Models and Strategies for Variants of the Job Shop Scheduling Problem

Recently, a variety of constraint programming and Boolean satisfiability approaches to scheduling problems have been introduced. They have in common the use of relatively simple propagation mechanisms and an adaptive way to focus on the most constrained part of the problem. In some cases, these methods compare favorably to more classical constraint programming methods relying on propagation algorithms for global unary or cumulative resource constraints and dedicated search heuristics. In particular, we described an approach that combines restarting, with a generic adaptive heuristic and solution guided branching on a simple model based on a decomposition of disjunctive constraints. In this paper, we introduce an adaptation of this technique for an important subclass of job shop scheduling problems (JSPs), where the objective function involves minimization of earliness/tardiness costs. We further show that our technique can be improved by adding domain specific information for one variant of the JSP (involving time lag constraints). In particular we introduce a dedicated greedy heuristic, and an improved model for the case where the maximal time lag is 0 (also referred to as no-wait JSPs).Comment: Principles and Practice of Constraint Programming - CP 2011, Perugia : Italy (2011

Constraint satisfaction adaptive neural network and heuristics combined approaches for generalized job-shop scheduling

Copyright @ 2000 IEEEThis paper presents a constraint satisfaction adaptive neural network, together with several heuristics, to solve the generalized job-shop scheduling problem, one of NP-complete constraint satisfaction problems. The proposed neural network can be easily constructed and can adaptively adjust its weights of connections and biases of units based on the sequence and resource constraints of the job-shop scheduling problem during its processing. Several heuristics that can be combined with the neural network are also presented. In the combined approaches, the neural network is used to obtain feasible solutions, the heuristic algorithms are used to improve the performance of the neural network and the quality of the obtained solutions. Simulations have shown that the proposed neural network and its combined approaches are efficient with respect to the quality of solutions and the solving speed.This work was supported by the Chinese National Natural Science Foundation under Grant 69684005 and the Chinese National High-Tech Program under Grant 863-511-9609-003, the EPSRC under Grant GR/L81468

The Complexity of Mean Flow Time Scheduling Problems with Release Times

We study the problem of preemptive scheduling n jobs with given release times on m identical parallel machines. The objective is to minimize the average flow time. We show that when all jobs have equal processing times then the problem can be solved in polynomial time using linear programming. Our algorithm can also be applied to the open-shop problem with release times and unit processing times. For the general case (when processing times are arbitrary), we show that the problem is unary NP-hard.Comment: Subsumes and replaces cs.DS/0412094 and "Complexity of mean flow time scheduling problems with release dates" by P.B, S.

Some recent results in the analysis of greedy algorithms for assignment problems

We survey some recent developments in the analysis of greedy algorithms for assignment and transportation problems. We focus on the linear programming model for matroids and linear assignment problems with Monge property, on general linear programs, probabilistic analysis for linear assignment and makespan minimization, and on-line algorithms for linear and non-linear assignment problems

Unified Concept of Bottleneck

The term `bottleneck` has been extensively used in operations management literature. Management paradigms like the Theory of Constraints focus on the identification and exploitation of bottlenecks. Yet, we show that the term has not been rigorously defined. We provide a classification of bottleneck definitions available in literature and discuss several myths associated with the concept of bottleneck. The apparent diversity of definitions raises the question whether it is possible to have a single bottleneck definition which has as much applicability in high variety job shops as in mass production environments. The key to the formulation of an unified concept of bottleneck lies in relating the concept of bottleneck to the concept of shadow price of resources. We propose an universally applicable bottleneck definition based on the concept of average shadow price. We discuss the procedure for determination of bottleneck values for diverse production environments. The Law of Diminishing Returns is shown to be a sufficient but not necessary condition for the equivalence of the average and the marginal shadow price. The equivalence of these two prices is proved for several environments. Bottleneck identification is the first step in resource acquisition decisions faced by managers. The definition of bottleneck presented in the paper has the potential to not only reduce ambiguity regarding the meaning of the term but also open a new window to the formulation and analysis of a rich set of problems faced by managers.

Batch Sequencing and Cooperation

Game theoretic analysis of sequencing situations has been restricted to manufactur- ing systems which consist of machines that can process only one job at a time. However, in many manufacturing systems, operations are carried out by batch machines which can simultaneously process multiple jobs. This paper aims to extend the game theoretical approach to the cost allocation problems arising from sequencing situations on systems that consist of batch machines. We first consider sequencing situations with a single batch machine and analyze cooperative games arising from these situations. It is shown that these games are convex and an expression for the Shapley value of these games is provided. We also introduce an equal gain splitting rule for these sequencing situa- tions and provide an axiomatic characterization. Second, we analyze various aspects of flow-shop sequencing situations which consist of batch machines only. In particular, we provide two cases in which the cooperative game arising from the flow-shop sequencing situation is equal to the game arising from a sequencing situation that corresponds to one specific machine in the flow-shop.Sequencing situations;sequencing games;batch machines

High-Level Object Oriented Genetic Programming in Logistic Warehouse Optimization

Disertační práce je zaměřena na optimalizaci průběhu pracovních operací v logistických skladech a distribučních centrech. Hlavním cílem je optimalizovat procesy plánování, rozvrhování a odbavování. Jelikož jde o problém patřící do třídy složitosti NP-težký, je výpočetně velmi náročné nalézt optimální řešení. Motivací pro řešení této práce je vyplnění pomyslné mezery mezi metodami zkoumanými na vědecké a akademické půdě a metodami používanými v produkčních komerčních prostředích. Jádro optimalizačního algoritmu je založeno na základě genetického programování řízeného bezkontextovou gramatikou. Hlavním přínosem této práce je a) navrhnout nový optimalizační algoritmus, který respektuje následující optimalizační podmínky: celkový čas zpracování, využití zdrojů, a zahlcení skladových uliček, které může nastat během zpracování úkolů, b) analyzovat historická data z provozu skladu a vyvinout sadu testovacích příkladů, které mohou sloužit jako referenční výsledky pro další výzkum, a dále c) pokusit se předčit stanovené referenční výsledky dosažené kvalifikovaným a trénovaným operačním manažerem jednoho z největších skladů ve střední Evropě.This work is focused on the work-flow optimization in logistic warehouses and distribution centers. The main aim is to optimize process planning, scheduling, and dispatching. The problem is quite accented in recent years. The problem is of NP hard class of problems and where is very computationally demanding to find an optimal solution. The main motivation for solving this problem is to fill the gap between the new optimization methods developed by researchers in academic world and the methods used in business world. The core of the optimization algorithm is built on the genetic programming driven by the context-free grammar. The main contribution of the thesis is a) to propose a new optimization algorithm which respects the makespan, the utilization, and the congestions of aisles which may occur, b) to analyze historical operational data from warehouse and to develop the set of benchmarks which could serve as the reference baseline results for further research, and c) to try outperform the baseline results set by the skilled and trained operational manager of the one of the biggest warehouses in the middle Europe.