An optimization of an inventory model of decaying-lot depleted by declining market demand and extended with discretely variable holding costs

Inventory management is considered as major concerns of every organization. In inventory holding, many steps are taken by managers that result a cost involved in this row. This cost may not be constant in nature during time horizon in which perishable stock is held. To investigate on such a case, this study proposes an optimization of inventory model where items deteriorate in stock conditions. To generalize the decaying conditions based on location of warehouse and conditions of storing, the rate of deterioration follows the Weibull distribution function. The demand of fresh item is declining with time exponentially (because no item can always sustain top place in the list of consumers’ choice practically e.g. FMCG). Shortages are allowed and backlogged, partially. Conditions for global optimality and uniqueness of the solutions are derived, separately. The results of some numerical instances are analyzed under various conditions.