ABSTRACT

The conventional assignment problem is unable to handle scenarios that may arise due to different working modes of machines leading to multiple cost and time entries corresponding to a job–machine pair. The present article deals with this problem and models it as a multi-choice bi-objective assignment problem, the two objectives being assignment cost and bottleneck time. Two different solution procedures are presented based on the Decision-Maker's (DM's) preference structure. First, when the DM provides his/her preference structure as goals, a solution methodology is proposed using goal programming and its different multi-choice variants. In the second case, when no preference is provided by the DM, a two-step approach is presented that iteratively solves a multi-choice cost-minimizing assignment problem to obtain all Pareto-optimal time–cost pairs and finally, based on the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS), a single efficient pair is obtained. The algorithm is successfully implemented using the CPLEX${}^{\circledR }$ optimization package and tested on various test problems.

摘要

传统的分配问题无法处理由于不同的机器工作模式而导致的情景，从而导致对应于作业机器对的多个成本和时间输入。本文处理此问题并将其建模为多选择双目标分配问题，这两个目标是分配成本和瓶颈时间。基于决策者（DM）的偏好结构，提出了两种不同的解决方案过程。首先，当决策者提供他/她的偏好结构作为目标时，将使用目标编程及其不同的多选择变量来提出一种解决方法。在第二种情况下，当DM没有提供任何首选项时，提出了一种分两步的方法，该方法迭代地解决了多选择成本最小化分配问题，以获得所有帕累托最优时间-成本对，最后，基于与理想解决方案相似的订单偏好技术（TOPSIS），获得单个有效对。使用CPLEX成功实现了该算法${}^{\circledR }$ 优化包并针对各种测试问题进行了测试。