Elsevier

Applied Soft Computing

Volume 54, May 2017, Pages 313-321
Applied Soft Computing

Determining the prices of remanufactured products, capacity of internal workstations and the contracting strategy within queuing framework

https://doi.org/10.1016/j.asoc.2017.01.027Get rights and content

Highlights

  • This paper deals a remanufacturing facility with several types of incoming nonconforming products.

  • The workstations have limited capacities so that an outsourcing strategy can be practiced.

  • A bi-objective mixed-integer nonlinear programming is built and solved.

  • To validate the results, the solutions of some test problems are compared with GAMS’s solutions.

  • The applicability of the proposed model and the solution procedure are shown with an example.

Abstract

This paper studies a remanufacturing facility with several types of incoming nonconforming products and different independent remanufacturing workstations. The workstations have limited capacities so that an outsourcing strategy can be practiced. Each workstation is modeled with an M/M/1/k queuing system considering k as a decision variable. Additionally, a binary decision variable is taken into account to determine the contracting strategy along with some decision variables for the prices of remanufactured products. Thus, a bi-objective mixed-integer nonlinear programming is built to obtain optimal values of the decision variables. The first objective attempts to maximize the total profit and the second minimizes the average length of queuing at workstations. To solve the complex bi-objective mixed-integer nonlinear programming problem, the best out of six multi-objective decision-making (MODM) methods is selected in order to make the bi-objective optimization problem a single-objective one. Afterward, a genetic algorithm (GA) is developed to find a near-optimum solution of the single-objective problem. Besides, all of the important parameters of the algorithm are calibrated using regression analysis. To validate the results obtained, the solutions of some test problems are compared to the ones obtained by the GAMS software. The applicability of the proposed model and the solution procedure are shown with an illustrative example.

Section snippets

Introduction and literature review

Recently, due to environmental regulations, legal pressures as well as potential economic incentives, manufacturers are more interested in product recovery processes. It is worth mentioning that a significant factor of product recovery is remanufacturing that has been applied in several industries such as cameras, automobile engine, computers, medical equipment, aircrafts, among others. According to Stock et al. [1], remanufacturing processes are profitable. For example, some well-known

Problem definition

Consider the remanufacturing facility as it is shown in Fig. 1, where all nonconforming products enter to a testing center at an arrival rate of λ are first screened 100% to be classified into m groups based on the severities of their nonconformities. Based on the limited capacity of the workstation and time constraint, each group of nonconforming products are either processed at internal workstation or they are sent to a contractor. Furthermore, each group of nonconforming products is

Problem formulation

In this section, the assumptions of the problem defined in Section 2 are first explicitly stated in Subsection 3.1. Then, the notation is introduced in Subsection 3.2. Finally, the mathematical model is derived in Subsection 3.3.

Solving methods

In this section, a genetic algorithm (GA) is developed to obtain a near-optimum solution of the complex mixed-integer nonlinear mathematical programming formulation developed in Section 3. Before employing this algorithm, six MODM methods are investigated in the next subsection to convert the bi-objective optimization problem into a single-objective optimization problem. Converting a regular bi-objective problem to a single one is a common practice in the literature and it is just an

Numerical examples

This section considers a remanufacturing facility with ten groups of nonconforming products and ten independent workstations. The initial data for the numerical example are randomly generated as shown in Table 1. Besides, the total arrival rate (λ), the total budget to increase the capacity of workstations (C), the total budget for outsourcing (B), and the test station cost (CT) are determined 100, 25000, 1000 and 1000, respectively. Furthermore, L, U and h are considered 3, 8 workstations and

Conclusion

This paper investigates a bi-objective remanufacturing problem within queuing framework in which an outsourcing strategy is considered. The objective functions are to maximize the total profit received by selling the remanufactured products and to minimize the average number of products in the queues at the workstations, simultaneously. The aim is to determine the capacity of each internal workstation, the contracting strategy, and the selling prices of remanufactured products. The problem is

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