Advanced: Calculation of stockholding costs, costs of stockouts when demand is uncertain and a discussion of JIT Rainbow Ltd is a manufacturer which uses alkahest in many of its products. At present the company has an alkahest plant on a site close to the company’s main factory. A summary of the alka¬ hest plant’s budget for the next year is shown below.

The budget covers costs up to and including the cost of piping finished alkahest to the main factory. At the main factory alkahest can be stored at a cost of £20 per annum per thousand litres, but addi¬ tional costs arise in storage because alkahest evaporates at a rate of 5% per annum. Production of alkahest is adjusted to meet the demands of the main factory; in addition safety stocks of 60 000 litres are maintained in case of disruption of supplies.
The alkahest plant has a limited remaining life and has been fully depreciated. The management of Rainbow Ltd is considering whether the plant should be retained for the time being or should be closed immediately. On closure the equipment would be scrapped and the site sold for £400 000. Employees would be redeployed within the company and supplies of alkahest would be bought from an outside supplier.
Rainbow Ltd has found that Alchemy pic can supply all its alkahest requirements at £370 per thousand litres. Transport costs of £30 per thou¬ sand litres would be borne by Rainbow Ltd. There would be administration costs of £15 000 per year, in addition to order costs of £60 for each delivery. It has been decided that if purchases are made from Alchemy pic the safety stock will be increased to 100 000 litres.
Rainbow Ltd has 250 working days in each year and a cost of capital of 15% per annum. The company’s current expectations for demand and costs apply for the foreseeable future.
Requirements:

(a) Calculate the total annual costs of the options available to Rainbow Ltd for its supply of alkahest and interpret the results for manage¬ ment. (10 marks)

(b) Calculate the expected annual stock-outs in litres implied by a safety stock of 100000 litres and calculate the stock-out cost per litre at which it would be worthwhile to increase safety stock from 100000 litres to 120 000 litres, under the following assumptions:
(i) for any delivery there is a 0.8 probability that lead time will be 5 days and a 0.2 probability that lead time will be 10 days, and (ii) during the lead time for any delivery there is a 0.5 probability that Rainbow Ltd will use alkahest at the rate of 10 000 litres per day and a 0.5 probability that the company will use alkahest at the rate of 14 000 litres per day. (6 marks)

(c) Explain the requirements for the successful adoption of a just-in-time inventory policy and discuss the relative costs and benefits of just-in-time policies compared with economic-order-quantity policies.

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Production 3 000 000 litres of alkahest Variable manufacturing costs 840 000 Fixed manufacturing costs 330000