An asymptotically optimal online algorithm to minimize the total completion time on two multipurpose machines with unit processing times

AbstractIn the majority of works on online scheduling on multipurpose machines the objective is to minimize the makespan. We, in contrast, consider the objective of minimizing the total completion time. For this purpose, we analyze an online-list scheduling problem of n jobs with unit processing times on a set of two machines working in parallel. Each job belongs to one of two sets of job types. Jobs belonging to the first set can be processed on either of the two machines while jobs belonging to the second set can only be processed on the second machine. We present an online algorithm with a competitive ratio of ρLB+O(1n), where ρLB is a lower bound on the competitive ratio of any online algorithm and is equal to 1+(−α+4α3−α2+2α−12α2+1)2 where α=13+16(116−678)1/3+(58+378)1/33(2)2/3≈1.918. This result implies that our online algorithm is asymptotically optimal

Robust Two-Stage Packing into Designated and Multipurpose Bins

International audienceMultitype bin packing is a natural extension of the classical bin packing with applications to shipping using climate-controlled containers and plain dry containers. In transportation and other logistics applications there may be significant uncertainty with respect to the exact quantities of different variants of products (or item types) that may need to be shipped at the time when the containers and packaging are procured. In the current paper we model the problem as a robust two-stage two-item type bin packing problem. In the first stage bins of different types are acquired (e.g., reefer containers and dry containers). In the second stage the items are packed into bins. The bins that are secured in the first phase must allow for all of the items to be packed in the "worst-case" demand scenario. We first develop an algorithm for the robust two-stage two-item type bin packing problem with general item-number uncertainty sets and certain box uncertainty sets for item sizes (or equivalently two item sizes). We then consider the special case of identical (or unit) item sizes. In this special case we develop closed-form solutions for the optimal solution. Our closed-form solution reveals that it is optimal to use a number of multipurpose bins that is linear in the number of items. This is in contrast with solutions of the online and offline deterministic version of our problem that use at most one multipurpose bin. Finally, we consider computational methods that are efficient in practice for a generalization with unit item sizes but with an arbitrary number of item and bin types and arbitrary compatibility structures

Model approximation for batch flow shop scheduling with fixed batch sizes

Batch flow shops model systems that process a variety of job types using a fixed infrastructure. This model has applications in several areas including chemical manufacturing, building construction, and assembly lines. Since the throughput of such systems depends, often strongly, on the sequence in which they produce various products, scheduling these systems becomes a problem with very practical consequences. Nevertheless, optimally scheduling these systems is NP-complete. This paper demonstrates that batch flow shops can be represented as a particular kind of heap model in the max-plus algebra. These models are shown to belong to a special class of linear systems that are globally stable over finite input sequences, indicating that information about past states is forgotten in finite time. This fact motivates a new solution method to the scheduling problem by optimally solving scheduling problems on finite-memory approximations of the original system. Error in solutions for these “t-step” approximations is bounded and monotonically improving with increasing model complexity, eventually becoming zero when the complexity of the approximation reaches the complexity of the original system.United States. Department of Homeland Security. Science and Technology Directorate (Contract HSHQDC-13-C-B0052)United States. Air Force Research Laboratory (Contract FA8750-09-2-0219)ATK Thiokol Inc

Scheduling with processing set restrictions : a survey

2008-2009 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

A cyclic approach to large-scale short-term planning in chemical batch production

We deal with the scheduling of processes on a multi-product chemical batch production plant. Such a plant contains a number of multi-purpose processing units and storage facilities of limited capacity. Given primary requirements for the final products, the problem consists in dividing the net requirements for the final and the intermediate products into batches and scheduling the processing of these batches. Due to the computational intractability of the problem, the monolithic MILP models proposed in the literature can generally not be used for solving large-scale problem instances. The cyclic solution approach presented in this paper starts from the decomposition of the problem into a batching and a batch-scheduling problem. The complete production schedule is obtained by computing a cyclic subschedule, which is then repeated several times. In this way, good feasible schedules for large-scale problem instances are found within a short CPU tim

Methods and algorithms for integrated multi-scale optimisation of production planning and scheduling

Imperial Users onl

Manufacturing production line modelling and classification of associated np-hard problems

Optimisation of production lines is known to be NP-Hard in the general case so many near-optimal approximation algorithms have been researched to overcome the challenge. In this paper we describe an approach to modelling production lines using a graph theoretic model. In particular, we focus on single machine and job shop problems. We show that the model can be extended to open shop problems. We also discuss how the model can be used to classify scheduling problems from the generated models.peer-reviewe

Study on application possibilities of Case-Based Reasoning on the domain of scheduling problems

Ces travaux concernent la mise en place d'un système d'aide à la décision, s'appuyant sur le raisonnement à partir de cas, pour la modélisation et la résolution des problèmes d'ordonnancement en génie des procédés. Une analyse de co-citation a été exécutée afin d'extraire de la littérature la connaissance nécessaire à la construction de la stratégie d'aide à la décision et d'obtenir une image de la situation, de l'évolution et de l'intensité de la recherche du domaine des problèmes d'ordonnancement. Un système de classification a été proposée, et la nomenclature proposée par Blazewicz et al. (2007) a été étendue de manière à pouvoir caractériser de manière complète les problèmes d'ordonnancement et leur mode de résolution. Les difficultés d'adaptation du modèle ont été discutées, et l'efficacité des quatre modèles de littérature a été comparée sur trois exemples de flow-shop. Une stratégie de résolution est proposée en fonction des caractéristiques du problème mathématique. ABSTRACT : The purpose of this study is to work out the foundations of a decision-support system in order to advise efficient resolution strategies for scheduling problems in process engineering. This decision-support system is based on Case-Based Reasoning. A bibliographic study based on co-citation analysis has been performed in order to extract knowledge from the literature and obtain a landscape about scheduling research, its intensity and evolution. An open classification scheme has been proposed to scheduling problems, mathematical models and solving methods. A notation scheme corresponding to the classification has been elaborated based on the nomenclature proposed by Blazewicz et al. (2007). The difficulties arising during the adaptation of a mathematical model to different problems is discussed, and the performances of four literature mathematical models have been compared on three flow-shop examples. A resolution strategy is proposed based on the characteristics of the scheduling problem