Customer order scheduling on a single machine with family setup times: complexity and algorithms

Cataloged from PDF version of article.We consider a situation where C customers each order various quantities (possibly zero in some cases) of products from P different families, which can be produced on a continuously available machine in any sequence (requiring a setup whenever production switches from one family to another). We assume that the time needed for a setup depends only on the family to be produced immediately after it, and we follow the item availability model (which implies that all units are ready for dispatch as soon as they are produced). However, an order is shipped only when all units required by a customer are ready. The time from the start (time zero) to the completion of a customer order is called the order lead time. The problem, which restates the original description of the customer order scheduling problem, entails finding a production schedule that will minimize the total order lead time. While this problem has received some attention in the literature, its complexity status has remained vexingly open. In this note, we show for the first time that the problem is strongly NP-hard. We proceed to give dynamic programming based exact solution algorithms for the general problem and a special case (where C is fixed). These algorithms allow us to solve small instances of the problem and understand the problem complexity more fully. In particular, the solution of the special case shows that the problem is solvable in polynomial time when C is fixed. 2006 Elsevier Inc. All rights reserved

Coordinated scheduling of customer orders with decentralized machine locations

Department of Logistics2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Coordinating production and distribution of jobs with bundling operations

Department of Logistics2006-2007 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Deterministic Assembly Scheduling Problems: A Review and Classification of Concurrent-Type Scheduling Models and Solution Procedures

Many activities in industry and services require the scheduling of tasks that can be concurrently executed, the most clear example being perhaps the assembly of products carried out in manufacturing. Although numerous scientific contributions have been produced on this area over the last decades, the wide extension of the problems covered and the lack of a unified approach have lead to a situation where the state of the art in the field is unclear, which in turn hinders new research and makes translating the scientific knowledge into practice difficult. In this paper we propose a unified notation for assembly scheduling models that encompass all concurrent-type scheduling problems. Using this notation, the existing contributions are reviewed and classified into a single framework, so a comprehensive, unified picture of the field is obtained. In addition, a number of conclusions regarding the state of the art in the topic are presented, as well as some opportunities for future research.Ministerio de Ciencia e Innovación español DPI2016-80750-

Order scheduling in dedicated and flexible machine environments

Order scheduling models are relatively new in the field of scheduling. Consider a facility with m parallel machines that can process k different products (job types). Each machine can process a given subset of different product types. There are n orders from n different clients. Each order requests specific quantities of the various different products that can be produced concurrently on their given subsets of machines; it may have a release date, a weight and a due date. Preemptions may be allowed. An order can not be shipped until the processing of all the products for the order has been completed. Thus, the finish time of an order is the time when the last job of the order has been completed. Even though the idea is somewhat new that order scheduling measures the overall completion time of a set of jobs (i.e., an order requesting different product types) instead of the individual completion time of each product type for any given order, many applications require that decision-makers consider orders rather than the individual product types in orders. Research into order scheduling models is motivated by their various real-life applications in manufacturing systems, equipment maintenance, computing systems, and other industrial contexts, where the components of each order can be processed concurrently on the parallel machines. In this research, two cases of order scheduling models are studied, namely, the fully dedicated environment in which each machine can produce one and only one product type, and the fully flexible machine environment in which each machine can produce all product types. With different side constraints and objective functions, the two cases include a lot of problems that are of interest. Special interest is focused on the minimization of the total weighted completion time, the number of late orders, the maximum lateness, and so on. On the one hand, polynomial time algorithms are proposed for some problems. One the other hand, for problems that are NP-hard, complexity proofs are shown and heuristics with their worst-case performance and empirical analyses are also presented

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