A bi-objective model for the single-machine scheduling problem with rejection cost and total tardiness minimization

We study the problem of scheduling jobs on a single machine with a rejection possibility, concurrently minimizing the total tardiness of the scheduled jobs and the total cost of the rejected ones. The model we consider is fully bi-objective, i.e. its aim is to enumerate the Pareto front. We tackle the problem both with and without the presence of hard deadlines. For the case without deadlines, we provide a pseudo-polynomial time algorithm, based on the dynamic program of Steiner and Zhang (2011), thereby proving that the problem is weakly NP-hard. For the case with deadlines, we propose a branch-and-bound algorithm and prove its efficiency by comparing it to an \u3b5-constrained approach on benchmark instances based on those proposed in the literature on similar problems

Mathematical Model and Meta-Heuristic Algorithm for Dual Resource Constrained Hybrid Flow-Shop Scheduling Problem with Job Rejection

In the real world, firms with hybrid flow-shop manufacturing environment generally facethe human resource constraint, salary cost increasment and efforts to make better use oflabor, in addition to machine constraint. Given the limitations of these resources, productdelivery requierements to customers have made the job rejection essential in order to meetdistinct customer requirements. Therefore, this research has studied the dual resourceconstrained hybrid flow-shop scheduling problem with job rejection in order to minimizethe total net cost (the sum of the total rejection cost and the total tardiness cost of jobs)which is widely used in many industries. In this article, a mixed integer linear programmingmodel has developed for the research problem. In addition, an improved sooty ternoptimization algorithm (ISTOA) has proposed to solve the large-sized problems as well asa decoding method due to the NP-hardness of the problem. In order to evaluate theproposed optimization algorithm, five well-known algorithms in the literature including(immunoglobulin-based artificial immune system (IAIS), genetic algorithm (GA), discreteartificial bee colony (DABC), improved fruit fly optimization (IFFO), effective modifiedmigrating birds optimization (EMBO)) have adapted with the proposed problem. Finally,the performance of the proposed optimization algorithm has investigated against theadapted algorithms. Results and evaluations show the good performance of the improvedsooty tern optimization algorithm