Integrating pricing and scheduling decisions in a production network with distance-price-sensitive orders

This paper studies the design of a production network for a make-to-order firm with geographically dispersed distribution centres (DCs), where the order volume of each DC depends on both pricing and its distance from the firm. The objective is to optimise pricing and order scheduling to maximise profit while minimising costs, including transportation, scheduling, and production expenses. Five scheduling cost measures are considered: maximum lateness, total tardy jobs, total weighted tardiness, weighted completion time, and maximum completion time. Initially, the problem is formulated as a mixed-integer nonlinear programme (MINLP). To address computational challenges, prices are discretized into levels, transforming the MINLP into a more manageable mixed-integer linear programme (MILP) solvable with standard optimisation techniques. In addition, novel MILP formulations are proposed to improve computational efficiency, and a customised genetic algorithm combined with reinforcement learning (GA-RL) is developed to provide approximate solutions. Numerical results reveal that while the CPLEX solver outperforms GA-RL on certain metrics, GA-RL excels in others. Sensitivity analyses demonstrate the effectiveness of price discretization and highlight the advantages of the integrated approach compared to a sequential one. The models are validated using real data from the energy drink industry, offering valuable managerial insights for decision-making.