Order quantities for style goods with two order opportunities and Bayesian updating of demand. Part I: no capacity constraints

Abstract

This paper is the first of two that study the problem of ordering a family of style-goods products where demand is uncertain and there are two order opportunities. The first opportunity has a long lead time and low unit cost. The second opportunity has a short lead time and high unit cost. During the time between the two order opportunities new information on demand becomes available. The information is used in a Bayesian estimation process to revise demand forecasts. There are no capacity constraints at the order opportunities. The second paper (Miltenburg, J. and Pong, H.C., Order quantities for style goods with two order opportunities and Bayesian updating of demand. Part 2: capacity constraints. Int. J. Prod. Res., 2007 (in press)) extends the results in this paper to the situation where there are capacity constraints. A number of inventory models having different information and computation requirements can be used to determine good order quantities. We find that complex models are appropriate for the most important A items. Simple models are best for other A items and for B and C items. The motivation for studying this problem is the experience of a real company. PTK has one medium-size factory and a chain of retail stores in Canada and the United States. The factory produces about one-third of the company's products. The other two-thirds are produced by suppliers, most of whom are located in China. About half of PTK's products are style-goods. There are two selling seasons for style-goods products: winter and summer. The style-goods products produced in China are ordered twice: first, about six months before the beginning of the products’ selling season, and second, very near the beginning of the selling season. The cost of products ordered at the first order opportunity is low because production cost and transportation cost are low. The cost of products ordered at the second order opportunity is high because production is expedited and transportation is speeded up. Demand for style-goods products is difficult to forecast. Forecast accuracy is poor at the first order opportunity. During the six months between the first and second order opportunities new information on competitors’ products, fashion trends, weather, the economy, promotional activity, and so on becomes available. This information is used to revise the demand forecast and adjust the order quantities.

Keywords:

• Style goods inventory problem
• Fashion goods inventory problem
• Bayesian estimation

Acknowledgements

This research was supported by Grant OGP5474 from the Natural Sciences and Engineering Research Council of Canada.

Notes

¹ The tilda symbol (∼) in means X is a random variable.