A lost sales inventory model with a compound poisson demand patternA lost sales inventory model with a compound poisson demand pattern
Faculty of Applied Economics
Department of Engineering Management
Faculteit Toegepaste Economische Wetenschappen
Antwerp :UA, 2005[*]2005
Research paper / UA, Faculty of Applied Economics ; 2005:17
University of Antwerp
In this paper, we study the decision problem of a retailer, who wants to optimize the amount of shelf inventory of a particular product, given that the demand for the product is stochastic and replenishment lead times (from the stores stockroom to the shelf) are negligible. The shelf inventory is managed according to a (0,B)-inventory policy: when the shelf inventory is sold out, the retailer gets a fixed amount of B units from the central stockroom to replenish the shelf inventory. To adequately reflect the shopping behavior of retail customers, the demand process is modeled as a compound Poisson process, with Poisson distributed purchase quantities. When the purchase quantity of a cus- tomer exceeds the amount of shelf inventory still available, the unsatisfied demand is considered to be lost sales. As the demand process is stochastic, the runout time of the shelf in- ventory will be stochastic too. The costs per cycle related to keeping inventory on the shelf can be split up into three components: average holding costs (which may be related to the scarcity of shelf space), a fixed handling cost (per replenishment trip), and an average lost sales cost. The purpose of the model is to determine the value of B that minimizes the average total cost per time unit.