Logic-based Benders decomposition for order acceptance and scheduling on heterogeneous factories with carbon caps

We study an integrated order acceptance and scheduling problem for heterogeneous factories with carbon caps, order-dependent processing speeds, and setup times. Three joint decisions including order selection, order assignment and order sequencing are made to maximize profits, i.e., total revenue minus total production and tardiness cost. Firstly, we develop a mixed integer programming model to simultaneously optimize the three decisions and propose several dominance rules to enhance the model. Secondly, due to the particular structure of the problem, we propose a logic-based Benders decomposition (LBBD) method that decomposes the complicated original problem into a master problem and a number of subproblems. The master problem aims to determine order acceptance and order assignment, and each subproblem is for determining order sequencing in each factory. A branch and bound algorithm is then designed to quickly solve the subproblems. The branch and check framework is implemented to accelerate the solving process of the LBBD. Finally, numerical experiments verify that the proposed dominance rules play a promising role in enhancing the model, and the results of the algorithm comparison experiments show the significant advantages of proposed LBBD algorithm combined with the branch and check framework. Sensitivity experiments reveal that carbon cap serves as a major constraint on order acceptance.