Logic-based Benders decomposition for order acceptance and scheduling in distributed manufacturing

This paper studies an order acceptance and scheduling problem in distributed manufacturing to minimize the total costs consisting of rejection cost, production cost, transportation cost and tardiness cost. Two mixed-integer programming models are formulated, which are further improved by the proposed enhancement techniques. A logic-based Benders decomposition (LBBD) method and a branch and check search framework are developed in an attempt to realize the optimal and intelligent decisions of order acceptance, order assignment and scheduling. The proposed LBBD method following the principle of “divide and conquer” divides the original problem into determining the master problem of order acceptance and assignment, and determining the subproblem of order sequencing in each factory. A dynamic programming algorithm is also proposed to efficiently solve the subproblems. Extensive computational experiments are conducted, and the results demonstrate the effectiveness and efficiency of the enhancement techniques for the formulations, as well as the LBBD method. Besides, the value of distributed manufacturing is verified and the sensitivity of key cost factors is presented.