A constrained single-row facility layout problem

The single-row facility layout problem (SRFLP) seeks the arrangement of given facilities along a straight row in such a way that the total material handling cost among the facilities is minimized The SRFLP is studied till date as an unconstrained problem allowing the placement of the facilities in any location in any order without any restriction. However, a practical SRFLP instance may need to satisfy different types of constraints imposed on the placement of its facilities, e.g., the operation sequencing with precedence constraints in a process planning can be modeled as a SRFLP with ordering constraints. Such a SRFLP model, named as the constrained SRFLP (cSRFLP), is introduced here by instructing to place some facilities in fixed positions, and/or in specified orders with or without allowing the placement of other facilities in between two ordered facilities. Since it would be computationally too expensive for any search technique to satisfy such constraints, a permutation-based genetic algorithm (pGA), named as the constrained pGA (cpGA in short), is also proposed with some specially designed operators for exploring only feasible solutions of cSRFLP. In the numerical experimentation, investigating three case studies of the operation sequencing problem of process planning as cSRFLP instances, the cpGA found new sequences of operations with the same best-known objective value for the smaller-size case study, while improved the best-known solutions of the other two case studies of larger sizes. Further, transforming some large-size benchmark instances of SRFLP into cSRFLP, the cpGA found marginally inferior solutions than their best-known SRFLP solutions, which is obvious due to the constraints imposed in the transformed cSRFLP instances.