Customers for retail merchandise can often be satisfied with one of several items. Accounting for demand substitution in defining customer service influences the choice of items to stock and the optimal inventory level for each item stocked. Further, when certain items are not stocked, the resulting substitutions increase the demand for other items, which also affects the optimal stock levels. In this paper, we develop a probabilistic demand model for items in an assortment that captures the effects of substitution and a methodology for selecting item inventory levels so as to maximize total expected profit, subject to given resource constraints. Illustrative examples are solved to provide insights concerning the behavior of the optimal inventory policies, using the negative binomial demand distribution, which has performed well in fitting retail sales data.

A series of 519 non-diabetic subjects had vibration thresholds at three points measured using a biothesiometer. Thresholds appeared to be log normally distributed and increased with age. Centile charts of this relation were derived from the data giving a range for normal thresholds.The biothesiometer provides a quick and reliable assessment of vibration thresholds, which when related to the centile charts gives an objective measure of the progress of diabetic peripheral neuropathy. IntroductionThe only method at present widely available for examining vibration sensation is the time honoured tuning fork. Although quick and simple for gross assessment, it is unsatisfactory for measuring the amplitude threshold at which vibration becomes perceptible. This threshold is raised in some diseases, including diabetic peripheral neuropathy.1 To examine the normal range of vibration thresholds and see how they varied with age, thresholds in 348 non-diabetic people in this hospital were measured using a biothesiometer. This machine has existed for at least 45 years2 but is not well known in Britain. The aim was to help the clinician decide whether a patient's threshold is within normal limits and to give an objective method of monitoring one aspect of peripheral neuropathy.

Clearance pricing and end of season inventory management are challenging and important problems in retailing. Sales rates depend upon price, seasonal effects, and the remaining assortment of items available to customers. There is little time to react to observed sales, and pricing errors result in either loss of potential revenue or excess inventory to be liquidated. This paper develops optimal clearance prices and inventory management policies that take into account the impact of reduced assortment and seasonal changes on sales rates. Versions of these policies have been tested and implemented at three major retail chains and these applications are summarized and discussed.Marketing, Pricing, Retailing

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