A stochastic goal-based economic order quantity model for multi-item inventory

The classical Economic Order Quantity (EOQ) assumes constant demand for a single item. This paper proposes a multiobjective goal programming model to optimize the EOQ of multiple items under stochastic demand. Adopting Markov chain methodologies, the model initially defines the demand transition matrix, inventory cost matrix, objective function, priorities, and goal constraints. The model seeks to minimize the deviation variables from the targeted EOQ and total inventory costs of items over a finite period planning horizon. The sum of deviations is minimized so that the actual EOQ and inventory costs meet the targeted levels of inventory items. Using the simplex method, an analytical solution is obtained, and a numerical example is presented to demonstrate the overachievement or underachievement of the targeted EOQ and inventory costs of items. The model's ability to reach the desired inventory levels and costs is demonstrated numerically for practical purposes.