The energy scheduling problem: Industrial case-study and constraint propagation techniques

This paper deals with production scheduling involving energy constraints, typically electrical energy. We start by an industrial case-study for which we propose a two-step integer/constraint programming method. From the industrial problem we derive a generic problem,the Energy Scheduling Problem (EnSP). We propose an extension of specific resource constraint propagation techniques to efficiently prune the search space for EnSP solving. We also present a branching scheme to solve the problem via tree search.Finally,computational results are provided

Clips: a capacity and lead time integrated procedure for scheduling.

We propose a general procedure to address real life job shop scheduling problems. The shop typically produces a variety of products, each with its own arrival stream, its own route through the shop and a given customer due date. The procedure first determines the manufacturing lot sizes for each product. The objective is to minimize the expected lead time and therefore we model the production environment as a queueing network. Given these lead times, release dates are set dynamically. This in turn creates a time window for every manufacturing order in which the various operations have to be sequenced. The sequencing logic is based on a Extended Shifting Bottleneck Procedure. These three major decisions are next incorporated into a four phase hierarchical operational implementation scheme. A small numerical example is used to illustrate the methodology. The final objective however is to develop a procedure that is useful for large, real life shops. We therefore report on a real life application.Model; Models; Applications; Product; Scheduling;

Solving job shop scheduling problem using genetic algorithm with penalty function

This paper presents a genetic algorithm with a penalty function for the job shop scheduling problem. In the context of proposed algorithm, a clonal selection based hyper mutation and a life span extended strategy is designed. During the search process, an adaptive penalty function is designed so that the algorithm can search in both feasible and infeasible regions of the solution space. Simulated experiments were conducted on 23 benchmark instances taken from the OR-library. The results show the effectiveness of the proposed algorithm

An exact extended formulation for the unrelated parallel machine total weighted completion time problem

The plethora of research on NP-hard parallel machine scheduling problems is focused on heuristics due to the theoretically and practically challenging nature of these problems. Only a handful of exact approaches are available in the literature, and most of these suffer from scalability issues. Moreover, the majority of the papers on the subject are restricted to the identical parallel machine scheduling environment. In this context, the main contribution of this work is to recognize and prove that a particular preemptive relaxation for the problem of minimizing the total weighted completion time (TWCT) on a set of unrelated parallel machines naturally admits a non-preemptive optimal solution and gives rise to an exact mixed integer linear programming formulation of the problem. Furthermore, we exploit the structural properties of TWCT and attain a very fast and scalable exact Benders decomposition-based algorithm for solving this formulation. Computationally, our approach holds great promise and may even be embedded into iterative algorithms for more complex shop scheduling problems as instances with up to 1000 jobs and 8 machines are solved to optimality within a few seconds

Shop scheduling with availability constraints

Scheduling Theory studies planning and timetabling of various industrial and human activities and, therefore, is of constant scientific interest. Being a branch of Operational Research, Theory of Scheduling mostly deals with problems of practical interest which can be easily (from a mathematical point of view) solved by full enumeration and at the same time usually require enormous time to be solved optimally. Therefore, one attempts to develop algorithms for finding optimal or near optimal solutions of the problems under consideration in reasonable time. If the output of an algorithm is not always an optimal solution then the worst-case analysis of this algorithm is undertaken in order to estimate either a relative error or an absolute error that holds for any given instance of the problem. Scheduling problems which are usually considered in the literature assume that the processing facilities are constantly available throughout the planning period. However, in practice, the processing facility, e.g. a machine, a labour, etc. can become non-available due to various reasons, e.g. breakdowns, lunch breaks, holidays, maintenance work, etc. All these facts stimulate research in the area of scheduling with non-availability constraints. This branch of Scheduling Theory has recently received a lot of attention and a considerable number of research papers have been published. This thesis is fully dedicated to scheduling with non-availability constraints under various assumptions on the structure of the processing system and on the types of non-availability intervals

Exact and Heuristic Algorithms for the Job Shop Scheduling Problem with Earliness and Tardiness Over a Common Due Date

Scheduling has turned out to be a fundamental activity for both production and service organizations. As competitive markets emerge, Just-In-Time (JIT) production has obtained more importance as a way of rapidly responding to continuously changing market forces. Due to their realistic assumptions, job shop production environments have gained much research effort among scheduling researchers. This research develops exact and heuristic methods and algorithms to solve the job shop scheduling problem when the objective is to minimize both earliness and tardiness costs over a common due date. The objective function of minimizing earliness and tardiness costs captures the essence of the JIT approach in job shops. A dynamic programming procedure is developed to solve smaller instances of the problem, and a Multi-Agent Systems approach is developed and implemented to solve the problem for larger instances since this problem is known to be NP-Hard in a strong sense. A combinational auction-based approach using a Mixed-Integer Linear Programming (MILP) model to construct and evaluate the bids is proposed. The results showed that the proposed combinational auction-based algorithm is able to find optimal solutions for problems that are balanced in processing times across machines. A price discrimination process is successfully implemented to deal with unbalanced problems. The exact and heuristic procedures developed in this research are the first steps to create a structured approach to handle this problem and as a result, a set of benchmark problems will be available to the scheduling research community

An Effective Multi-Population Based Hybrid Genetic Algorithm for Job Shop Scheduling Problem

The job shop scheduling problem is a well known practical planning problem in the manufacturing sector. We have considered the JSSP with an objective of minimizing makespan. In this paper, a multi-population based hybrid genetic algorithm is developed for solving the JSSP. The population is divided in several groups at first and the hybrid algorithm is applied to the disjoint groups. Then the migration operator is used. The proposed approach, MP-HGA, have been compared with other algorithms for job-shop scheduling and evaluated with satisfactory results on a set of JSSPs derived from classical job-shop scheduling benchmarks. We have solved 15 benchmark problems and compared results obtained with a number of algorithms established in the literature. The experimental results show that MP-HGA could gain the best known makespan in 13 out of 15 problems

A hybrid shifting bottleneck-tabu search heuristic for the job shop total weighted tardiness problem

In this paper, we study the job shop scheduling problem with the objective of minimizing the total weighted tardiness. We propose a hybrid shifting bottleneck - tabu search (SB-TS) algorithm by replacing the reoptimization step in the shifting bottleneck (SB) algorithm by a tabu search (TS). In terms of the shifting bottleneck heuristic, the proposed tabu search optimizes the total weighted tardiness for partial schedules in which some machines are currently assumed to have infinite capacity. In the context of tabu search, the shifting bottleneck heuristic features a long-term memory which helps to diversify the local search. We exploit this synergy to develop a state-of-the-art algorithm for the job shop total weighted tardiness problem (JS-TWT). The computational effectiveness of the algorithm is demonstrated on standard benchmark instances from the literature

An Effective Multi-Population Based Hybrid Genetic Algorithm for Job Shop Scheduling Problem

The job shop scheduling problem is a well known practical planning problem in the manufacturing sector. We have considered the JSSP with an objective of minimizing makespan. In this paper, a multi-population based hybrid genetic algorithm is developed for solving the JSSP. The population is divided in several groups at first and the hybrid algorithm is applied to the disjoint groups. Then the migration operator is used. The proposed approach, MP-HGA, have been compared with other algorithms for job-shop scheduling and evaluated with satisfactory results on a set of JSSPs derived from classical job-shop scheduling benchmarks. We have solved 15 benchmark problems and compared results obtained with a number of algorithms established in the literature. The experimental results show that MP-HGA could gain the best known makespan in 13 out of 15 problems