Designing a robust bi-objective mathematical model for integrated supply chain planning and dynamic virtual cell formation

Cell formation، as one of the most important decision problems in designing a cellular manufacturing system، consists of grouping parts into part families and machines into cells. In a dynamic environment، the part demand/mix change is considered over a planning horizon divided into periods. Hence، the formation of cells for one period may no longer be effective for other periods and therefore، reconfiguration of cells is essential. Due to the variation of demand and the need for cells reconfiguration، virtual cell formation concept is introduced by researchers to take the advantage of cell formation without incurring reconfiguration charges. On the other hand، Simultaneous consideration of supply chain issues and cell formation results in lower distribution and procurement costs and faster response to customers. In traditional manufacturing systems، first، the supply chain is designed، the number of production facilities is determined and the facilities are assigned to support each market for each product; then، the organization of the processes (product line، process or cell formation) within factory is decided. In this paper، a new bi-objective robust optimization mathematical model is developed for integrating procurement، production and distribution planning considering various conflicting objectives simultaneously as well as the uncertainty of some critical parameters such as customer demands. The augmented ε-constraint method is utilized to solve the proposed mathematical model and to find a preferred compromise solution. Moreover، a real world industrial case is provided to justify the applicability of the proposed model.