An integrated multi-objective multi-product inventory managed production planning problem under uncertain environment

Integrating inventory with production–distribution operations has critical importance realized by several companies’ top management a long time before; however, challenging. The management has to decide where to shift products, which demand to fulfil, from which distribution centre (s), how much inventory to keep and a host of critical and complex decisions. As the organization increase in size and complexity, more robust optimization tools required to help analyze and comprehend these complex decisions. In this study, inventory, production and distribution problems with planned shortages, back-ordered quantity and delay in replenishment studied under uncertainty. A multi-objective multi-product model for minimizing the inventory, production and shipment costs and delivery time developed for the integrated system. The study considers the model’s different input parameters under a fuzzy and stochastic environment. The fuzziness converted to deterministic using interval type-2 trapezoidal fuzzy number. The randomness follows the Maxwell–Boltzmann distribution in which the deterministic form obtained using chance-constrained programming. The developed integrated model illustrated a numerical example in a manufacturing firm and solved using three robust goal programming variants. The results indicated inventory, production and transshipment costs are 99% minimized with 100% delivery time achievement.