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An integrated decision in supply chain is a significant principle in order to compete in today’s market. This paper proposes a novel mathematical model in a two-stage supply chain scheduling to cooperate procurement and manufacturing activities. The supply chain scheduling along with the production approach of cellular manufacturing under demand, processing time, and transportation time uncertainties makes business environment sustainably responsive to the changing needs of customers. Uncertainties are formulated by queuing theory. In this paper, a new mixed-integer nonlinear programming formulation is used to determine types of vehicles to carry raw materials, suppliers to procure, priority of each part in order to process, and cell formation to configure work centers. The goal is to minimize total tardiness. A linearization method is used to ease tractability of the model. A genetic algorithm is developed due to the NP-hard nature of the problem. The parameters of the genetic algorithm are set and estimated by Taguchi’s experimental design. Numerous test problems are employed to validate the effectiveness of the modeling and the efficiency of solution approaches. Finally, a real case study and a sensitivity analysis are discussed to provide significant managerial insights and assess the applicability of the proposed model.

In operations research, bi-level programming is a mathematical modeling which has another optimization problem as a constraint. In the present research, regarding the current intense competition among large manufacturing companies for achieving a greater market share, a bi-level robust optimization model is developed as a leader-follower problem using Stackelberg game in the field of aggregate production planning (APP). The leader company with higher influence intends to produce new products, which can replace the existing products. The follower companies, as rivals, are also seeking more sales, but they do not have the intention and ability to produce such new products. The price of the new products is determined by the presented elasticity relations between the uncertain demand and price. After linearization, using the KKT conditions, the bi-level robust model is transformed into an ordinary uni-level model. Due to the NP-hard nature of the problem, Benders decomposition algorithm (BDA) is proposed for overcoming the computational complexities in large scale. Finally, using the real data of Sarvestan Sepahan Co as a leader company, the validity of the developed model as well as efficiency and convergence of the BDA are investigated. The computational results clearly show the efficiency and effectiveness of the proposed BDA.

In this paper, we addressed a multi-product unrelated parallel machines scheduling problem with the possibility of producing imperfect jobs. Rework processes in the problem are studied and a Mixed-Integer Nonlinear Programming (MINLP) model to formulate this problem is proposed. Rework activities are used to upgrade imperfect jobs to a preset standard quality level. It is assumed that the defective production probability for each job on machines can be estimated through historical data acquisition. Since the problem is strongly NP-hard, exact algorithms are inefficient for medium and large-sized problems. Thus, some heuristic methods focusing on the rework processes are developed based on dispatching rules. In order to evaluate the efficiency of the presented algorithms, makespan is used as the objective function. Computational experiments show the efficacy of the modified shortest processing time (MSPT) heuristic, in terms of computational time and objective value for randomly generated test problems.