Real Scheduling Problems Research Articles

Query-driven Qualitative Constraint Acquisition

Many planning, scheduling or multi-dimensional packing problems involve the design of subtle logical combinations of temporal or spatial constraints. Recently, we introduced GEQCA-I, which stands for Generic Qualitative Constraint Acquisition, as a new active constraint acquisition method for learning qualitative constraints using qualitative queries. In this paper, we revise and extend GEQCA-I to GEQCA-II with a new type of query, universal query, for qualitative constraint acquisition, with a deeper query-driven acquisition algorithm. Our extended experimental evaluation shows the efficiency and usefulness of the concept of universal query in learning randomly-generated qualitative networks, including both temporal networks based on Allen’s algebra and spatial networks based on region connection calculus. We also show the effectiveness of GEQCA-II in learning the qualitative part of real scheduling problems.

A branch-and-bound approach to minimise the value-at-risk of the makespan in a stochastic two-machine flow shop

Planning and scheduling approaches in real manufacturing environments entail the need to cope with random attributes and variables to match the characteristics of real scheduling problems where uncertain events are frequent. Moreover, the capability of devising robust schedules, which are less sensitive to the disruptive effects of unexpected events, is a major request in real applications. In this paper, a branch-and-bound approach is proposed to solve the two-machine permutation flow shop scheduling problem with stochastic processing times. The objective is the minimisation of the value-at-risk of the makespan, to support decision-makers in the trade-off between the expected performance and the mitigation of the impact of extreme scenarios. A Markovian Activity Network (MAN) model is adopted to estimate the distribution of the makespan and assess the value-at-risk for both partial and complete schedules. Phase-type distributions are used to enable general distributions for processing times while maintaining the capability to exploit a Markovian approach. The effectiveness and performance of the proposed approach are demonstrated through a set of computational experiments.

A Rolling-Horizon Approach for a Surgery Case Scheduling Problem with Sterilizing Constraints

In this paper, we study a real scheduling problem which consists in scheduling a set of elective surgical cases that arrive over the time taking into account the uncertainties on their duration, and the delay to sterilize surgical instruments. The objectives are to schedule as many surgeries as possible, and to minimize the overtime of the surgical block staff and the number of instruments processed in emergency in the sterilizing unit. This research was performed in collaboration with the University Hospital of Angers in France, which has also provided historical data for the experiments. We propose a rolling horizon approach based on the iterative resolution of a robust mixed integer linear programming model, in which the objective functions are taken into account in a lexicographic order. The experiments on real data show a reduction of more than 50% of overtime, and around 87% less stress situations in the sterilizing unit.

Petri Net Based Solution Supervision and Local Search for Job Shop Scheduling

Abstract Petri nets are a promising tool for development of distributed scheduling approaches and integrating these developments with state-of-the-art schedule optimization algorithms. A Petri net-based solution representation of job shop scheduling problems in a local search optimization context is studied in this paper. A novel sequence repairing scheme is proposed and evaluated in the case of standard scheduling benchmark problems. The results show the applicability of the approach, and the strength of Petri net models opens a way toward solving complex and realistic scheduling problems.

Tabu search and constraint programming-based approach for a real scheduling and routing problem

Constraint programming method (CPM) has gained much attention in the last years since it proved a great efficiency to model and solve many combinatorial problems like scheduling, assignment and routing problems. In this paper, we first present a CPM model for a real scheduling and routing problem (SRP) faced by a company of water and electricity distribution. The problem aims to minimise the total distance travelled by the company's technicians to the clients' locations in order to carry out some services. To solve the studied SRP three CPM-based solution methods are proposed: an exact method (branch and prune), a local search meta-heuristic and a hybrid algorithm which combine tabu search and constraint programming method. The proposed solution methods have been tested using three sets of instances. The two first sets are generated randomly, they represent small and large scale instances, while the third one contain the real instances provided by the company with which we are working. The results obtained by the three methods show clearly the superiority of the hybrid algorithm over the two others methods.

