Modelling and solving the supply marketing order allocation problem with time consistency and bundle discounts

The optimizations with respect to the supply chain management have far-reaching effects on enterprise development as well as people's livelihood. By this fact, it is important to solve the order allocation problem in a real scenario. We focus on optimising a supply marketing order allocation problem (SMOAP) with various constraints from an algorithmic aspect. The SMOAP considers how to match the orders between purchasers and suppliers to maximise the platform's benefits. We first formulate it as a constrained optimisation problem and then prove that SMOAP is NP-hard. The formulation describes a new trading mode with bundle discounts, time consistency and transportation cost in a real scenario. Based on this trading mode, satisfiability modulo theories (SMT) and constraint programming (CP) optimisers are performed to gain efficient solutions. Moreover, we further propose a tabu search (TS) with two-level perturbation mechanism, score-based heuristic and preprocessing techniques to search for promising solutions. The efficiency of our approaches is confirmed by experiments on real data instances from an electronic commerce trading platform in Jiutai district of Changchun city, Jilin province, China. Experimental results reveal that the proposed method is quite effective.