quantity, given the following price breaks for purchasing the item? What price should the firm pay per unit? What is the total annual cost at the optimal behavior? Quantity 1-9 10 - 999 1,000 - 4,999 5,000 or more Price $2.95 per unit $2.50 per unit $2.30 per unit $1.85 per unit The firm should pay $1.85 per unit by ordering 5000 units at a time. This is above the 2014 EOQ of the next higher price break. Since the firm is not ordering an EOQ amount, ordering costs and carrying costs will not be equal, but total costs are still minimized. Data Demand rate, D Setup cost, S Holding cost %, I 10000 75 20% Range 1 1 2.95 Range 2 10 2.5 Range 3 1000 2.3 Range 1 Range 2 Range 3 1805.7878 1805.7878 Range 4 2013.46817 5000 $415.33 $415.33 $925.00 $150.00 $23,000.00 $18,500.00 Total cost, Tc $23,830.66 (Inventory models for independent demand, moderate) $19,575.00 Minimum quantity Unit Price, P Range 4 5000 1.85 Results Q* (Square root formula) Order Quantity Holding cost Setup cost Unit costs 132. The annual demand for an item is 40,000 units. The cost to process an order is $40 and the annual inventory holding cost is $3 per item per year. What is the optimal order quantity, given the following price breaks for purchasing the item? Quantity 1-1,499 1,500 - 4,999 5,000 or more Price $2.50 per unit $2.30 per unit $2.25 per unit a. What is the optimal behavior? b. Does the firm take advantage of the lowest price available? Explain. a. Purchase 1500 units at a time, paying $2.30 each. b. It is not advantageous to pay $2.25 if that requires ordering 5000 units. The annual cost is $97,820.00 at the $2.25 price versus $95,316.67 annual cost at the $2.30 price. Data Demand rate, D Setup cost, S Holding cost, H 40000 40 3 Range 1 Minimum quantity Unit Price, P 1 2.5 Range 2 Range 3 1500 5000 2.3 2.25 Results Q* (Square root formula) Order Quantity Holding cost Setup cost Range 1 Range 2 Range 3 1032.795559 1032.79556 1032.79556 1032.795559 1500 5000 $1,549.19 $1,549.19 $2,250.00 $1,066.67 $7,500.00 $320.00 $100,000.00 $92,000.00 $90,000.00 Total cost, Tc $103,098.39 $95,316.67 (Inventory models for independent demand, moderate) $97,820.00 Unit costs 133. A local artisan uses supplies purchased from an overseas supplier. The owner believes the assumptions of the EOQ model are met reasonably well. Minimization of inventory costs is her objective. Relevant data, from the files of the craft firm, are annual demand (D) =150 units, ordering cost (S) = $42 per order, and holding cost (H) = $4 per unit per year a. How many should she order at one time? b. How many times per year will she replenish its inventory of this material? c. What will be the total annual inventory costs associated with this material? d. If she discovered that the carrying cost had been overstated, and was in reality only $1 per unit per year, what is the corrected value of EOQ? a & b. She should order 56 units at a time, 2.67 times per year. c. The inventory costs are $112 for holding and $112 for ordering, or $224 total. d. At the lower value for H, the EOQ will be double, and order frequency will be cut in half. Data Demand rate, D Setup cost, S Holding cost, H Results Optimal Order Quantity, Q* Maximum Inventory Average Inventory Number of Setups 150 42 4 56.1248608 56.1248608 28.0624304 2.67261242 Holding cost $112.25 Setup cost $112.25 (Inventory models for independent demand, moderate) 134. Groundz Coffee Shop uses 4 pounds of a specialty tea weekly; each pound costs $16. Carrying costs are $1 per pound per week because space is very scarce. It costs the firm $8 to prepare an order. Assume the basic EOQ model with no shortages applies. Assume 52 weeks per year, closed on Mondays. a. How many pounds should Groundz order at a time? b. What is total annual cost (excluding item cost) of managing this item on a costminimizing basis? c. In pursuing lowest annual total cost, how many orders should Groundz place annually? d. How many days will there be between orders (assume 310 operating