A bi-objective model for the assembly flow shop scheduling problem with sequence dependent setup times and considering energy consumption

The two-stage assembly flowshop scheduling problem has been studied in this research. Suppose that a number of products of different kinds are needed to be produced. Each product is consists of several parts. There are m uniform machines in the first stage to manufacture the components (parts) of products and there is one assembly station in the second stage to assembled parts into products. Setup operation should be done when a machine starts processing a new part and setup times are treated as separate from processing times. Two objective functions are considered: (1) minimizing the completion time of all products (makespan) as a classic objective, and (2) minimizing the cost of energy consumption as a new objective. Processing speed of each machine is adjustable and the rate of energy consumption of each machine is dependent of its processing speed. At first, this problem is described with an example, and then needed parameters and decision variables are defined. After that, this problem is modeled as a mixed integer linear programming (MILP) and GAMS software is applied to solve small problems. To solve this bi-objective model, Epsilon Constraint algorithm is used on some test problems obtained standard references. Data of test problems were obtained from previous references and new parameters have been adjusted for considered problem. Conflicting of two considered objective functions has been valid through the result. In additional, result of solving test problems and sensitivity analysis show that how we can reduce energy consumption by adjusting completion times.