Practice Questions-Deterministic Inventory Models

Practice questions-Deterministic inventory models Q.1 The production department of a company requires 3600 kg of raw material for manufacturing a particular item per year. It has been estimated that the cost of placing an order is Rs. 36 and the cost of carrying inventory is 25 % of the investment in the inventories. The price is Rs. 10 per kg. Help the purchase manager to determine the optimal order quantity, minimum yearly variable inventory cost and total minimum yearly inventory cost. Q.2 A company that operates for 50 weeks in a year is concerned about its stocks of copper cable. This costs Rs. 240 per meter and there is a demand for 8000 meters per week. Each replenishment costs Rs. 1050 for administration and Rs. 1650 for delivery, while holding costs are estimated at 25% of value held a year. Assuming no shortages are allowed, what is the optimal inventory policy for the company? How would this analysis differ if the company wanted to maximize its profits rather than minimize cost? What is the gross profit if the company sells the cable for Rs. 360 per meter. Q.3 Each unit of an item costs a company Rs. 40. Annual holding costs are 18% of unit cost for interest charges, 1% for insurance, 2% allowances for obsolescence Rs. 2 for building overheads, Rs. 1.5 for damage and loss, and Rs. 4 for miscellaneous costs. The annual demand for the item is constant at 1000 units. Placing each order costs the company Rs. 100. (i) Calculate Economic Order Quantity (EOQ) and the total costs associated with stocking the item. (ii) If the supplier of the item will only deliver batches of 250 units, how are the stock holding costs affected? (iii) if the supplier relaxes his order size requirement, but the company has limited warehouse space and can stock a maximum of 100 units at any time, what would be the optimal ordering policy and associated costs. Q.4 A chemical company is trying to find the optimal batch size for the reorder of concentrated sulphuric acid. The management accountant has supplied the following information: (i) The purchase price of H2SO4 is Rs. 150 per gallon. (ii) The clerical and data processing costs are Rs. 500 per order All the goods are transported by rail. Each time the special line to the factory is opened, the company is charged Rs. 2000. A charge of Rs. 20 per gallon is also made. The company uses 40000 gallons per year. Maintenance costs of stock are

Rs. 200 per gallon per year. Each gallon requires 0.5 Sqft. of storage space. If warehouse space is not used, it can be rented out to another company at Rs. 200 per sqft per annum. The available warehouse is 1000 sqft and the overhead costs being Rs. 5000 per annum. Assume that all free warehouse space can be rented out. (i) (ii)

Calculate EOQ Calculate the minimum total annual cost of holding and reordering stock.

Q. 5 A contractor has to supply 10000 bearings per day to an automobile manufacturer. He finds that when he starts production run, he can produce 25000 bearings per day. The cost of holding a bearing in stock for a year is Rs. 2 and the setup cost of a production run is Rs. 180. How frequently should production run be made? Q.6 A product is sold at the rate of 50 pieces per day and is manufactured at a rate of 250 pieces per day. The set up cost of the machines is Rs. 1000 and the storage cost is found to be Rs. 0.0015 per piece per day with labour charges of Rs. 3.2 per piece, material cost at Rs. 2.10 per piece and overhead cost of Rs. 4.10 per piece. Find the minimum cost batch size if the interest charges are 8% (assume 300 working days in a year). Compute the optimal number of cycles required in a year for manufacturing of this product. Q.7 At present a company purchases an item X from outside suppliers. The consumption of this item is 10000 units per year. The cost of the item is Rs. 5 per unit and the ordering cost is estimated to be Rs. 100 per order. The cost of carrying inventory is 25%. If the consumption rate is uniform, determine the economic purchasing quantity? In the above problem, assume that company is going to manufacture the item with the equipment that is estimated to produce 100 units per day. The cost of the unit thus produced is Rs. 3.5 per unit. The set-up cost is Rs. 150 per set-up and the inventory carrying charge is 25%. Compare the costs incurred to company is both the above cases. Q.8 The annual demand of a product is 10000 units. Each unit costs Rs. 100 if the orders are placed in quantities below 200 units. For orders of 200 or above, however, the price is Rs. 95. The annual inventory holding costs is 10% of the value of the item and the ordering cost is Rs. 5 per order. Find the economic lot size and hence the total minimum inventory cost. Q.9 A factory requires 1500 units of an item per month, each costing Rs. 27. The cost per order is Rs. 150 and the inventory carrying charges work out to be 20% of the average inventory. Find the economic order quantity and the number of orders per year. Would you accept a 2% discount on a minimum supply quantity of 1200 units? Compare the total costs in both the cases.

Q.10 A shopkeeper estimates the annual requirement of an item as 2000 units. He buys it from his supplier at a cost of Rs. 10 per item and the cost of ordering is Rs. 50 per order. If the stockholding costs are 25% per year of stock value, how frequently should he replenish his stocks? Further suppose the supplier offers a 10% discount on orders between 400 and 699 items, and a 20% discount on orders exceeding or equal to 700. Can the shopkeeper reduce his costs by taking advantage of either of these discounts? Q.11 Find the optimum order quantity of a product for which the price breaks are as follows: Quantity Range 0
Price per unit (Rs.) 20

100<=Q2<200 200<=Q3

18 16

The monthly demand for the product is 400 units. The storage cost is 20% of the unit cost of the product and the cost of ordering is Rs. 25 per order. Q.12 Find the optimum order quantity of a product for which the price breaks are as follows: Quantity Range 0
Price per unit (Rs.) 10

500<=Q2<750 750<=Q3

9.25 8.75

The monthly demand for the product is 200 units. The storage cost is 2% of the unit cost of the product and the cost of ordering is Rs. 350 per order.