Algorithms for Minimizing Resource Consumption Over Multiple Machines With a Common Due Window

Abstract

Scheduling on multiple machines has attracted considerable attention recently. However, most of traditional studies focused only on commercial cost and customer satisfaction. In fact, we are able to alleviate environmental damages via proper scheduling. This study explores a multi-machine scheduling problem with a due window. The objective is to minimize the total cost (including environmental cost). We develop a branch-and-bound algorithm (B&B) and two complementary lower bounds for optimally solving the problem when n <16. Moreover, we propose an imperialist competitive algorithm (ICA) to obtain near-optimal schedules for large problem instances. Experimental results are provided to show the performance of the proposed algorithms. INDEX TERMS Chemical industry, multi-machine scheduling, resource consumption, due window, imperialist competitive algorithm, branch-and-bound algorithm.

A makespan minimization problem for versatile developers in the game industry

“…Second, the proposed branch-and-bound algorithm is relatively efficient. For traditional machine scheduling problems, e.g., [63], 𝑛 = 25 is the maximal size for their branch-and-bound algorithms. Note that their machines are identical and all of them process jobs at a fixed pace; i.e., they are easier problems.…”

“…Clearly, branch-and-bound algorithms are of little practicality for the real-world problem instances. For example, branch-and-bound algorithms schedule identical machines well only for small instances, e.g., 𝑛 ≤ 15 in [63]. However, the optimal solutions can be used as benchmarks for evaluating other metaheuristic algorithms.…”

“…Compared with multi-machine scheduling, multi-developer scheduling is more interesting but also more complicated. In a heterogeneous-machine environment, e.g., [63,64], a capable machine always processes jobs efficiently in terms of processing speed. However, in the game industry, there are many types of jobs, such as storyboarding, storytelling, prototyping, figure modeling, scene design, sound design, visual effects, rendering, physics, mechanics, programming, and testing [58].…”

Joint maintenance planning and production scheduling optimization model for green environment

“…A numerical example is presented to illustrate the applicability of the proposed integrated model. The data for an industrial case study is derived from (Wang, 2019) with minor modifications to match the goal of the developed model. It is related to a milling machine operating at three speeds and with different environmental costs, i.e.…”

“…The objective function minimizes the makespan of the schedule. This study is motivated by some industrial applications that include similar interrelationships between speed, footprint and health, such as scheduling the process of asphalt milling machines (Wang, 2019) and vehicle routing problems (Mansouri et al. , 2016).…”