Scheduling a cellular manufacturing system based on price elasticity of demand and time-dependent energy prices

Abstract

Cellular manufacturing system (CMS) is a novel production system adaptable to the make-to-order production. The present study focuses on scheduling CMS aimed at maximizing total profits as a function of the revenues earned from sales as well as energy consumption cost and order tardiness penalties. The components to be considered in the problem in hand include the time-dependency of energy price, price elasticity of demand, and speed-based power consumption of machines. Two linearization approaches are used to determine order quantities. The first chooses lot sizes from a continuous range while the second chooses them among prespecified discrete levels. Especially developed mathematical models are used to solve the problem in either approach. For the second linearization approach, a constraint programming model, and a hybrid algorithm based on the fix-and-optimize and variable neighborhood search metaheuristic (FOVNS, for short) are additionally developed. Changing the branching procedure as a technique and three dominance rules are also proposed to improve the performance of the CP and FOVNS models while their effectiveness is examined using the full factorial design of experiments. Also, the parameters of the FOVNS are tuned using the Taguchi method. Exact methods are found capable of optimizing medium-size problems in less than an hour while FOVNS is able to optimize large-size ones in 822 seconds on average with a deviation of 1.8% from the optimal solution. Statistical analysis show that considering a time-dependent energy price in the scheduling decreases the energy cost by about 40%.