Tabu search and constraint programming-based approach for a real scheduling and routing problem

Tabu search and constraint programming-based approach for a real scheduling and routing problem

GRASP algorithm for the unrelated parallel machine scheduling problem with setup times and additional resources

This paper provides practitioners with new approaches for solving realistic scheduling problems that consider additional resources, which can be implemented on expert and intelligent systems and help decision making in realistic settings. More specifically, we study the unrelated parallel machine scheduling problem with setup times and additional limited resources in the setups (UPMSR-S), with makespan minimization criterion. This is a more realistic extension of the traditional problem, in which the setups are assumed to be done without using additional resources (e.g. workers). We propose three metaheuristics following two approaches: a first approach that ignores the information about additional resources in the constructive phase, and a second approach that takes into account this information about the resources. Computational experiments are carried out over a benchmark of small and large instances. After the computational analysis we conclude that the second approach shows an excellent performance, overcoming the first approach.

Secuenciación con Almacenes Limitados. Una Revisión de la Literatura

Tradicionalmente, en la aproximación formal a la secuenciación de producción denominada en inglés Theory of Scheduling (o simplemente scheduling), se suele obviar la limitación de capacidad entre los diferentes recursos de cara a establecer el programa de producción. Sin embargo, el paradigma Lean Manufacturing ha dejado patente que la limitación de capacidad física en los sistemas productivos es una característica que influye en los resultados de los programas de producción, por lo que las configuraciones empezando a ser objeto de estudio en la dirección de operaciones. En este artículo se hace una revisión de las principales características de la secuenciación con almacenes limitados que se han abordado bajo la teoría de secuenciación y se resumen las referencias más importantes publicadas durante los últimos años. Finalmente, se presentan una serie de conclusiones con el objetivo de clarificar algunas líneas de interés para los investigadores del tema.

An Effective Improvement to Main Non-periodic Train Scheduling Models by a New Headway Definition

In the railway industry, making a time management schedule for freight and passenger train plays a vital role in optimal use of railway resources such as tracks, fleet and human resources. In the last few years, there has been a growing interest in using non-periodic mathematical models for scheduling of train movements between researches. In the main mathematical model of train scheduling, which is used in a variety of single-objective and multi-objective models, there are some constraints that prevent the collision of trains with each other. The present study tries to take a closer look at the models and reduce these constraints. To this end, in this article an improved non-periodic train scheduling model is suggested by presenting a new definition of headway time. Our claims and results of the improved and the main models are evaluated using two hypothetical and one real examples. The results illustrate that the new proposed model, which has less constraints and complexity, works more effectively than the main model and is more suitable for solving real train scheduling problems.

A heuristic model for dynamic flexible job shop scheduling problem considering variable processing times

In real scheduling problems, unexpected changes may occur frequently such as changes in task features. These changes cause deviation from primary scheduling. In this article, a heuristic model, inspired from Artificial Bee Colony algorithm, is proposed for a dynamic flexible job-shop scheduling (DFJSP) problem. This problem consists of n jobs that should be processed by m machines and the processing time of jobs deviates from estimated times. The objective is near-optimal scheduling after any change in tasks in order to minimise the maximal completion time (Makespan). In the proposed model, first, scheduling is done according to the estimated processing times and then re-scheduling is performed after determining the exact ones considering machine set-up. In order to evaluate the performance of the proposed model, some numerical experiments are designed in small, medium and large sizes in different levels of changes in processing times and statistical results illustrate the efficiency of the proposed algorithm.

Surgical case scheduling with sterilising activity constraints

In this paper, we study a real scheduling problem which consists in scheduling a set of elective surgical cases requiring surgical instruments and tools in several operating rooms. The objectives are to minimise the overtime of the surgical unit staff, the number of operating rooms used and the number of instruments processed in emergency in the sterilising unit while respecting the current level of service represented by the total number of patients operated per month at the orthopaedic surgery unit. This research was performed in collaboration with the University Hospital of Angers in France (CHU Angers), which has also provided historical data for the experiments. We propose a mixed integer linear programming model for the problem which is solved in a lexicographic fashion. We also propose a robust formulation to deal with the uncertain surgery durations. Both the deterministic and robust formulations are then compared over a set of instances provided by the CHU. The solutions obtained are competitive in terms of number of operating rooms and significantly improve those implemented operationally at the CHU in terms of overtime and emergencies at the sterilising unit.

