1.Practice Problems: Chapter 12, Inventory Management Problem 1: ABC Analysis Stock NumberAnnual $ VolumePercent of Annual $ VolumeJ2412,50046.2R269,00033.3L023,20011.8M121,5505.8P336202.3T72650.2S67530.2Q47320.1V20300.1 = 100.0What are the appropriate ABC groups of inventory items?

2. Problem 2: A firm has 1,000 A items (which it counts every week, i.e., 5 days), 4,000 B items (counted every 40 days), and 8,000 C items (counted every 100 days). How many items should be counted per day? Problem 3: Assume you have a product with the following parameters: Demand = 360 Holding cost per year = $1.00 per unit Order cos t: = $100 per order What is the EOQ? Problem 4: Given the data from Problem 3, and assuming a 300-day work year; how many orders should be processed per year? What is the expected time between orders? Problem 5: What is the total cost for the inventory policy used in Problem 3? Problem 6: Assume that the demand was actually higher than estimated (i.e., 500 units instead of 360 units). What will be the actual annual total cost? Problem 7: If demand for an item is 3 units per day, and delivery lead-time is 15 days, what should we use for a re-order point? Problem 8: Assume that our firm produces type C fire extinguishers. We make 30,000 of these fire extinguishers per year. Each extinguisher requires one handle (assume a 300 day work year for daily usage rate purposes). Assume an annual carrying cost of $1.50 per handle; production setup cost of $150, and a daily production rate of 300. What is the optimal production order quantity? 3. Problem 9: We need 1,000 electric drills per year. The ordering cost for these is $100 per order and the carrying cost is assumed to be 40% of the per unit cost. In orders of less than 120, drills cost $78; for orders of 120 or more, the cost drops to $50 per unit. Should we take advantage of the quantity discount? Problem 10: Litely Corp sells 1,350 of its special decorator light switch per year, and places orders for 300 of these switches at a time. Assuming no safety stocks, Litely estimates a 50% chance of no shortages in each cycle, and the probability of shortages of 5, 10, and 15 units as 0.2, 0.15, and 0.15 respectively. The carrying cost per unit per year is calculated as $5 and the stockout cost is estimated at $6 ($3 lost profit per switch and another $3 lost in goodwill, or future sales loss). What level of safety stock should Litely use for this product? (Consider safety stock of 0, 5, 10, and 15 units) Problem 11: Presume that Litely carries a modern white kitchen ceiling lamp that is quite popular. The anticipated demand during lead time can be approximated by a normal curve having a mean of 180 units and a standard deviation of 40 units. What safety stock should Litely carry to achieve a 95% service level? 4. ANSWERS Problem 1: ABC Groups ClassItemsAnnual VolumePercent of $ VolumeAJ24, R2621,50079.5BL02, M124,75017.6CP33, T72, S67, Q47, V208002.9 = 100.0Problem 2: Item ClassQuantityPolicyNumber of Items to Count Per DayA1,000Every 5 days1000/5 = 200/dayB4,000Every days40 4000/40=100/dayC8,000Every days100 8000/100=80/dayTotal items to count: 380/day 5. Problem 3: EOQ =2 * Demand * Order cost = Holding cost2 * 360 * 100 = 72000 = 268 items 1Problem 4:N=Demand 360 = = 134 orders per year . Q 268T=Working days = 300 / 1.34 = 224 days between orders Expected number of ordersProblem 5:TC =Demand * Order Cost (Quantity of Items) * ( Holding Cost ) 360 * 100 268 * 1 + = + = 134 + 134 = $268 Q 2 268 2Problem 6:TC =Demand * Order Cost (Quantity of Items) * ( Holding Cost ) 500 * 100 268 * 1 + = + = 186.57 + 134 = $320.57 Q 2 268 2Note that while demand was underestimated by nearly 50%, annual cost increases by only 20% (320 / 268 = 1.20) an illustration of the degree to which the EOQ model is relatively insensitive to small errors in estimation of demand. Problem 7: ROP = Demand during lead - time = 3 * 15 = 45 unitsProblem 8:Q* = p2 * Demand * Order Cost = Daily Usage Rate Holding Cost 1 Daily Pr oduction RateProblem 9:F G HI J K( 2)(30,000)(150) = 3000 units 100 150 1 . 300F I G J H K 6. Q* ($78) = p(2)(1000)(100) = 80 units (0.4)(78)Q* ($50) = p(2)(1000)(100) = 100 units = 120 to take advantage of quantity discount. (0.4)(50)Ordering 100 units at $50 per unit is not possible; the discount does not apply until 120 the order equals 120 units. Therefore, we need to compare the total costs for the two alternatives. Demand * Order Cost ( Quantity of Items) * ( Holding cos t ) + Q 2Total cos t = Demand * Cost +Total cos t ($78) = (1000)(78) +(1000)(100) (80)(0.4)(78) + = $80,498 80 2Total cos t ($50) = (1000)(50) +(1000)(100) (120)( 0.4)(50) + = $52,033 120 2Therefore, we should order 120 each time at a unit cost of $50 and a total cost of $52,033. Problem 10: Safety stock = 0 units: Carrying cost equals zero.Stockout cos ts = (Stockout cos t * possible units of shortage * probability of shortage * number of orders per year ) S0 = 6 * 5* 0.2 *1350 1350 1350 + 6 * 10 * 015* . + 6* 15* 015* . = $128.25 300 300 300Safety stock = 5 units: Carrying cos t = $5 per unit * 5 units = $25. Stockout cost: S5 = 6* 5* 015*1350 1350 + 6 * 10 * 015* . = $60.75 300 300 7. Total cos t = carrying cos t + stockout cos t = $25 + $60.75 = $85.75 Safety stock = 10 units: Carrying cos t = 10 * 5 = $50.00. Stockout cost: S10 = 6* 5* 015*1350 = $20.25 300Total cos t = carrying cos t + plus stockout cos t = $50.00 + $20.25 = $70.25 Safety stock = 15: Carrying cos t = 15* 5 = $75.00 Stockout cos ts = 0 (there is no shortage if 15 units are maintained) Total cos t = carrying cos t + stockout cos t = $75.00 + $0 = $75.00 Therefore: Minimum cost comes from carrying a 10-unit safety stock. Problem 11: To find the safety stock for a 95% service level it is necessary to calculate the 95th percentile on the normal curve. Using the standard Normal table from the text, we find the Z value for 0.95 is 1.65 standard units. The safety stock is then given by: (165* 40) + 180 = 66 + 180 = 246 Ceiling Lamps .