Retail Inventory Control with Sales Dependent on the Stock Level Available to Purchase

Situations exist where the quantities of a commodity held in stock can have an influence on the selling rate of this commodity. Examples include: items displayed in quantities on the shelves in supermarkets, consumer goods that are offered in a number of varieties (such as size, colour, style, etc) and the like. The identification and definition of a possible connection between quantities of stock and selling rate falls in the realm of marketing. Microbehavioural sales models are used to describe the effect of availability, along with other factors, on the level of retail sales (see, for example,). Elton and Mercer discuss specific methods for estimating the effect of variety on sales. For the following analysis it will be assumed that this effect is partially linear and known.