Integrating process optimization with energy-efficiency scheduling to save energy for paper mills

With the surging energy price and environmental concerns, measures to improve energy efficiency have attracted increasing concerns of the manufacture sector, especially energy-intensive manufacturing industries such as tissue paper mills. Energy-efficiency scheduling, as a novel energy-efficient method, has attracted the attention of an increasing number of researchers in recent years. Drying process is the most energy-intensive production process in tissue paper mills, which has a great energy-saving potential. This paper aims to reduce the energy costs for the tissue paper mill, consisting of processing energy cost and set-up energy cost, through integrating drying process optimization with energy-efficient scheduling. First, the energy cost model and the scheduling model were built. Then, the energy cost of the drying process of every job in a given scheduling problem was optimized using particle swarm optimization (PSO). Afterwards, the energy cost was further optimized using energy-efficiency scheduling. In addition, a hybrid non-dominated sorting genetic algorithm II (NSGA-II) was utilized to solve the energy-efficiency scheduling problem. Finally, several real scheduling problems from a real tissue paper mill were addressed using the proposed approach to demonstrate its effectiveness in energy saving. The experiment result showed that there is a great energy-saving potential in the drying process, accounting for up to 12.53% of the total energy consumption. Moreover, the maximum energy saving ratio of the proposed approach could reach 9.03%. On the whole, the proposed approach can provide a new energy-saving method for tissue paper mills or other manufacturing industries.

Evaluating Typical Algorithms of Combinatorial Optimization to Solve Continuous-Time Based Scheduling Problem

We consider one approach to formalize the Resource-Constrained Project Scheduling Problem (RCPSP) in terms of combinatorial optimization theory. The transformation of the original problem into combinatorial setting is based on interpreting each operation as an atomic entity that has a defined duration and has to be resided on the continuous time axis meeting additional restrictions. The simplest case of continuous-time scheduling assumes one-to-one correspondence of resources and operations and corresponds to the linear programming problem setting. However, real scheduling problems include many-to-one relations which leads to the additional combinatorial component in the formulation due to operations competition. We research how to apply several typical algorithms to solve the resulted combinatorial optimization problem: enumeration including branch-and-bound method, gradient algorithm, random search technique.

Dynamic Priority Rule Selection for Solving Multi-objective Job Shop Scheduling Problems

In this paper, a new approach has been suggested for solving the multi-objective job shop scheduling problem, in which, simple priority rules are used dynamically, according to the varied state of the scheduling environment. The rules assign priority to the jobs that waiting in queues based on their features and/or the scheduling environment. Since the real scheduling environments are generally dynamic, it is better to use different rules during the scheduling according to the state of the shop floor at each decision time. Based on this approach, a new algorithm is designed, which uses different rules over the scheduling time. This approach can be easily applied to solve the real scheduling problems of the manufacturing systems. The algorithm has been compared with some classic rules from the literature. The results show that the proposed approach is more effective than using a fixed priority rule.

A realistic variant of bi-objective unrelated parallel machine scheduling problem: NSGA-II and MOACO approaches

The problem investigated in this study involves an unrelated parallel machine scheduling problem with sequence-dependent setup times, different release dates, machine eligibility and precedence constraints. This problem has been inspired from a realistic scheduling problem in the shipyard. The optimization criteria are to simultaneously minimize mean weighted flow time and mean weighted tardiness. To formulate this complicated problem, a new mixed-integer programming model is presented. Considering the NP-complete characteristic of this problem, two famous meta-heuristics including a non-dominated sorting genetic algorithm (NSGA-II) and a multi-objective ant colony optimization (MOACO) which is a modified and adaptive version of BicriterionAnt algorithm are developed. Obviously, the precedence constraints increase the complexity of the scheduling problem in strong sense in order to generate feasible solutions, especially in parallel machine environment. Therefore a new corrective algorithm is proposed to obtain the feasibility in all stages of the algorithms. Due to the fact that appropriate design of parameter has a significant effect on the performance of algorithms, we calibrate the parameters of these algorithms by using new approach of Taguchi method. The performances of the proposed meta-heuristics are evaluated by a number of numerical examples. The results indicated that the suggested MOACO statistically outperformed the proposed NSGA-II in solving the test problems. In addition, the application of the proposed algorithms is justified by a real block erection scheduling problem in the shipyard.

