Interval valued demand related inventory model under all units discount facility and deterioration via parametric approach

In the yard of business organization, due to a major number of competitors and uncertainty of customers’ demand, everyone faces some disturbances for smoothly running of their business. To survive in the fierce competition some modern business policies are required and accordingly the formulation of an advanced inventory model is indispensable by handling the uncertainty of customers’ demand. In this model formulation, discount facility is considered as a business policy whereas interval valued demand is proposed to tackle the uncertainty of customers’ demand. The purpose of this work is to analyze a model with interval valued parameters for deteriorating items considering two situations (with shortages and without shortage) in the discount environment. Moreover, deterioration rate is taken into account as interval valued and unit carrying cost is supposed to be a function of the length of storage time as well as interval valued purchase cost. Also, the interval valued purchase cost is assumed to be a step function (decreasing) of lot size under discount business policy. Considering without shortage and with shortages separately, using parametric approach of interval differential equations, the proposed model is formulated in two different cases. After formulating the proposed model properly, the corresponding profit functions are obtained for two different cases (without shortage and with shortages). In order to optimize the profit, various types of meta-heuristic algorithms (weighted quantum behaved particle swarm optimization and Gaussian quantum behaved particle swarm optimization) are used and then the obtained results are compared. Finally, to justify the reality of the model, numerical illustrations are presented and also post optimality analyses are performed with the changes of known parameters.