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We consider m-machine permutation flow shop problems with an outsourcing option for a special case where each job's processing time equals the job's processing requirement plus a characteristic value of the machine. The objective is to minimize the sum of the performance measure for in-house jobs (the total completion time or the makespan) and the total outsourcing cost. We prove that two problems are polynomially solvable when the number of machines is fixed.

This paper addresses a scheduling problem in a flexible supply chain where the jobs can be either processed in house, or outsourced to a third-party supplier with the goal of minimizing the sum of holding and delivery costs subject to an upper bound on the outsourcing cost. The problem with identical job processing times has been proved as binary ${𝒩}{𝒫}$-hard one and a fully polynomial time approximation scheme (FPTAS) that runs in $O(\frac{n^8}{{\epsilon }^2})$ time has also been given. The aim of this paper is to derive a more effective FPTAS running in $O(\frac{n^{4}lognlogmax\{n,1/\epsilon \}}{{\epsilon }^2})$ time for this problem.

In this paper, we address a supply chain scheduling model with outsourcing and transportation. A job can be scheduled either on a single machine at a manufacturer’s plant or outsourced to a subcontractor. We assume that there are a sufficient number of vehicles at the manufacturer and the subcontractor such that each completed job can be transported to its customer immediately. For a given set of jobs, the decisions we need to make include the selection of jobs to be outsourced and the schedule of all the jobs. When the objective functions are to minimize the weighted sum of common scheduling measures and the total cost, we present their complexity analysis and a $2$-approximation algorithm for the second problem.

In recent times, sustainability has become more important for businesses. Accordingly, product remanufacturing has emerged as an interesting topic, as it is generally considered as a profitable and environmentally friendly end-of-use management option for several products. While extant literature on remanufacturing has comprehensively studied the topic of outsourcing, it has failed to recognize that retailers also have the flexibility to engage in remanufacturing. However, in recent years, several brand name retailers have established remanufacturing operations. The following question arises: Should original equipment manufacturers (OEMs) outsource their remanufacturing operations to their retailers? To answer this question, two models are developed in which an OEM interacts with an independent retailer on remanufacturing operations with the option to either remanufacture all products in-house (Model M) or outsource remanufacturing to their retailer (Model R). The result shows that although model M potentially facilitates greater economic, social, and environmental sustainability, it has costs for the retailer. Finally, a revenue-sharing contract is proposed to achieve a “win-win-win” outcome that has economic, social, and environmental benefits for all parties.