Static Inventory Models: Single Purchase Decisions

Static inventory models pertaining to optimal order quantity for the single relevant period have been developed in this chapter. These problems become particularly challenging if the item is expensive and the demand during the period is probabilistic. A number of situations where these models are applicable have been outlined. Models for items procured for consumption such as insurance spares to be ordered along with the ordering of main equipment have been developed with or without salvage value. MTBF-based approach using cumulative Poisson probability is proposed if data on probability of demand is not easily available. In the case of items stocked for sale to maximize the total expected profit, the model has been presented as a kind of famous “Newsboy” Problem. For normal distribution of demand, a simpler approach employing normal distribution tables has been shown to be very handy. For multi-item problems with budget or space constraint, a model based on the method of Lagrange multipliers has been presented with an iterative solution methodology. The value of Lagrange multiplier is shown to be the shadow price per unit of resource constraint and can be very insightful for rationally addressing the issue of adding extra budget or increasing storage space.