Reducing Carbon Emissions in a Closed-Loop Production Routing Problem with Simultaneous Pickups and Deliveries under Carbon Cap-and-Trade

Xuanjing Fang, Yanan Du, Yuzhuo Qiu
2017 Sustainability  
The incorporation of reverse logistics into production routing problems can promote and coordinate the implementation of sustainable development for supply chains. This study aims to incorporate reverse logistics into production routing problems and investigate the reduction of carbon emissions under carbon cap-and-trade. Mixed-integer programming models are proposed for the production routing problem with reverse logistics by considering simultaneous pickups and deliveries in vehicle routing
more » ... bproblems. To solve this problem, we propose a solution method of a branch-and-cut guided search algorithm based on adaptation of known valid inequalities. Computational results highlight the trade-offs among various performance indicators, including emission levels and operational costs of production, inventory holding, fuel consumption, and drivers. Sustainability 2017, 9, 2198 2 of 15 been addressed, with only a few notable exceptions such as the PRP with carbon emissions [1], and the multi-objective pollution production routing problem with a time window [15] . However, reverse logistics, to the best of our knowledge, have been largely ignored. Pickup-and-delivery problems for goods transportation and various available algorithms were reviewed in [16] . The vehicle routing problem with simultaneous pickups and delivery (VRPSPD) has become increasingly popular. The VRPSPD has wide applications in the electric appliances industry, beverage industry, returnable/reusable transport items (RTI), and returnable/reusable logistical packaging. New solution methods of exact algorithms, e.g., the branch-and-cut method [17] , and branch-price-and-cut method [18, 19] have just appeared. Inventory routing problems with simultaneous pickups and deliveries (IRPSPD) have also been explored only recently [6, 20, 21] . A natural step forward is to extend these problems and methods to the PRP. Among various carbon policies, the "cap-and-trade" policy works for energy-intensive industries. The carbon cap specifies the upper limit, i.e., tons of carbon dioxide equivalents (CO 2 e), that a company may emit per year. Under "cap-and-trade" policy, if the cap is exceeded by a company, the company must buy additional allowances. If a company has not met with the carbon cap, the company can sell carbon credits on the carbon trading market. Our aim is thus to design a model and algorithm for a closed-loop production routing problem with simultaneous pickups and deliveries (PRPSPD) under carbon cap-and-trade. The PRP involves combinatorial optimization of both delivery and routing decisions. Exact algorithms, such as branch-and-price [1,22,23] and branch-and-cut [9,10], can solve small and medium-sized problems. Other studies have often used heuristics, e.g., approximation algorithms [24], the decoupled heuristic [25], the greedy randomized adaptive search procedure [26], memetic algorithms [27], tabu searches [28,29], adaptive large neighborhood searches [30], iterative mixed-integer programming [31], particle-swarm optimization [15], the mathematical programming heuristic [32], and the multiphase heuristic [33]. Thus, we intend to develop a hybrid algorithm for the PRPSPD under carbon cap-and-trade. The contributions of this paper can be summarized as follows. First, we introduce a real-world variant of the PRP with reverse logistics. Reverse logistics are modeled with simultaneous pickups and deliveries. Second, we formulate the PRPSPD under carbon cap-and-trade as a mixed-integer linear programming (MILP) problem. Third, we adapt known valid inequalities to tighten the MILP formulation and design a branch-and-cut guided search algorithm as the solution method. Finally, we conduct extensive computational experiments to assess the performance of the proposed algorithm and develop managerial implications through sensitivity analysis. The model, algorithm, and computational results can serve as a stepping stone for further research of the PRP with return flow [2] . The rest of the paper is organized as follows. Section 2 describes the PRPSPD under carbon cap-and-trade and introduces a mathematical formulation. Section 3 elaborates a solution method of a branch-and-cut guided search algorithm. Extensive computational results are provided in Section 4. We conclude in Section 5 with discussions on future research directions.
doi:10.3390/su9122198 fatcat:qeqfhker5bbulftfjbvpcmxwku