A fuzzy vendor managed inventory of multi-item economic order quantity model under shortage: An ant colony optimization algorithm

- Considering fuzzy environment and VMI supply chain simultaneously.
- Proposing a new modeling to the fuzzy VMI problem with multi items and shortage.
- Not only storage capacity and total order quantity of all items but also demand are considered fuzzy.
- Employing three meta-heuristic algorithms (ACO, GA, and DE) to solve a FNIP problem.
- Providing a case study in an Iranian automobile SC (the SAPCO Company) to apply the proposed model.

In this study, a multi-item economic order quantity model with shortage under vendor managed inventory policy in a single vendor single buyer supply chain is developed. This model explicitly includes warehouse capacity and delivery constraints, bounds order quantity, and limits the number of pallets. Not only the demands are considered imprecise, but also resources such as available storage and total order quantity of all items can be vaguely defined in different ways. An ant colony optimization is employed to find a near-optimum solution of the fuzzy nonlinear integer-programming problem with the objective of minimizing the total cost of the supply chain. Since no benchmark is available in the literature, a genetic algorithm and a differential evolution are developed as well to validate the result obtained. Furthermore, the applicability of the proposed methodology along with a sensitivity analysis on its parameter is demonstrated using five numerical examples containing different numbers of items.