Rolling Horizon-based Heuristics for Solving a Production-Routing Problem with Price-Dependent Demand

This paper studies a production-routing problem with price-dependent demand (PRP-PD). The problem is formulated as a mixed-integer nonlinear program (MINLP) and solved within an outer approximation (OA) framework where the primal and master problems are solved iteratively. In order to solve the computationally expensive master problem, which is a mixed-integer program (MIP), four different rolling horizon-based heuristics are developed. The efficiency of the proposed heuristic algorithms is benchmarked against the existing methods in the literature to solve the PRP-PD for both linear and nonlinear demand functions. Our results show that by adopting proper freezing and simplification strategies, the rolling horizon-based heuristic can solve the large problem instances significantly faster than the existing methods in the literature, with little to no reduction in solution quality. For large problem instances with linear demand functions, the proposed heuristic provides solutions within 1.5-3 min. The quality of these solutions deviates at most 3.5% from the solutions provided by the existing exact methods, which take more than 2 h. Our solutions are also higher in quality compared to the near-optimal solutions provided in the literature, and they are achieved with a 90% reduction in computational time. With nonlinear demand functions, one-third of the instances require more than 2 h to be solved by the exact methods in the literature, while they are solved within 0.5-3.5 min using our heuristic, with less than 2% deviation in solution quality.