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C hapter 31

SOLUTIONS. C hapter 31. INVENTORY MANAGEMENT. PROBLEM 31.10. The following information is available relating to the stock-out of a firm: Stock-out (units) Number of times 800 2 600 3 400 5 200 10 0 30 50

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C hapter 31

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  1. SOLUTIONS Chapter 31 INVENTORY MANAGEMENT

  2. PROBLEM 31.10 • The following information is available relating to the stock-out of a firm: • Stock-out (units) Number of times • 800 2 • 600 3 • 400 5 • 200 10 • 0 30 • 50 • The selling price of each unit is Rs 200. The carrying costs are Rs 20 per unit. The stock-out costs are Rs 50 per unit. • (a) If the firm wishes never to miss a sale, what should be its safety stock? What is the total cost associated with this level of safety stock? • (b) What is the optimum safety stock level?

  3. SOLUTION 31.10 (i) Computation of expected stock-out cost Safety stock Stock-out Stock-out Probability of Expected Total expected level (units) costs (Rs 50 stock-out stock-out cost at stock-out per unit ) this level costs 800 0 0 0 0 0 600 200 Rs 10,000 0.04 Rs 400 Rs 400 400 400 20,000 0.04 800 200 10,000 0.06 600 1,400 200 600 30,000 0.04 1,200 400 20,000 0.06 1,200 3,400 200 10,000 0.10 1,000 0 800 40,000 0.04 1,600 600 30,000 0.06 1,800 400 20,000 0.10 2,000 7,400 200 10,000 0.20 2,000 (ii) Computation of total safety costs Safety stock Expected stock- Carrying cost Total safety (units) out costs (Rs 19 per unit) stock cost 0 Rs 7,400 0 Rs 7,400 200 3,400 Rs 3,800 7,200 400 1,400 7,600 9,000 600 400 11,400 11,800 800 0 15,200 15,200 (i) The safety stock should be 800 units if the firm never wishes to miss a sale. The total cost associated with this level of safety stock is Rs 15,200. (ii) The optimal safety stock is 200 units.

  4. PROBLEM 31.12 • (a) From the following determine the EOQ: • (i) List price of product (Rs 800 per gross). • (ii 40 per cent trade discount is allowed on list price on purchases in gross lots. • (iii) Freight cost is Rs 20 per gross from the transport company to the factory premises. • (iv) Annual usage of product, X: 36 gross per year. • (v) Cost of placing an order is Rs 10, the cost of receiving an order is Rs 20. • (vi) Carrying cost is 20 per cent per year of the effective purchase price of goods. • (vii) Insurance taxes are approximately 12 per cent of the net delivered cost of inventory. • (b) Determine the total annual cost of the inventory based on uniform order lot sizes of one, two, three, four, five and six gross of product X. • (c) Determine the minimum stock and reorder point for product X, given the following: • (i) working days, 240; • (ii) normal delivery time to receive an order, 20 working days from the date a purchase request is initiated; • (iii) safety stock, 1 gross.

  5. = = 19.28 (2X36X30)/112 SOLUTION 31.12 • (i) EOQ (in gross lots) • 4.4 or 4 gross (as purchases are allowed in gross lots). The figure is not revised upward (as is normally done to 5) as it will require 7.2 orders (36 ÷ 5). • Working notes • B =Cost of placing an order Rs 10 • Plus cost of receiving an order 20 • Total buying cost per order 30 • C = List price per gross 800 • Less 40 per cent trade discount 320 • Net price 480 • Plus freight cost per gross 20 • Plus insurance and taxes (0.12 ´ Rs 500) 60 • Effective purchase price per gross 560 • Carrying cost per gross = 0.2XRs 560 112 • (ii) Statement showing total annual cost of inventory • 1 Size of quantity order (gross) 1 2 3 4 5 6 • 2 Number of orders 36 18 12 9 8* 6 • 3 Cost per order (Rs) 30 30 30 30 30 30 • 4 Total order cost (2 ´ 3) 1,080 540 360 270 240 180 • 5 Carrying cost per gross (Rs) 112 112 112 112 112 11 • 6 Average inventory (size of order ÷ 2) 0.5 1 1.5 2 2.5 3 • 7 Total carrying cost (5 ´ 6) 56 112 168 224 280 336 • 8 Total annual cost (4 + 7) 1,136 652 528 494 520 516 • *More than 7 orders are to be placed to have 36 gross quantity and, therefore, 8 orders. • (iii) Re-order level (minimum stock): = Safety stock + (daily usage ´ lead time) = 1 gross + (36 gross/240 days) ´ 20 days = 4 gross.

  6. FINANCIAL END OF THE CHAPTER MANAGEMENT

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