days) if Groundz practices EOQ behavior? a. Groundz should order 8 pounds per order b. 26 times per year, (or a reasonable integer combination nearby). c. The firm will spend $516 managing this time in inventory. d. Days between orders will be 312/26 or approximately every 12 working days. Data Demand rate, D Setup cost, S Holding cost, H Results Optimal Order Quantity, Q* Maximum Inventory Average Inventory Number of Setups 208 8 52 8 8 4 26 Holding cost $208.00 Setup cost $208.00 (Inventory models for independent demand, moderate) 135. Pointe au Chien Containers, Inc., manufactures in batches; the manufactured items are placed in stock. Specifically, the firm is questioning how best to manage a specific wooden crate for shipping live seafood, which is sold primarily by the mail/phone order marketing division of the firm. The firm has estimated that carrying cost is $4 per unit per year. Other data for the crate are: annual demand 60,000 units; setup cost $300. The firm currently plans to satisfy all customer demand from stock on hand. Demand is known and constant. a. What is the cost minimizing size of the manufacturing batch? b. What is the total cost of this solution? The cost-minimizing batch size is 3000 crates. This will cost $12,000 per year in inventory management costs. Data Demand rate, D Setup cost, S Holding cost, H 60000 300 4 Results Optimal Order Quantity, Q* Maximum Inventory Average Inventory Number of Setups 3000 3000 1500 20 Holding cost $6,000.00 Setup cost $6,000.00 (Inventory models for independent demand, moderate) 136. Holding costs are $35 per unit per year, the ordering cost is $120 per order, and sales are relatively constant at 300 per month. What is the optimal order quantity? Order size is 157; annual inventory expenses are $5,499.10 Data Demand rate, D Setup cost, S Holding cost, H Results Optimal Order Quantity, Q* Maximum Inventory Average Inventory Number of Setups 3600 120 35 157.116881 157.116881 78.5584405 22.9128785 Holding cost $2,749.55 Setup cost $2,749.55 (Inventory models for independent demand, moderate) 137. The inventory management costs for a certain product are S=$8 to order, and H=$1 to hold for a year. Annual demand is 2400 units. Consider the following ordering plans: a. Order all 2400 at one time b. Order 600 once each quarter c. Order 200 once each month Calculate the annual costs associated with each plan. Plot these values. Is there another plan, cheaper than any of these? Calculate this, and plot it. Label your graph carefully. 2400 TC 8 1  1  2 2400 EOQ 1208; 600 TC 8 4  1  2 600 322; 200 TC 8  12 1  2 200 2 24008 196 is the cheapest solution. 1 The graph cannot easily show the difference between Q = 196 and Q - 200, but the increase in cost for Q=600 and Q=2400 are dramatic. (Inventory models for independent demand, difficult) 138. An organization has had a policy of ordering 70 units at a time. Their annual demand is 340 units, and the item has an annual carrying cost of $2. The assumptions of the EOQ are thought to apply. For what value of ordering cost would this order size be optimal? 70 2( 340)S , solving for S results in S = $14.41 2 (Inventory models for independent demand, difficult) 196 139. Joe's Camera shop has a favorite model that has annual sales of 145. The cost to place an order to replenish inventory is $25 per order, and annual inventory costs are $20. Assume the store is open 350 days per year. a. What is the optimal order size? b. What is the optimal number of orders per year? c. What is the optimal number of days between orders? d. What is the annual inventory cost? a. The EOQ is approximately 19. b. The optimal number of orders per year is 7.62. c. The optimal number of days between orders is 350/7.62 = 45.9 days. d. The annual inventory cost is $380.78. 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 145 25 20 19.0394328 19.0394328 9.51971638 7.61577311 Holding cost $190.39 Setup cost $190.39 (Inventory models for independent demand, difficult)