A hybrid constraint programming approach to?the?log-truck scheduling problem

Scheduling problems in the forest industry have received significant attention in the recent years and have contributed many challenging applications for optimization technologies. This paper proposes a solution method based on constraint programming and mathematical programming for a log-truck scheduling problem. The problem consists of scheduling the transportation of logs between forest areas and woodmills, as well as routing the fleet of vehicles to satisfy these transportation requests. The objective is to minimize the total cost of the non-productive activities such as the waiting time of trucks and forest log-loaders and the empty driven distance of vehicles. We propose a constraint programming model to address the combined scheduling and routing problem and an integer programming model to deal with the optimization of deadheads. Both of these models are combined through the exchange of global constraints. Finally the whole approach is validated on real industrial data.     

ARMMS: Analogical reasoning model management system for multicriteria vehicle scheduling

The transportation industry problem of scheduling vehicles combines the spatial characteristics of routing with time domain considerations of activity schedules. The problem is complex because of the numerous interacting constraints in the spatial and time domains. Further, some of the constraints are flexible and some arise in real-time. The scheduling problem is often presented with multiple objectives that are not all economic in nature and which can be contradictory to one another. In response to these needs, this paper describes an analogical reasoning model management system, called ARMMS, designed in the domain of vehicle scheduling. ARMMS consists of knowledge bases and data bases, a truth maintenance system, a user interface, an inference engine, a learning mechanism, and a model library. Given a scheduling problem, ARMMS searches its memory for solutions. If no solution is available, ARMMS falls back on an analogical problem solving approach in which similar experience can be recalled, and solutions to new, but similar, problems can be constructed. If no similar experience exists, ARMMS intelligently selects an appropriate algorithmic model from its model library, based on the input parameters and problem type, to solve the given problem. By combining experts' knowledge, analogical problem-solving approaches, and algorithmic methods, ARMMS provides an efficient problem-solving approach for vehicle scheduling and routing. ARMMS is also a feasible base for the development of intelligent model management systems.     

A Queueing Framework for Routing Problems with Time-dependent Travel Times

Assigning and scheduling vehicle routes in a dynamic environment is a crucial management problem. Despite numerous publications dealing with efficient scheduling methods for vehicle routing, very few addressed the inherent stochastic and dynamic nature of travel times. In this paper, a vehicle routing problem with time-dependent travel times due to potential traffic congestion is considered. The approach developed introduces the traffic congestion component based on queueing theory. This is an innovative modelling scheme to capture the stochastic behavior of travel times as it generates an analytical expression for the expected travel times as well as for the variance of the travel times. Routing solutions that perform well in the face of the extra complications due to congestion are developed. These more realistic solutions have the potential to reduce real operating costs for a broad range of industries which daily face routing problems. A number of datasets are used to illustrate the appropriateness of the novel approach. Moreover it is shown that static (or time-independent) solutions are often infeasible within a congested traffic environment which is generally the case on European road networks. Finally, the effect of travel time variability (obtained via the queueing approach) is quantified for the different datasets.      

Vehicle dispatching system based on Taguchi-tuned fuzzy rules

This paper presents the development of a dispatching system for a fleet of automated guided vehicles in a flexible manufacturing environment which is based on a hybrid Fuzzy–Taguchi approach. A fuzzy decision-making system emulates the human behavior necessary for multi-objective directed decision making in a dynamically evolving environment. A statistical approach based on the Taguchi method tunes the fuzzy rules to achieve near optimal performance. Simulation results demonstrate the effectiveness of this marriage of computational tools in dealing with the well-known NP-complete scheduling problem.     

A Vehicle-scheduling System for Delivering School Meals

This paper reports an application of vehicle-scheduling for the Inner London Education Authority. A semi-interactive, microcomputer-based system was designed and implemented to assist the scheduling of vehicles which deliver meals from kitchens to schools. The scheduling methodology used was heuristic in nature, being based in part on the well-known savings concept and also incorporating a novel approach to the problem of ‘time-window’ constraints on the collection and delivery of meals.     

HOPS – Hamming-Oriented Partition Search for production planning in the spinning industry

In this paper, we investigate a two-stage lot-sizing and scheduling problem in a spinning industry. A new hybrid method called HOPS (Hamming-Oriented Partition Search), which is a branch-and-bound based procedure that incorporates a fix-and-optimize improvement method is proposed to solve the problem. An innovative partition choice for the fix-and-optimize is developed. The computational tests with generated instances based on real data show that HOPS is a good alternative for solving mixed integer problems with recognized partitions such as the lot-sizing and scheduling problem.     

Constraint-Based Job Shop Scheduling with IILOG SCHEDULER

We introduce constraint-based scheduling and discuss its main principles. An approximation algorithm based on tree search is developed for the job shop scheduling problem using ILOG SCHEDULER. A new way of calculating lower bounds on the makespan of the job shop scheduling problem is presented and we show how such results can be used within a constraint-based approach. An empirical performance analysis shows that the algorithm we developed performs well. Finally, taking the job shop scheduling problem as a start point, we discuss how constraint-based scheduling can be used to solve more general scheduling problems.     

