Resource Cost Aware Scheduling Problems

Managing the consumption of non-renewable and/or limited resources has become an important issue in many different settings. In this dissertation we explore the topic of resource cost aware scheduling. Unlike the purely scheduling problems, in the resource cost aware setting we are not only interested in a scheduling performance metric, but also the cost of the resources consumed to achieve a certain performance level. There are several ways in which the cost of non-renewal resources can be added into a scheduling problem. Throughout this dissertation we will focus in the case where the resource consumption cost is added, as part of the objective, to a scheduling performance metric such as weighted completion time and weighted tardiness among others. In our work we make several contributions to the problem of scheduling with non-renewable resources. For the specific setting in which only energy consumption is the important resource, our contributions are the following. We introduce a model that extends the previous energy cost models by allowing more general cost functions that can be job-dependent. We further generalize the problem by allowing arbitrary precedence constraints and release dates. We give approximation algorithms for minimizing an objective that is a combination of a scheduling metric, namely total weighted completion time and total weighted tardiness, and the total energy consumption cost. Our approximation algorithm is based on an interval-and-speed-indexed IP formulation. We solve the linear relaxation of this IP and we use this solution to compute a schedule. We show that these algorithms have small constant approximation ratios. Through experimental analysis we show that the empirical approximation ratios are much better than the theoretical ones and that in fact the solutions are close to optimal. We also show empirically that the algorithm can be used in additional settings not covered by the theoretical results, such as using flow time or an online setting, with good approximation and competitiveness ratios

Optimal Algorithms for Scheduling under Time-of-Use Tariffs

We consider a natural generalization of classical scheduling problems in which using a time unit for processing a job causes some time-dependent cost which must be paid in addition to the standard scheduling cost. We study the scheduling objectives of minimizing the makespan and the sum of (weighted) completion times. It is not difficult to derive a polynomial-time algorithm for preemptive scheduling to minimize the makespan on unrelated machines. The problem of minimizing the total (weighted) completion time is considerably harder, even on a single machine. We present a polynomial-time algorithm that computes for any given sequence of jobs an optimal schedule, i.e., the optimal set of time-slots to be used for scheduling jobs according to the given sequence. This result is based on dynamic programming using a subtle analysis of the structure of optimal solutions and a potential function argument. With this algorithm, we solve the unweighted problem optimally in polynomial time. For the more general problem, in which jobs may have individual weights, we develop a polynomial-time approximation scheme (PTAS) based on a dual scheduling approach introduced for scheduling on a machine of varying speed. As the weighted problem is strongly NP-hard, our PTAS is the best possible approximation we can hope for.Comment: 17 pages; A preliminary version of this paper with a subset of results appeared in the Proceedings of MFCS 201

An Enhanced Estimation of Distribution Algorithm for Energy-Efficient Job-Shop Scheduling Problems with Transportation Constraints

[EN] Nowadays, the manufacturing industry faces the challenge of reducing energy consumption and the associated environmental impacts. Production scheduling is an effective approach for energy-savings management. During the entire workshop production process, both the processing and transportation operations consume large amounts of energy. To reduce energy consumption, an energy-efficient job-shop scheduling problem (EJSP) with transportation constraints was proposed in this paper. First, a mixed-integer programming model was established to minimize both the comprehensive energy consumption and makespan in the EJSP. Then, an enhanced estimation of distribution algorithm (EEDA) was developed to solve the problem. In the proposed algorithm, an estimation of distribution algorithm was employed to perform the global search and an improved simulated annealing algorithm was designed to perform the local search. Finally, numerical experiments were implemented to analyze the performance of the EEDA. The results showed that the EEDA is a promising approach and that it can solve EJSP effectively and efficiently.This work was supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 17KJB460018), the Innovation Foundation for Science and Technology of Yangzhou University (No. 2016CXJ020 and No. 2017CXJ018), Science and Technology Project of Yangzhou under (No. YZ2017278), Research Topics of Teaching Reform of Yangzhou University under (No. YZUJX2018-28B), and the Spanish Government (No. TIN2016-80856-R and No. TIN2015-65515-C4-1-R).Dai, M.; Zhang, Z.; Giret Boggino, AS.; Salido, MA. (2019). An Enhanced Estimation of Distribution Algorithm for Energy-Efficient Job-Shop Scheduling Problems with Transportation Constraints. Sustainability. 11(11):1-23. https://doi.org/10.3390/su11113085S1231111Wu, X., & Sun, Y. (2018). 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An investigation into minimising total energy consumption and total weighted tardiness in job shops

Manufacturing enterprises nowadays face the challenge of increasing energy prices and requirements to reduce their emissions. Most reported work on reducing manufacturing energy consumption today focuses on the need to improve the efficiency of resources (machines) largely ignoring the potential for energy reducing on the system-level where the operational method can be employed as the energy saving approach. The advantage is clearly that the scheduling and planning approach can also be applied across existing legacy systems and does not require large investment. Therefore, a multi-objective scheduling method is developed in this paper with reducing energy consumption as one of the objectives. This research focuses on classical job shop environment which is widely used in the manufacturing industry. A model for the bi-objectives problem that minimises total electricity consumption and total weighted tardiness is developed and the Non-dominant Sorting Genetic Algorithm is employed as the solution to obtain the Pareto front. A case study based on a modified 10 × 10 job shop is presented to show the effectiveness of the algorithm and to prove the feasibility of the model