AUGUST 2020 (50 MARKS] Question 1 (25) Hayes Electronics stocks and sells a particular brand of laptop. It costs the firm R450 each time it places an order with the manufacturer for the laptops. The cost of carrying one laptop in inventory for a year is R170. The store manager estimates that the total annual demand for the laptops will be 1,200 units, with a constant demand rate throughout the year. Orders are received within hours after placement from a local warehouse maintained by the manufacturer. The store policy is never to have stockouts of the laptops. The store is open for business every day of the year except Christmas Day. Determine the following: Optimal order quantity per order b. Minimum total annual inventory costs The number of orders per year The time between orders (in working days) The company is not a 100%certain that the ordering cost is R450/order and the inventory carrying cost is R170/unit/year, since these inventory model parameters are frequently only estimates that are subject to some degree of uncertainty. Consider the following cases of variation in the model parameters: Both ordering cost and carrying cost are 10 percent less than originally estimated 2 Ordering cost is 10 percent higher and carrying cost is 10 percent lower than originally estimated Determine the optimal order quantity and total inventory cost for each of the two cases. Prepare a table with values from these variations and compare (discuss) the sensitivity of the model solution to changes in parameter values. Question 2 (12) A supplier has a large number of widgets in stock. In order to get rid of the stock they are offering a discount on larger orders. The supplier decides to offer a 40 cents/unit discount if 500 or more widgets are ordered. The annual demand for widgets at a specific customer, The annual demand for widgets at a specific customer, which operates under a national franchise, is 1 000 units and they currently pay R10/widget. The company's working capital is tied up in the inventory and funds have been borrowed from a bank at a simple annual interest rate of 10%. In addition, the company must pay a franchise tax of 7% of the annual inventory value and another 8% for theft insurance. The order processing cost is R50. Do you think this customer should accept this offer? (Assume that the transit time for the bigger order is the same as for any other order). Question 3 (13) VarProd (VP), a distributor of various products in Germiston receives their products from suppliers in Johannesburg, Durban and Cape Town. Management is concerned with the supply cost of a specific product that is supplied by a manufacturer in Cape Town. Currently VP uses a 3PL service provider to transport the order from Cape Town by road. The company's director of logistics has asked the logistics manager to evaluate rail transport for the shipment from Johannesburg to Cape Town. The logistics manager has obtained the following information: Annual demand (widgets) 30 000 Product value R6 500 Inventory carrying cost 20% Order cost R350 In-transit inventory carrying cost 12% Transit time (rail) 5 days Transit time (road) 2 days Rail rate R2.75/product Road rate R3.25/product 3.1 What is the economic order quantity for VP? 3.2 What is the total inventory cost (excluding transport cost) of the EOQ? 3.3 What is the total cost using road transport? 3.4 What is the total cost using rail transport? 3.5 Which transport mode should VP use
