Integrated optimization of multiproduct multiperiod transportation and inventory under a carbon cap constraint for online retailers

This study aims to solve the problem of multiproduct multiperiod integrated transportation and inventory optimization for online retailers. A carbon cap constraint and multitype of capacitated trucks are simultaneously incorporated into the proposed mixed-integer program. A simulated annealing (SA) algorithm is designed. CPLEX 12.9.0 is used to solve the submodel obtained from the neighbourhood search and is also used to get the optimal solutions for instances. Experimental results show that the simulated annealing algorithm can find satisfactory solutions within a reasonable time. When the problem size increases, the growth of the computational time of the SA algorithm is significantly smaller than that of the CPLEX. A sensitivity analysis for the carbon cap is also conducted. The results indicate that if the carbon cap is gradually tightened, the total cost increases first with a gentle slope, and then with a remarkable slope, same as for the total number of trucks used; the total carbon emissions first decrease with a gentle slope, and then decline with a significant slope. When the carbon cap is strict, only a few different types of trucks will be considered. The percentage changes of the total cost increase and the total carbon emission reduction are also compared. When the allowed carbon emissions are gradually reduced, situation of a higher amount of carbon emission reduction and a lower amount of cost increase can be achieved. Additionally, using multiple types of trucks in the integrated optimization of transportation and inventory decisions can achieve greater cost savings with lower increments of carbon emission.