Constraint Programming

Balancing the production system’s resources like budget, equipment, and workers is one of the most important concerns of production managers. Managers seek to find an optimal way to balance their resources in production systems. By evaluating U-shaped assembly line papers, this investigation adds the literature on U-shaped assembly lines to the simultaneous examination of the balance ergonomic risks of human workers and current costs in the system when government offers tax benefits for using disabled workers. The mentioned outlook was not considered in previous papers. This study proposes a two-objective model to evaluate the effects of considering both robots and human workers in a U-shaped assembly line. The first objective is to minimize the system costs, and the second is to minimize the ergonomic risks. Human workers are divided into normal and disabled. The disabled workers are hired to enable tax benefits from the government. The constraint programming model for small and medium-sized problems and the grasshopper optimization algorithm (GOA) for big problems are developed to dissolve the problem. Numerical results show that two objective functions can also level system costs and ergonomic risks. The sensitivity analysis section analyzes three effective parameters (Production cycle time, Fatigue rate of human workers, and government tax benefit). It is shown that production cycle time directly affects using a robot or human workers (due to their mean time of speed), fatigue rate determines the allocation of tasks, and tax benefit helps to determine whether using disabled workers or not according objective functions. Also, it should be noticed the efficiency of GOA is shown by a comparison of several examples. Therefore, it is used for big-scale test problems.

The multi-skill resource constrained project scheduling problem (MS-RCPSP) is an important and challenging issue in project management. Two key factors that turn this topic into a challenging problem are the assumptions that are considered to approximate the model to a problem existing in real- world and its exact solution. In this paper, we study this problem which has a set of resources and each of them masters a set of skills. To consider real-word situations, we take into account calendars specifying time intervals during which the resources are available. The problem with and without calendars constraint are modeled with mathematical programming (MP) and constraint programming (CP). The MP is based on the model which was proposed in the literature. Computational results show that the proposed approach can efficiently solve real-size instances, and the performance of CP approach is evaluated by comparing Time-Indexed Model (TIM) and Branch and Price (B&P) approaches and computational results show the superiority of CP in terms of computational time.