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# Post Graduate Diploma in Management Supply Chain Modelling- Numerical Problems Inventory &amp;amp; Supply Chain Management 1. An item has annual...

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Post Graduate Diploma in Management Supply Chain Modelling– Numerical Problems Inventory & Supply Chain Management 1. An item has annual demand of 10000 units. Annual carrying cost is at the rate of 20%. Ordering cost is Rs 150 per order & purchase cost is Rs. 5.00 per unit. Calculate EOQ, Annual cost of ordering, Annual cost of carrying & Time between orders. 2. If in the above question the item is manufactured at the production rate of 500 units per week, what will be the EMQ, Annual cost of ordering, Annual cost of carrying & Time between orders. 3. A manufacturer buys cardboard boxes from a supplier. The monthly demand is 3000 boxes and is uniform throughout the year. The cost of each box is Rs. 4.00. The estimated order cost is Rs. 6.00 and the carrying cost is 2.5% per month. (a) What are the EOQ, the annual order & carrying cost? (b) If the actual demand turns out to be 6000 per month, and you have used the EOQ as calculated in sec (a), what would be the annual order & carrying cost? 4. A company manufactures cardboard box. The annual demand is 36000 boxes and is uniform throughout the year. The cost of each box is Rs. 4.00. The estimated set up cost is Rs. 6.00 and the carrying cost is 30% per year. The production rate is 200 boxes per day. The company works for 5 days a week. What are the EMQ, the annual order & carrying cost? Calculate the purchase order cycle time. 5. A computer reseller stocks three brands of PCs; HCL, Zenith & LG. Annual demands for three brands are 12000 for HCL PCs, 1200 for Zenith PCs & 120 for LG PCs. Assume that each model costs the reseller Rs. 25000. A fixed transportation cost of Rs. 15000 is incurred each time an order is delivered. For each brand ordered and delivered on the same truck, an additional fixed cost of Rs. 2500 is incurred for receiving & storage. The reseller incurs a holding cost of 20 percent. ()a Evaluate the lot sizes that the manager at the reseller should order if lot for each brand are ordered & delivered independently. ()b What would be the optimal lot size for each brand if the manager decides to aggregate and order all three brands each time he places order. 6. A TV reseller stocks three brands of 21” TVs; LG, ONIDA & Bestavision. Annual demands for three brands are 15000 for LG TVs, 1500 for ONIDA TVs & 150 for Bestavision TVs. Assume that each model costs the reseller Rs. 6000. A fixed transportation cost of Rs. 4000 is incurred each time an order is delivered. For each brand ordered and delivered on the same truck, an additional fixed cost of Rs. 500 is incurred for receiving & storage. The reseller incurs a holding cost of 20 percent. (a) Evaluate the lot sizes that the manager at the reseller should order if lot for each brand are ordered & delivered independently. (b) What would be the optimal lot size for each brand if the manager decides to aggregate and order all three brands each time he places order. 7. Twinkle Industries, a small scale unit, is a supplier of speedometers to Jumbo Corporation, a large 150 cc two wheeler manufacturer. It supplies 20,000 speedometers to Jumbo annually. At Jumbo the ordering cost per order is Rs. 5.00 and the carrying cost is 2.5% of the product price. The price of a single unit is Rs. 200. The company presently has a policy of placing 10 orders every year. Advise the management of Jumbo as to whether it should continue with its present policy or switch over to EOQ model. SCM July 2012 1 Dr. A. K. Dey
8. Mr. Jain is a retailer of computer peripherals in Nehru Place. The fastest moving item from his shop is Samsung 15 inch colour monitor. Demand for monitors from his shop is 1500 per month. Mr. Jain incurs a fixed order placement, transportation and receiving cost of Rs. 3200 each time an order is placed. Each monitor costs Rs 3600 and the holding cost is 20%. ()a Evaluate the number of monitors Mr. Jain should order in each replenishment lot. ()b If Mr. Jain wishes to reduce the lot size to 200, by how much the order cost per lot should be reduced? 9. Assume the weekly demand of 1 Kg pack of mango pickles at a Panch Ranga (a famous brand of pickles) outlet is normally distributed with mean of 1500 and standard deviation of 300. The manufacturer takes one week to fill an order placed by the outlet. The store manager currently orders 2,000 1Kg packs when the inventory on hand drops to 2000. Evaluate the safety inventory and the average inventory carried by the outlet. Also evaluate the average time spent by a pack of 1 Kg pickle at the outlet. 10. A museum of natural history opened a gift shop two years ago. Managing inventories has become a problem. Low inventory is squeezing profit margins and causing cash flow problems. One of the top selling items in the container group at the museum’s gift shop is a bird feeder. Sales are 18 units per week, and the supplier charges Rs 60 per unit. The cost of placing an order with the supplier is Rs 45. Annual holding cost is 25 per cent of a feeder’s value, and the museum operates 52 weeks per year. Management chose a 390-unit lot size so that new orders could be placed less frequently. (a) What is the annual cost of the current policy of using a 390-unit lot size? (b) Calculate EOQ and its total cost. (c) How frequently the orders be placed if the EOQ is used? (d) If we mistakenly calculate the inventory holding cost to be Rs 30/unit/year, what is the new order quantity? How much is the percentage change from the old EOQ of 75 units? (e) With this new order quantity how much is the total cost? 11. Annual demand is of 20000 boxes. Cost of placing an order is Rs. 100. Inventory carrying cost is 20% and the purchase price of each box is Rs. 10. What should be the order quantity? If the supplier offers a discount of 1% on an order of 4000 units in one lot, would you accept this discount? 12. Consider the following set of data pertaining to an inventory system and work out the inventory policy i.e., (a) EOQ and ROP when demand rate is constant and supply lead time is fixed (b) EOQ and ROP with uncertain demand but fixed lead time (c) EOQ and ROP with uncertain demand and uncertain lead time Annual average demand = 20000 units Standard deviation of the demand per week = 54 units Unit price = Rs. 700 Ordering cost = Rs. 4000 Inventory carrying cost = 5% Average lead time = 4 weeks Standard deviation of the lead time = 2 weeks Service level = 75% 13. Daily demand of a product is 20 units with standard deviation of 4 units. The review period is 30 days and lead time is 19 days. There are 250 working days in a year. The cost of the product is Rs. 200 and the carrying cost is 2.5% per month. Management has set a policy of satisfying 98% of customer demand from items in the stock. At the beginning of the review period there are 150 units in the stock. How many units should be ordered? SCM July 2012 2 Dr. A. K. Dey
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