# The challenge for Logistics

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Problem 25.23. Calculating the cost of inventories and expenses due to shortages when demand is uncertain, a discussion of the type of "just in time".
Rainbow Ltd is a manufacturer, which is for the manufacture of many of its products using a universal solvent. Currently, the company has a plant for the production of such a solvent, it is located close to the main company. Below are the details of the budget of the plant for the next year:
Production of 3 million liters of universal solvent
Variable production costs, £ 840 000
Constant production costs, £ 330,000
The estimate provides for all expenses, including for pumping the solvent to the main business. The main company solvent can be stored at a cost of £ 20 for the year 1000 l. However, the storage requires additional cost, as 5% of the solvent evaporates during the year. Production of solvent adjusted to meet the requirements of the main production, in addition, the company retained a reserve stock of 60 000 liters in case of a supply disruption.
Plant for the production of solvent has a limited life remaining and already fully deducted by him all the amortization payments. Management of the company Rainbow Ltd is currently considering options to said plant can be saved or should be closed immediately. If it is closed, its equipment will be sent to the scrap, and the place where it is located, sold for £ 400 000. The employees will be moved to new locations within the company, while the supply of the universal solvent will come from an external supplier.
Rainbow Ltd found that the company Alchemy plc can provide a supply of the necessary amount of a solvent at a cost of £ 370 per 1000 liters. Transportation costs for 1000 liters of solvent is £ 30. For the year administrative expenses are equal to £ 15 000, and each placing an order costs £ 60. It is estimated that if the purchases do in Alchemy plc, the reserve stock will have to increase to 100 000 l.
The company annually Rainbow Ltd has 250 working days, the cost of its capital is 15% per year. An estimated performance of current demand and expense is saved in the near future.
You must do the following:
A. Calculate the total annual costs for the various options available Rainbow Ltd for the supply of a universal solvent and comment on the results obtained in terms of the management.
B. Calculate the expected value of the deficit for the year in liters when establishing the level of safety stock 100 000 liters, and calculate the cost of shortages per liter at which it would be appropriate to increase the reserve of 100 000 l 000 l to 120 the following assumptions:
(A) any delivery of 0.8 is likely that the lead time is 5 days and 0.2 - that it will be 10 days;
(B) during execution of the order for any delivery is likely to 0.5 Rainbow Ltd company will use a universal solvent at 10 to 000 liters per day, and the probability of 0.5 - 000 l at a rate of 14 per day.
Q. Explain the requirements for the successful implementation of the policy of inventory management such as "just in time" and to express their views on the relative costs and benefits of this policy over the method, which is based on an economically viable size of the order.
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