Practice question (inventory models)
pratiksha saxena
Q.1 XYZ manufacturer expects to produce 2,000 widgets during the year ending June 20, 1999 to supply a demand that is uniform throughout the year. The set up cost of each production run of widgets is Rs. 144 and the variable cost of producing each widget is Rs. The cost of carrying one in inventory is Rs. 20 per year. After a batch of widgets is produced and placed in inventory, it is sold at a uniform rate and inventory is exhausted when the next batch of widgets is completed.
Management wants an equation to describe this situation and determine the optimum quantity of widgets to produce in each run in order to minimize total production and inventory carrying costs.
Problems 10.1
Q.2 A trading company buys and sells 10,000 bottles of pain- balm every year. The cost per bottle is Rs. 2 and company’s cost of placing an order of pain- balm is Rs 100 the Company’s standard annual rate of return on working capitals funds is 15%. The cost of physical storage of the pain-balm is fixed (i) Determine the optimum order quantity cycle duration for the pain- balm, (ii) Haw many orders should be placed each year? (iii) Find the total variable annual inventory cost for the pain-balm.
Problems 10.6
Q.3 The Deena paints Ltd. Would like to improve its inventory managements policies for the supply of paint used for automobiles. Annual demand for such paint is 50,000 liters, and the paint, which costs Rs. 20 per litre, is use at a constant rate. Annual carrying costs are estimated at per cent of the value of paint held. Each order costs Rs. 80. Determine:
(I). How much Paint should be ordered each time?
(ii). How often should paint be ordered ?
(iii) Time between two consecutive orders
(iv). what is the total annual cost associated with this policy?
Problems 10.10
Q.4 (i) XYZ company buys in lots of 500 boxes which is a 3 month supply. The cost per box is Rs. 125 and the ordering cost is Rs. 150. The inventory carrying cost is estimated at 20% of unit value. What is the total cost of the existing inventory policy?
(i) How much money could be saved by employing the economic order quantity?
Problems 10.13
Q.5 A company works 50 week in year. For a certain part, included in the assembly of several parts, there is an annual demand of 10,000 units.
This part may be obtained from either an outside supplier or a subsidiary company. The following data relating to the part are given.
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From outside supplier from subsidiary company Rs Rs |
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Purchase price per unit 12 13 Cost of placing an order 10 10 Cost of receiving an order 20 15 Storage and all carrying costs Including capital cost per unit Per annual 02 02
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(i) What purchase quantity and from which source would you recommend?
(ii) What would be the minimum total cost?
Problem 10.15
Q.6 A Company manufacturing automobiles decides to make a particular item A in batches. Following data are available:
(I) Cost of setting up special tooling: Rs. 900
(ii) Annual rate of interest, depreciation, ect.,:20%
(iii) Consumption of part in assembly shop : 60 per month
(iv) Processing of each item take 4 hour on the machine. Labour rate is Rs. 24 per 8 hour- day. Material cost: Rs 9 per item.
(v) Overhead expenditure calculated on prime cost is at 150%
Find out the economic batch size for machining and also during of batch run, assuming that machine loading factor is 90%
Problem 10.18
Q.7 A product is sold at the rate of 50 pieces per day and is manufacturing at a rate of 250 pieces per day. The set up cost of machines are Rs. 2000 and the storage costs are found to be Re. 0.0030 per piece per day. With labour charges of Rs. 640 per piece, material cost at Rs. 4.20 per piece and overhead of Rs. 8.20 per piece. Find the minimum cost batch size if the interest charges are 12 per cent, ( Assume 300 working days in a year.
Problem 10.19
Q.8 (a) At present a company is purchasing an item ‘X’ from outside suppliers. The consumption is 10,000 units per year. The cost of the item is Rs. 5 per unit and the ordering cost of estimated to be Rs. 100 per order. The cost of carrying inventory is 25% if the consumption rate the uniform, determine the economic purchasing quantity.
(b) In the above problem assume that company is going to manufacture the above item with the equipment that is estimate to produce 100 units per day. The cost of the unit thus produced is Rs. 3.50 per unit. The set-up cost is 150 per set-up and the inventory carrying charge is 25%. How has your answer changed?
(Assume 250 working days in the year)
Problem 10.18
Q.9 A dealer supplies you the following information with regard to a product dealt in by him:
Annual demand: 10,000 units: ordering cost: Rs. 10 per order: price : Rs. 20 per unit
Inventory carrying cost: 20% of the value of inventory per year.
The dealer is considering the possibility of allowing some back order (stock out) to occur. He has estimated that the annual cost of backordering will be 25% of the value of inventory,
(i) What should be the optimum number of unit of the product he should buy in one lot?
(ii) What quantity of the product should be allowed to be back –ordered, if any?
(iii) What would be the maximum quantity of inventory at any time of the year?
(iv) Would you recommend allowing back- ordered? If so, what would be the annual cost saving by adopting the policy of back- ordering.
Problem 10.22
Q.10 Consider the following data:
Unit cost : Rs. 100
Order Cost : Rs. 160
Inventory carrying cost : Rs. 20
Back-order cost : Rs. 10
(Stock out cost)
Annual demand : Rs. 1,000 units
Computing the following:
(i) Minimum cost order quantity (ii) Time between orders, (iii) Maximum number of back order, (iv) Overall annual cost.
Problem 10.18
Q.11 A purchase Manager has decided to place order for a minimum quantity of 500 numbers of a particular item in order to get or discount of 10%. From the past records, it was found out that in the last year, 8 orders each of size 200 units ware placed. Give the ordering cost = Rs. 500 per order, inventory carrying cast of 40% of the inventory value and the price of the item of Rs. 400 per unit. Is the purchase manager justified in his decision? What is the effect of his decision to the company?
Problem 10.29
Q.12 A material manager has the following data for procuring a particular item. Annual demand = 1000, ordering cost = 800, inventory carrying cost = 40%, cost per item = RS. 60. If the order quantity is more than or equal to 300, a discount of 10% is given. For how the order in much should be place order to minimize the total variable cost.
Problem 10.18
Q.13 A hardware store procures and sells hardware goods. Data for an item are given bellow:
Expected sales per year =2500 units
Ordering cost per year = 12.50
Holding Cost = 25% of average yearly inventory
Number of working days per year =250
The item can be bought according to any of the three prices and the price schedule is:
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Unit Price Lot size (units) |
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Rs. 4.00 1-259 Rs. 3.60 260-999 Rs. 3.24 1,000 and above |
Daily demand can be considered a constant value. Determine the inventory policy that will yield a minimum total inventory cost.
Problem 10.31
Q.14 The annual demand for a product is 64,000 units ( for 1228 units per week ) The buying cost per order is Rs. 10 and the estimated cost of carrying one unit of stock for a year is 20%. The annual price of the product is Rs. 10 per unit. However, the supplier offers a quantity discount of 2% on an order of at least 1000 units at a time, and a discount of 5% if the order is for at least 5,000 units,
Suggest the most economic purchase quantity per order.
Problem 10.32
Q.15 A shopkeeper has a uniform demand of an item as the rate of 100 items per month. He buys from supplier at accost of Rs. 12 per time and the cost of ordering is Rs. 10 each time If the stock holding costs are 20 per cent per year of stock value, how frequency should be replenish his stock? Further, suppose the supplier offers a 5 per cent discount on order between 200 and 999 items, and a 10 per cent discount an orders exceeding or equal to 1000, can the shopkeeper reduces his cost by taking advantage of either of these discounts?
