Application of Branch and Bound Method for Optimal Two Stage Flow Shop Scheduling Problem with Group Job-Restrictions

This paper studies two stage flow shop scheduling problem in which equivalent job for group job, processing times on each machine are given. The objective of the study is to get optimal sequence of jobs in order to minimize the total elapsed time. The given problem is solved with branch and bound method.The method is illustrated by numerical example. Keywords: Equivalent job, processing time, elapsed time, Branch and Boun

Efficiency of the solution representations for the hybrid flow shop scheduling problem with makespan objective

In this paper we address the classical hybrid flow shop scheduling problem with makespan objective. As this problem is known to be NP-hard and a very common layout in real-life manufacturing scenarios, many studies have been proposed in the literature to solve it. These contributions use different solution representations of the feasible schedules, each one with its own advantages and disadvantages. Some of them do not guarantee that all feasible semiactive schedules are represented in the space of solutions –thus limiting in principle their effectiveness– but, on the other hand, these simpler solution representations possess clear advantages in terms of having consistent neighbourhoods with well-defined neighbourhood moves. Therefore, there is a trade-off between the solution space reduction and the ability to conduct an efficient search in this reduced solution space. This trade-off is determined by two aspects, i.e. the extent of the solution space reduction, and the quality of the schedules left aside by this solution space reduction. In this paper, we analyse the efficiency of the different solution representations employed in the literature for the problem. More specifically, we first establish the size of the space of semiactive schedules achieved by the different solution representations and, secondly, we address the issue of the quality of the schedules that can be achieved by these representations using the optimal solutions given by several MILP models and complete enumeration. The results obtained may contribute to design more efficient algorithms for the hybrid flow shop scheduling problem.Ministerio de Ciencia e Innovación DPI2016-80750-

Minimizing The Number of Tardy Jobs in Hybrid Flow Shops with Non-Identical Multiple Processors

Two-stage hybrid flow shops (a.k.a., flow shops with multiple processors (FSMPs)) are studied wherein the multiple processors at a stage are non-identical, but related (a.k.a., uniform) in their processing speeds.   The impact of ten different dispatching procedures on a due-date based criterion (specifically, the number of tardy jobs) is analyzed over a set of 1,800 problems of varying configurations wherein the number of jobs per problem is between 20 and 100 and their due dates are randomly assigned.  Results indicate that the modified due date (MDD), earliest due date (EDD), slack (SLK), shortest processing time (SPT), and least work remaining (LWR) rules are statistically inseparable but yield superior performance to the other rules included in this study.  The longest processing time (LPT) and most work remaining (MWR) rules provide the poorest performance

A speed-up procedure for the hybrid flow shop scheduling problem

Article number 115903During the last decades, hundreds of approximate algorithms have been proposed in the literature addressing flow-shop-based scheduling problems. In the race for finding the best proposals to solve these problems, speedup procedures to compute objective functions represent a key factor in the efficiency of the algorithms. This is the case of the well-known Taillard’s accelerations proposed for the traditional flow shop with makespan minimisation or several other accelerations proposed for related scheduling problems. Despite the interest in proposing such methods to improve the efficiency of approximate algorithms, to the best of our knowledge, no speed-up procedure has been proposed so far in the hybrid flow shop literature. To tackle this challenge, we propose in this paper a speed-up procedure for makespan minimisation, which can be incorporate in insertion-based neighbourhoods using a complete representation of the solutions. This procedure is embedded in the traditional iterated greedy algorithm. The computational experience shows that even incorporating the proposed speed-up procedure in this simple metaheuristic results in outperforming the best metaheuristic for the problem under consideration.Junta de Andalucía(España) US-1264511Ministerio de Ciencia e Innovación (España) PID2019-108756RB-I0

Programación de la producción en un sistema flow shop híbrido sin esperas y tiempos de preparación dependientes de la secuencia.

Se estudia la programación de la producción en sistemas flow shop híbrido con tiempos de preparación dependientes de la secuencia de piezas a fabricar. Las piezas pueden pertenecer a diferentes familias y las máquinas requerirán un tiempo de preparación cada vez que se deba cambiar de familia. Se han desarrollado procedimientos heurísticos para el caso monocriterio en el que el objetivo buscado en la programación de la producción es la minimización del retraso medio, equivalente a minimizar la suma de retrasos de las piezas, y para el caso bicriterio en el que se tendrá en cuenta tanto la minimización de una función objetivo formada por la suma ponderada del retraso medio más la suma de los tiempos medios de proceso. Además se han adaptado los métodos implementados para trabajar bajo la restricción nowait

Analysis of Staff Scheduling Effect on Hospitality Staffing Service Efficiency During High-Occupancy Conditions Using Discrete Event Simulation (DES)