Integration of production planning and scheduling using an expert system and a genetic algorithm

In the traditional approaches, processes of planning and scheduling are done sequentially, where the process plan is determined before the actual scheduling is performed. This simple approach ignores the relationship between the scheduling and planning. Practical scheduling systems need to be able to react to significant real-time events within an acceptable response time and revise schedules appropriately. Therefore, the author proposes a new methodology with artificial intelligence to support production planning and scheduling in supply net. In this approach, the production planning problem is first solved, and then the scheduling problem is considered with the constraint of the solution. The approach is implemented as a combination of expert system and genetic algorithm. The research indicates that the new system yields better results in real-life supply net than using a traditional method. The results of experiments provide that the proposed genetic algorithm produces schedules with makespan that is average 21% better than the methods based on dispatching rules.     

Multi-depot vehicle scheduling problems with time windows and waiting costs

The multi-depot vehicle scheduling problem with time windows (MDVSPTW) consists of scheduling a fleet of vehicles to cover a set of tasks at minimum cost. Each task is restricted to begin within a prescribed time interval and vehicles are supplied by different depots. The problem is formulated as an integer nonlinear multi-commodity network flow model with time variables and is solved using a column generation approach embedded in a branch-and-bound framework. This paper breaks new ground by considering costs on exact waiting times between two consecutive tasks instead of minimal waiting times. This new and more realistic cost structure gives rise to a nonlinear objective function in the model. Optimal and heuristic versions of the algorithm have been extensively tested on randomly generated urban bus scheduling problem (UBSP) and freight transport scheduling problem (FTSP). The results show that such a general solution methodology outperforms specialized algorithms when minimal waiting costs are used, and can efficiently treat the case with exact waiting costs.     

Integrated machine scheduling and vehicle routing with time windows

This paper integrates production and outbound distribution scheduling in order to minimize total tardiness. The overall problem consists of two subproblems. The first addresses scheduling a set of jobs on parallel machines with machine-dependent ready times. The second focusses on the delivery of completed jobs with a fleet of vehicles which may differ in their loading capacities and ready times. Job-dependent processing times, delivery time windows, service times, and destinations are taken into account. A genetic algorithm approach is introduced to solve the integrated problem as a whole. Two main questions are examined. Are the results of integrating machine scheduling and vehicle routing significantly better than those of classic decomposition approaches which break down the overall problem, solve the two subproblems successively, and merge the subsolutions to form a solution to the overall problem? And if so, is it possible to capitalize on these potentials despite the complexity of the integrated problem? Both questions are tackled by means of a numerical study. The genetic algorithm outperforms the classic decomposition approaches in case of small-size instances and is able to generate relatively good solutions for instances with up to 50 jobs, 5 machines, and 10 vehicles.     

Integrated production and material handling scheduling using mathematical programming and constraint programming

In this article, we propose an integrated formulation of the combined production and material handling scheduling problems. Traditionally, scheduling problems consider the production machines as the only constraining resource. This is however no longer true as material handling vehicles are becoming more and more valuable resources requiring important investments. Their operations should be optimized and above all synchronized with machine operations. In the problem addressed in this paper, a job shop context is considered. Machines and vehicles are both considered as constraining resources. The integrated scheduling problem is formulated as a mathematical programming model and as a constraint programming model which are compared for optimally solving a series of test problems. A commercial software (ILOG OPLStudio) was used for modeling and testing both models.     

Crossdocking— Just in Time scheduling: an alternative solution approach

In this paper, a scheduling problem which allows a warehouse to function as a crossdock where transit storage time for cargo is minimized according to Just in Time scheduling is studied. A model that uses the machine scheduling notation to describe the problem is written. As the problem is NP-hard, a solution approach based on a combination of two metaheuristics, Reactive GRASP and Tabu Search (RGTS), is provided. Experiments are carried out to determine the usefulness of this approach. The results obtained from the exact method that uses the ILOG CPLEX 9.1 solver for 16 problem instances and the results obtained from the RGTS metaheuristic scheduling algorithm and two other algorithms proposed by other authors for the same problem instances are discussed. Analysis and comparisons are made.     

A multilevel machine and vehicle scheduling in a flexible manufacturing system

The paper presents a multilevel decision model for simultaneous machine and vehicle scheduling in a flexible manufacturing system. The system is composed of various machine types and a set of automated guided vehicles that permit each part to move between any pair of machines. The upper level of the decision model involves machine loading and part routing for which a bicriterion integer formulation is presented with the objective of balancing machine workloads and intermachine flows of parts. The lower level involves simultaneous scheduling of machines and vehicles for which a period-by-period heuristic is proposed based on a family of complex dispatching rules. The scheduling objective is to meet all part type requirements in a minimum time. Computational examples are included to illustrate the approach proposed.     

