Optimizing Distribution Network Design Using Conic Relaxation for Maximum Cut Formulations

In the home appliance retail industry, delivery services have faced challenging situations caused by cross-area distributions in recent years, making it necessary to determine the service area to reduce the distribution coupling of different areas. Given the special characteristics of home appliance products, we first propose a multidimensional weight model by incorporating a designed fuzzy membership function that corrects the cost errors brought about by travel distance. Determination of the service area is then formulated as multiple maximum cut problems. Moreover, with good theoretical properties, a linear conic programming (LCoP) algorithm is developed to obtain the proximate global optimum solution for the maximum cut problem by applying conic relaxation. The proposed LCoP algorithm is applied iteratively to solve the formulated maximum cut problems. From numerical results, the LCoP algorithm produces a better approximated maximum cut than Williamson and Goemans’ algorithm and quantum approximate optimization algorithm, both of which become increasingly less effective as the problem size increases. Compared to the original RiRiShun Logistics (RRS) distribution network and tested algorithm, implementing the proposed planning approach benefit more to RRS with respect to the cross-area distribution frequency and transportation costs.