This study utilized discrete event simulation (DES) in order to optimize the staff scheduling within the housekeeping department for hotel operation during high-occupancy conditions. High-occupancy situations within hotels occur during peak season times in which guests occupy a greater number of rooms than throughout the year. A literature review showed that DES has been used to optimize various types of schedules. This study was unique in the case that it incorporates computer modeling into the staffing portion of lodging establishments; an area with limited amount of research. Data was collected from historical records and through actual observations. A validated computerized model of the hotel was constructed using Arena 13 to determine an optimal staff schedule, which would decrease guests\u27 waiting times as well as payroll costs in the housekeeping department. A sensitivity analysis was conducted in order to determine the number housekeepers to employ and their length of schedule depending on the acceptable wait time allowed for guests and the number of checkouts. The product of this study was a model that could be used by other lodging establishments to determine how many housekeepers to employ based on the number of rooms checking out and staying over. Future studies could incorporate the rate to stay at the establishment and how that could have an effect on the arrival rate of guests and their willingness to stay at the hotel

Energy aware hybrid flow shop scheduling

Only if humanity acts quickly and resolutely can we limit global warming' conclude more than 25,000 academics with the statement of SCIENTISTS FOR FUTURE. The concern about global warming and the extinction of species has steadily increased in recent years

Heuristics for scheduling in a flow shop with multiple processors

European Journal of Operational Research1131113-122EJOR

Hybrid flow-shop scheduling with different constraints: Heuristic solutions and lp-based lower bounds

Während der Herstellung von Stahl ist es erforderlich, kontinuierlich dessen Qualität zu überwachen. Aus diesem Grund werden an verschiedenen Positionen in einem Stahlwerk fortlaufend Produktproben entnommen und analysiert. Ein großer deutscher Stahlerzeuger betreibt zu diesem Zweck ein vollautomatisiertes Labor. Die Proben werden per Rohrpost in dieses Labor gesendet und dort mit Hilfe verschiedener Maschinen untersucht. Notwendige Transporte zwischen diesen Maschinen werden unter Verwendung mehrerer Roboter durchgeführt. Die Belegungsplanung der Maschinen sowie das entsprechende Routing der Roboter bilden ein komplexes Scheduling-Problem. Dabei soll eine möglichst geringe Aufenthaltsdauer der Proben im Labor realisiert werden. Insgesamt kann diese Aufgabe als dynamisches Hybrid Flow-Shop-Problem mit Transporten und Minimierung der gewichteten Gesamtfertigstellungszeit (resp. gewichtete Gesamtflusszeit) klassifiziert werden, da die Ankunftszeit der Proben a priori nicht bekannt ist. Weil die Analyse einer Probe im Labor zudem maximal wenige Minuten dauern darf, steht nur eine sehr geringe Rechenzeit zur Lösung dieses Scheduling-Problems zur Verfügung. Die Entwicklung eines neuen Entscheidungssystems zur Optimierung der Arbeitsabläufe in einem solchen Labor ist ein Bestandteil der vorliegenden Dissertation. Dazu wird ein mehrstufiges heuristisches Lösungsverfahren entwickelt, welches auf einem Dekompositionsansatz, (engpass-orientierten) Prioritätsregeln und einer job-orientierten List Scheduling Strategie basiert. Die Arbeitsweise des Verfahrens für das Labor wird im Rahmen einer Fallstudie simuliert und die erzielten Lösungen mit dem Ist-Zustand des Labors verglichen. In der entsprechenden Analyse kann ein enormes Verbesserungspotential gegenüber dem derzeit verwendeten Planungstool nachgewiesen werden. Neben diesem anwendungsorientierten Teil der Arbeit wird die Performance des vorgestellten Verfahrens auch für allgemeinere Situationen empirisch untersucht. Zur Auswertung der erzielten Lösungen für verschiedene zufällig generierte Datensätze (insgesamt 1500 Probleminstanzen), werden zwei LP-basierte untere Schranken verwendet, welche auf einer zeit-indizierten gemischt-ganzzahligen Modellierung des Problems beruhen. Darüber hinaus werden diese Schranken auch auf theoretischer Ebene analysiert und mit weiteren in der Literatur gebräuchlichen Schranken verglichen.During the manufacture of steel, its quality has to be monitored continuously. Therefore, samples are taken at several stages of the production process and their chemical composition is analyzed. A big German steel producer uses an automatic laboratory to perform this task. The samples are sent to this laboratory under usage of a pneumatic post system and afterwards they are processed by different machines. Arising transportation tasks between those operations are managed by a fleet of robots. The imetabling of the several machines as well as the related routing of the robots is a complex scheduling problem. Therein the flow time of the samples should be minimized. Altogether, this task can be classified as a dynamic hybrid flow-shop scheduling problem with transportation and total weighted completion time or total weighted flow time objective, because the arrival times of the samples are not known in advance. Because the analysis of one sample should at most last a few minutes, the available computational time to perform the required real-time optimization is strictly limited. The development of a decision support system to optimize the workflow in such a laboratory is one part of this dissertation. Therefore, a multi-stage heuristic algorithm is designed, which is based on a decomposition approach, (bottleneck related) dispatching rules as well as a job-oriented list scheduling strategy. The performance of this method in case of the laboratory is simulated and compared to the current control system. It can be shown that the new approach is able to reduce the total weighted flow time significantly. Beneath this application part of the thesis, the performance of the method is further evaluated in a more theoretical fashion. Therefore, an extensive empirical analysis is performed, where lower bounds are used to benchmark the heuristic solutions to 1500 random problem instances under consideration. These bounds are based on the lp relaxation of two time-indexed mixed-integer formulations of the problem. Furthermore, they are also compared to different other bounds introduced in literature