# The slight difference in relevant ordering costs 8272

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The slight difference in relevant ordering costs (\$8,272) and relevant carrying costs (\$8,268) is because of rounding down the number of packages from 1,378.4 in the EOQ formula to 1,378. 3. As summarized below, the new Mona Lisa web-based ordering system, by lowering the EOQ to 1,378 packages, will lower the carrying and ordering costs by \$6,260. Soothing Meadow will spend \$2,150 to train its purchasing assistants on the new system. Overall, Soothing Meadow will still save \$4,110 in the first year alone. Total relevant costs at EOQ (from Requirement 2) \$16,540 Annual cost benefit over old system (\$22,800 – \$16,540) \$ 6,260 Training costs 2,150 Net benefit in first year alone \$ 4,110 20-13
20-27 (30 min.) EOQ, uncertainty, safety stock, reorder point . 1. 2 DP 2 120,000 \$250 EOQ C \$2.40 = 5,000 pairs of shoes 2. Weekly demand = Monthly demand ÷ 4 = 10,000 ÷ 4 = 2,500 pairs of shoes per week Purchasing lead time = 1 week Reorder point = 2,500 pairs of shoes per week × 1 week = 2,500 pairs of shoes 3. Solution Exhibit 20-27 presents the safety stock computations for Warehouse OR2 when the reorder point excluding safety stock is 2,500 pairs of shoes. The exhibit shows that annual relevant total stockout and carrying costs are the lowest (\$1,080) when a safety stock of 250 pairs of shoes is maintained. Therefore, Warehouse OR2 should hold a safety stock of 250 pairs. As a result, Reorder point with safety stock = 2,500 pairs + 250 pairs = 2,750 pairs. Reorder quantity is unaffected by the holding of safety stock and remains the same as calculated in requirement 1. Reorder quantity = 5,000 pairs Warehouse OR2 should order 5,000 pairs of shoes each time its inventory of shoes falls to 2,750 pairs. SOLUTION EXHIBIT 20-27 Computation of Safety Stock for Warehouse OR2 When Reorder Point is 2,500 Units Safety Stock Level in Units (1) Demand Levels Resulting in Stockouts (2) Stockout in Units a (3)= (2)–2,500–(1) Probability of Stockouts (4) Relevant Stockout Costs b (5)=(3)×\$2 Number of Orders per Year c (6) Expected Stockout Costs d (7)- (4)×(5)×(6) Relevant Carrying Costs e (8)= (1)×\$2.40 Relevant Total Costs (9)=(7)+(8) 0 2,750 250 0.20 \$ 500 24 \$2,400 3,000 500 0.04 1,000 24 960 \$3,360 \$ 0 \$3,360 250 3,000 250 0.04 500 24 \$ 480 \$ 600 \$1,080 500 -- -- -- -- -- \$ 0 f \$1,200 \$1,200 a Demand level resulting in stockouts – Inventory available during lead time (excluding safety stock), 2,500 units – Safety stock. b Stockout in units × Relevant stockout costs of \$2.00 per unit. c Annual demand, 120,000 ÷ 5,000 EOQ = 24 orders per year. d Probability of stockout × Relevant stockout costs × Number of orders per year. e Safety stock × Annual relevant carrying costs of \$2.40 per unit (assumes that safety stock is on hand at all times and that there is no overstocking caused by decreases in expected usage). f At a safety stock level of 500 units, no stockout will occur and, hence, expected stockout costs = \$0. 20-14
20.28 (25 min.) MRP, EOQ, and JIT. 1. Under a MRP system: Annual cost of producing and carrying J-Pods in inventory = Variable production cost + Setup cost + Carrying cost = \$54 × 48,000 + (\$10,000 × 12 months) + [\$17 × (4,000 ÷ 2)] = \$2,592,000 + \$120,000 + \$34,000 = \$2,746,000 2. Using an EOQ model to determine batch size: 2 48,000 \$10,000 2 DP EOQ C \$17 = 7,515 J-Pods per batch Production of 48,000 per year divided by a batch size of 7,515 would imply J-Pods would be produced in 6.4 batches per year. Rounding this up to the nearest whole number yields 7 batches per year, which means a production size of 48,000 ÷ 7 or 6,857 J-Pods per batch.