Energy Consumption Optimization for Two-Machine Bernoulli Serial Lines with Time-Sensitive Constraint and General Bounds on Machine Efficiencies*

In many production systems with high energy use, machines consume a large amount of energy during operation. To deal with this issue, it is important to find ways to reduce energy consumption. This paper studies how to minimize energy use in a two-machine Bernoulli serial production line with time-sensitive constraint. It presents general lower and upper bounds on machine efficiencies. Specifically, the energy optimization problem with production rate and time-sensitive constraint is formulated as a nonlinear programming problem. Then, two relaxation problems and the structures of their feasible regions are analyzed. Based on these explorations, the optimal solution to the original energy optimization problem for two-machine Bernoulli production line, which includes time-sensitive constraint and general bounds on machine efficiencies, is constructed from the solutions of the relaxation problems (i.e., the problem without general bounds on machine efficiencies).