Cell Formation (CF) is the initial step in the configuration of cell assembling frameworks. This paper proposes a new mathematical model for the CF problem considering aspects of production planning, namely inventory, backorder, and Subcontracting. In this paper, for the first time, backorder is considered in cell formation problem. The main objective is to minimize the total fixed and variable costs, including the machine related costs, intercellular movements, deviation between the levels of cell utilizations, inventory, backorder, and sub-contracting costs. The presented mathematical model is validated using GAMS software, and various test problems are solved by Genetic Algorithm (GA) and Discrete Particle Swarm Optimization (DPSO) algorithm. The performance of the algorithms is compared with the results obtained by the GAMS. The results demonstrate, there is no significant difference between the results of algorithms. Finally, some sensitive analyses are carried out to analyze the effects of backorder and inventory holding costs.