Bi-objective optimization of a single machine batch scheduling problem with energy cost consideration

Abstract

With the increasing energy price, the rapid growth of electricity demand and severe challenges for sustainable development, energy-efficient scheduling is becoming more and more important for power-intensive manufacturing industry, especially for batch production companies. This paper investigates a bi-objective single machine batch scheduling problem with non-identical job sizes, the time-of-use (TOU) electricity prices, and different energy consumption rates of the machine. The first objective is to minimize the makespan and the second is to minimize the total energy costs, by considering both the machine utilization and the economic cost. The problem is formulated as an integer programming model. Then, an exact-constraint method is adapted to obtain the exact Pareto front. To deal with large scale problems, based on decomposition ideas, two heuristic methods are developed to obtain approximate Pareto fronts. Computational experiments on randomly generated instances show the effectiveness of the methods. A study case of a real-world glass manufacturing company is also conducted to show that the proposed methods are promising for practical usages.

A survey of case studies in production scheduling: Analysis and perspectives

“…Different release date constraints and dynamic arrival of jobs was discussed in [38] and in [64,65], respectively. Batch processing scheduling problems appeared in [81,85]. The possibility of a processed job returning to a previous stage (re-entrant flow) was found in [18,15].…”

“…In the ceramic and glass sector, Ruiz and Maroto [70] developed a genetic algorithm to minimize the makespan in a ceramic tile factory, considering various realistic constraints such as different resources working in parallel at various stages, eligibility of machines and sequence-dependent setup times. For glass factories, Alvarez-Valdes et al [3] proposed a heuristic to minimize a multiobjective lateness function and Wang et al [85] formulated a MILP model for a bi-objective single machine batch problem to minimize makespan and total energy cost.…”

Bi-criteria parallel batch machine scheduling to minimize total weighted tardiness and electricity cost

“…Cheng et al (2017) propose a heuristic variant of the ε-constraint method for the same scheduling problem, but on/off switching of the machines is allowed. A similar single-machine batch scheduling problem is considered by Wang et al (2016). The energy consumption depends on the selected temperature of the machine.…”

Optimization-Based Scheduling for the Process Industries: From Theory to Real-Life Industrial Applications

“…The results show that the operational cost was reduced by up to 6.2% by applying the proposed approach. Wang et al [122] investigated the bi-objective single machine batch scheduling problem of a real-world scheduling problem in a glass company located in Shanghai, China. An exact ε-constraint method was adapted to the MILP model in order to minimize the makespan and the total energy costs.…”