Flexible job-shop scheduling with flexible workdays, preemption, overlapping in operations and satisfaction criteria: an industrial application

This paper addresses a real scheduling problem, namely, a complex flexible job-shop scheduling problem (FJSP) with special characteristics (flexible workdays, preemption and overlapping in operations), where the objective is to maximise a satisfaction criterion defined through goal programming. To allow for flexible workdays, the solution representation of the classical FJSP is extended to consider overtime decisions and a sequence of time-cell states, which is used to model resource capability. A new temporal-constraint-handling method is proposed to solve the problem of overlapping in operations in a flexible-workday environment. Three solution methods are proposed to solve this scheduling problem: a heuristic method based on priority rules, a goal-guided tabu search (GGTS) and an extended genetic algorithm (EGA). In the GGTS, the neighbourhood functions are defined based on elimination approaches, and five possible neighbourhood functions (N0 ⊇ N1 ⊇ N2 ⊇ N3 ⊇ N4) are presented. The effectiveness and efficiency of the three solution methods are verified using dedicated benchmark instances. Computational simulations and comparisons indicate that the proposed N4-based GGTS demonstrates performance competitive with that of the EGA and the GGTSs based on the other neighbourhood functions (N0, N1, N2 and N3) for solving the scheduling problem.

Move blocking strategy applied to re-entrant manufacturing line scheduling

Model predictive control (MPC)-based approach to fab-wide scheduling has been suggested to solve constraint-aware production optimization and in-process inventory level control simultaneously at each scheduling instance. However, application of this approach to real fab suffers from computational difficulties brought by the need to solve a huge optimization problem on-line as real fab scheduling problems are characterized by long cycle times, multiple product types, hundreds of machines/processing steps and re-entrant product flows. This study explores the use of an offset-blocking strategy combined with a modified recursive least square (RLS) estimation in the fab-wide scheduler, in order to alleviate the difficulty. The strategy is tested on a modified version of published case study called Intel Mini-Fab (IMF) problem. Despite its simplicity, the blocking strategy showed excellent performance in the face of realistic demand changes and plant/model mismatch.

Scheduling Mixed-Model Production on Multiple Assembly Lines with Shared Resources Using Genetic Algorithms: The Case Study of a Motorbike Company

The authors deal with the topic of the final assembly scheduling realized by the use of genetic algorithms (GAs). The objective of the research was to study in depth the use of GA for scheduling mixed-model assembly lines and to propose a model able to produce feasible solutions also according to the particular requirements of an important Italian motorbike company, as well as to capture the results of this change in terms of better operational performances. The “chessboard shifting” of work teams among the mixed-model assembly lines of the selected company makes the scheduling problem more complex. Therefore, a complex model for scheduling is required. We propose an application of the GAs in order to test their effectiveness to real scheduling problems. The high quality of the final assembly plans with high adherence to the delivery date, obtained in a short elaboration time, confirms that the choice was right and suggests the use of GAs in other complex manufacturing systems.

A real scheduling problem for hospital operation room

This paper provides a classification of real scheduling problems. Various ways have been examined and described on the problem. Scheduling problem faces tremendous challenges and difficulties in order to meet the preferences of the consumer. Dealing with scheduling problem is complicated, inefficient and time-consuming. This study aims to develop a mathematical model for scheduling the operating theatre during peak and off peak time. A simplified version of the real operation scheduling problem was used in this study. Scheduling problem is a well-known optimization problem and the goal is to find the best possible optimal solution. Therefore, in this paper, we used Integer linear programming (ILP) and Linear Programming (LP) technique for scheduling problem in a high level of synthesis. In addition, time and resource constrained scheduling was used. An optimal result was fully obtained by using the software GLPK/AMPL. This model can be adopted to solve other scheduling problems, such as the Lecture Theatre, Cinemas and Work Shift.

Solving tri-objective multistage hybrid flow shop scheduling problems using a discrete firefly algorithm

Hybrid flow shop (HFS) scheduling problems turn into a fascinating area of research for the past several decades. However, most of the researchers consider only single objective and makespan is the most vital objective function. The real industrial scheduling problems involve multiple conflicting objectives. The HFS scheduling problems were proved to be NP-hard (non-deterministic polynomial time hard) problems. In this paper, we present a discrete firefly algorithm (DFA) to minimise the makespan, total flow time and machine idle time in a multistage HFS environment consisting of n jobs and k stages with identical parallel machines. The performance of the proposed algorithm is tested with a real industrial case study data and random problem instances. Computational results proved the effectiveness of the proposed algorithm.