Discrete stochastic EOQ model for deteriorating inventory in supply chain using Hamilton–Jacobi–Bellman equation
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In an ideal environment, an optimal replenishment point is required for the best output performance with maximized profit for a classical economic order quantity (EOQ) model. However, in practice, most supply chains experience variations that affect the theoretical results. Most products are perishable, which implies that their quality deteriorates over time. This issue must be resolved promptly before the cycle ends because unsold items result in revenue loss. This study presents an EOQ model in a discrete domain with uncertainties in the systematic parameters. The demand for products depends linearly on the pricing scheme of the enterprise, which must be analyzed optimally to achieve the maximum profit in the replenishment cycle. To solve this optimization problem, an optimal control technique named the Hamilton–Jacobi–Bellman (HJB) equation is introduced, which has been proven successful in solving similar issues. The convergence constraints of the HJB equation and the optimal reordering quantity are analyzed. The performance of the proposed approach is revealed via simulations, in which the behavior of the inventory system in perfect and imperfect scenes is demonstrated. The final result indicates that the optimal solution is admissible and robust as it remains valid in varying environments, with a difference of less than 5% in the ideal case.
Abstract
In an ideal environment, an optimal replenishment point is required for the best output performance with maximized profit for a classical economic order quantity (EOQ) model. However, in practice, most supply chains experience variations that affect the theoretical results. Most products are perishable, which implies that their quality deteriorates over time. This issue must be resolved promptly before the cycle ends because unsold items result in revenue loss. This study presents an EOQ model in a discrete domain with uncertainties in the systematic parameters. The demand for products depends linearly on the pricing scheme of the enterprise, which must be analyzed optimally to achieve the maximum profit in the replenishment cycle. To solve this optimization problem, an optimal control technique named the Hamilton–Jacobi–Bellman (HJB) equation is introduced, which has been proven successful in solving similar issues. The convergence constraints of the HJB equation and the optimal reordering quantity are analyzed. The performance of the proposed approach is revealed via simulations, in which the behavior of the inventory system in perfect and imperfect scenes is demonstrated. The final result indicates that the optimal solution is admissible and robust as it remains valid in varying environments, with a difference of less than 5% in the ideal case.
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