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Safety Inventory and Availability Problem Set 1. Epson produces printers in its Taiwan factory for sale in Europe. Printers sold in different countries differ in terms of the power outlet as well as the language of the manuals. Currently, Epson assembles and packs printers for sale in individual countries. The distribution of weekly demand in different countries is normally distributed, with means and standard deviations as shown in the Table below.

Weekly Demand for Epson Printers in Europe Country

Mean Demand

Standard Deviation

France

3,000

2,000

Germany

4,000

2,200

Spain

2,000

1,400

Italy

2,500

1,600

Portugal

1,000

800

UK

4,000

2,400

(a) Assume demand in different countries to be independent. Given that the lead time from the Taiwan factory is eight weeks, how much safety inventory does Epson require in Europe if it targets a CSL of 95 percent? (b) Epson decides to build a central DC in Europe. It will ship base printers (without power supply) to the DC. When an order is received, the DC will assemble power supplies, add manuals, and ship the printers to the appropriate country. The base printers are still to be manufactured in Taiwan with a lead time of eight weeks. How much saving of safety inventory can Epson expect as a result? (c) Each printer costs Epson $200, and the holding cost is 25 percent. What saving in holding cost can Epson expect as a result of building the European DC? If final assembly in the European DC adds $5 to the production cost of each printer, would you recommend the

move? (d) Suppose that Epson is able to cut the production and delivery lead time from its Taiwan factory to four weeks using good information systems. How much savings in holding cost can Epson expect without the European DC? How much savings in holding cost can the firm expect with the European DC? (e) Assume that demand in different countries is not independent. Demand in any pair of countries is correlated with a correlation coefficient of ρ = 0.4. Evaluate the holding cost savings that Epson gains as a result of building a European DC.

2. The Knitting Company (TKC) is planning production for its four sweater styles that are popular during Christmas. All four styles have demand that is normally distributed. The bestselling style has an expected demand of 30,000 and a standard deviation of 5,000. Each of the other three styles has an expected demand of 10,000 with a standard deviation of 4,000. Currently, all sweaters are produced before the start of the season. Production cost is $20 per sweater, and they are sold for a wholesale price of $35. Any unsold sweaters at the end of the season are discounted to $15, and they all sell at that price. It costs $2 to hold the sweater in inventory for the entire season if it does not sell.

(a) How many sweaters of each type should TKC manufacture? (b) What is the expected profit from this policy? (c) How many sweaters does TKC expect to sell at a discount? (d)

TKC is considering the postponement of knitting and using flexible machines. This will require the base sweaters to be made in advance (identical for each of the four types) and the final patterns to be knit later. This will increase production cost per sweater to $21.40. How many sweaters should TKC manufacture with postponement? What is the expected profit from this policy?

(e)

Another option is to produce the popular style without postponement and the other three styles using postponement. What is the expected profit under this policy?