In this paper, an integrated layout model has been considered to incorporate intra and inter-department layout. In the proposed model, the arrangement of facilities within the departments is obtained through the QAP and from the other side the continuous layout problem is implemented to find the position and orientation of rectangular shape departments on the planar area. First, a modified version of QAP with fewer binary variables is presented. Afterward the integrated model is formulated based on the developed QAP. In order to evaluate material handling cost precisely, the actual position of machines within the departments (instead of center of departments) is considered. Moreover, other design factors such as aisle distance, single or multi row intra-department layout and orientation of departments have been considered. The mathematical model is formulated as mixed-integer programming (MIP) to minimize total material handling cost. Also due to the complexity of integrated model a heuristic method has been developed to solve large scale problems in a reasonable computational time. Finally, several illustrative numerical examples are selected from the literature to test the model and evaluate the heuristic.

This paper examines the optimization of production involving a tandem two-machine system producing a single part type, with each machine being subject to random breakdowns and repairs. An analytical model is formulated with a view to solving an optimal stochastic production problem of the system with machines having up-downtime non-exponential distributions. The model developed is obtained by using a dynamic programming approach and a semi-Markov process. The control problem aims to find the production rates needed by the machines to meet the demand rate, through a minimization of the inventory/shortage cost. Using the Bellman principle, the optimality conditions obtained satisfy the Hamilton-Jacobi-Bellman equation, which depends on time and system states, and ultimately, leads to a feedback control. Consequently, the new model enables us to improve the coefficient of variation (CVup/down) to be less than one while it is equal to one in Markov model. Heuristics methods are used to involve the problem because of the difficulty of the analytical model using several states, and to show what control law should be used in each system state (i.e., including Kanban, feedback and CONWIP control). Numerical methods are used to solve the optimality conditions and to show how a machine should produce.