Possibility and necessity constraints and their uses in inventory control system

In this paper, analogous to chance constraints, real‐life necessary and possibility constraints in the context of a multi‐item inventory control system are defined and defusified following fuzzy relations. Hence, a realistic multi‐item inventory model without shortages and fuzzy constraints has been formulated and solved for minimum objective cost. Here, demand of the items is constant and known. The space required per unit item, available storage space is assumed to be imprecise. The space constraints are of necessity and/or possibility types. The models are formulated for different types of necessity or possibility constraints and solved using the Kuhn–Tucker conditions and Generalised Reduced Gradient (GRG) technique. The model is illustrated numerically, and values of demand and stock level are presented in tabular form.