Advanced: Safety stocks and uncertain demand and quantity discounts Runswick Ltd is a company that purchases toys
Question:
Advanced: Safety stocks and uncertain demand and quantity discounts Runswick Ltd is a company that purchases toys from abroad for resale to retail stores. The company is concerned about its stock (inventory) management operations. It is considering adopting a stock management system based upon the economic order quantity (EOQ) model.
The company’s estimates of its stock manage¬ ment costs are shown below:
The purchase price of the toys to Runswick Ltd is £4.50 per unit. There is a two week delay between the time that new stock is ordered from suppliers and the time that it arrives.
The toys are sold by Runswick at a unit price of £6.30. The variable cost to Runswick of selling the toys is £0.30 per unit. Demand from Runswick’s customers for the toys averages 10000 units per week, but recently this has varied from 6000 to 14 000 units per week. On the basis of recent evidence the probability of unit sales in any two week period has been estimated as follows:
If adequate stock is not available when demanded by Runswick’s customers in any two week period approximately 25% of orders that cannot be satis¬ fied in that period will be lost, and approximately 75% of customers will be willing to wait until new stock arrives.
Required:
(a) Ignoring taxation, calculate the optimum order level of stock over a one year planning period using the economic order quantity model. (3 marks)
(b) Estimate the level of safety stock that should be carried by Runswick Ltd. (6 marks)
(c) If Runswick Ltd were to be offered a quantity discount by its suppliers of 1% for orders of 30000 units or more, evaluate whether it would be beneficial for the company to take advantage of the quantity discount. Assume for this calculation that no safety stock is carried. (4 marks)
(d) Estimate the expected total annual costs of stock management if the economic order quantity had been (i) 50% higher (ii) 50% lower than its actual level. Comment upon the sensitivity of total annual costs to changes in the economic order quantity. Assume for this calculation that no safety stock is carried.
(4 marks)
(e) Discuss briefly how the effect of seasonal sales variations might be incorporated within the model.
(f) Assess the practical value of this model in the management of stock.
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