Constraint programming model for resource-constrained assembly line balancing problem

Abstract

The literature studies assume that resources used to be perform the tasks are certain and homogenous in any assembly line. However, tasks may need to be processed by general resource requirements in real life. These general resources could be classified by usage of resources such as simple or multiple, alternative and concurrent. The problem which is related to assignment of the task to any workstation and assignment of resources needed by the task simultaneously is defined as resource-constrained assembly line balancing problems (RCALBPs). In this study, a multiobjective model with minimization of cycle time and resource usage for a given number of stations is modeled to solve the RCALBP for the first time. Alternative and general resource types for tasks and using more than two resource type requirements are also considered. A constraint programming model is developed and solved to find the optimal solutions of these problems. The proposed models are tested with sample scenarios to show the effectiveness of the model.

Appendix

SALBP-2 model is given below for using as the maximum number of resources bound.

Objective:

$$ {\text{Min}}\quad {\text{ct}} $$

(16)

Subject to:

$$ \sum\limits_{k = 1}^{\left| W \right|} {x_{ik} = 1\,} \quad \forall i \in T $$

(17)

$$ \sum\limits_{k = 1}^{\left| W \right|} {k * x_{ik} } \le \sum\limits_{l = 1}^{\left| W \right|} {l * } \,x_{jl} \quad (i,j) \in \Pr $$

(18)

$$ ct \ge \sum\limits_{i = 1}^{\left| T \right|} {\tau_{i} * x_{ik} } \quad \forall k \in W $$

(19)