A guaranteed service model with continuous review (r,Q) policy

This paper introduces a generalized Guaranteed Service Model (GSM) for production systems that operates under a continuous review inventory control policy (r,Q). The model incorporates dependencies between processing time and order quantity, as well as controllable setup times, offering a more realistic framework for inventory management. The optimization problem is formulated as a non-linear integer programming problem with a non-convex objective function. To solve this, we propose a hybrid approach that combines the Difference of Convex functions Algorithm (DCA) with a heuristic adjustment technique, enabling efficient computation of high-quality solutions. Numerical experiments demonstrate the effectiveness of the proposed method, achieving competitive performance compared to the Baron solver in terms of cost minimization.