Optimizing Preventive Maintenance Models

We deal with the problem of scheduling preventive maintenance (PM) for a system so that, over its operating life, we minimize a performance function which reflects repair and replacement costs as well as the costs of the PM itself. It is assumed that a hazard rate model is known which predicts the frequency of system failure as a function of age. It is also assumed that each PM produces a step reduction in the effective age of the system. We consider some variations and extensions of a PM scheduling approach proposed by Lin et al. [6]. In particular we consider numerical algorithms which may be more appropriate for hazard rate models which are less simple than those used in [6] and we introduce some constraints into the problem in order to avoid the possibility of spurious solutions. We also discuss the use of automatic differentiation (AD) as a convenient tool for computing the gradients and Hessians that are needed by numerical optimization methods. The main contribution of the paper is a new problem formulation which allows the optimal number of occurrences of PM to be determined along with their optimal timings. This formulation involves the global minimization of a non-smooth performance function. In our numerical tests this is done via the algorithm DIRECT proposed by Jones et al. [19]. We show results for a number of examples, involving different hazard rate models, to give an indication of how PM schedules can vary in response to changes in relative costs of maintenance, repair and replacement. Part of this work was carried out while the first author was a Visiting Professor in the Department of Mechanical Engineering at the University of Alberta in December 2003.     

A branch-and-bound procedure for the multi-mode resource-constrained project scheduling problem with minimum and maximum time lags

The paper presents an exact procedure for a general resource-constrained project scheduling problem where multiple modes are available for the performance of the individual activities and minimum as well as maximum time lags between the different activities may be given. The objective is to determine a mode and a start time for each activity such that all constraints are observed and the project duration is minimized. Project scheduling problems of this type occur, e.g. in process industries. The solution method is a depth-first search based branch-and-bound procedure. It makes use of a branching strategy where the branching rule is selected dynamically. The solution approach is an integration approach where the modes and start times are determined simultaneously. Within an experimental performance analysis this procedure is compared with existing solution procedures.     

Tri-directional Scheduling Scheme: Theory and Computation

In this paper we introduce a new scheduling scheme based on so called tri-directional scheduling strategy to solve the well known resource constrained project scheduling problem. In order to demonstrate the effectiveness of tri-directional scheduling scheme, it is incorporated into a priority rule based parallel scheduling scheme. Theoretical and numerical investigations show that the tri-directional scheduling scheme outperforms forward, backward and even bidirectional schemes depending on the problem structure and the priority rule used. Based on empirical evidence, it seems that as the number of activities are increased, the tri-directional scheduling scheme performs better irrespective of the priority rule used. This suggests that tri-directional scheme should also be applied within the category of heuristic methods.     

Exploiting process plan flexibility in production scheduling: A multi-objective approach

When solving a product/process design problem, we must exploit the available degrees of freedom to cope with a variety of issues. Alternative process plans can be generated for a given product, and choosing one of them has implications on manufacturing functions downstream, including planning/scheduling. Flexible process plans can be exploited in real time to react to machine failures, but they are also relevant for off-line scheduling. On the one hand, we should select a process plan in order to avoid creating bottleneck machines, which would deteriorate the schedule quality; on the other one we should aim at minimizing costs. Assessing the tradeoff between these possibly conflicting objectives is difficult; actually, it is a multi-objective problem, for which available scheduling packages offer little support. Since coping with a multi-objective scheduling problem with flexible process plans by an exact optimization algorithm is out of the question, we propose a hierarchical approach, based on a decomposition into a machine loading and a scheduling sub-problem. The aim of machine loading is to generate a set of efficient (non-dominated) solutions with respect to the load balancing and cost objectives, leaving to the user the task of selecting a compromise solution. Solving the machine loading sub-problem essentially amounts to selecting a process plan for each job and to routing jobs to the machines; then a schedule must be determined. In this paper we deal only with the machine loading sub-problem, as many scheduling methods are already available for the problem with fixed process plans. The machine loading problem is formulated as a bicriterion integer programming model, and two different heuristics are proposed, one based on surrogate duality theory and one based on a genetic descent algorithm. The heuristics are tested on a set of benchmark problems.     

Multicriteria scheduling optimization using an elitist multiobjective population heuristic: the h-NSDE algorithm

In today’s manufacturing industry more than one performance criteria are considered for optimization to various degrees simultaneously. To deal with such hard competitive environments it is essential to develop appropriate multicriteria scheduling approaches. In this paper consideration is given to the problem of scheduling n independent jobs on a single machine with due dates and objective to simultaneously minimize three performance criteria namely, total weighted tardiness (TWT), maximum tardiness and maximum earliness. In the single machine scheduling literature no previous studies have been performed on test problems examining these criteria simultaneously. After positioning the problem within the relevant research field, we present a new heuristic algorithm for its solution. The developed algorithm termed the hybrid non-dominated sorting differential evolution (h-NSDE) is an extension of the author’s previous algorithm for the single-machine mono-criterion TWT problem. h-NSDE is devoted to the search for Pareto-optimal solutions. To enable the decision maker for evaluating a greater number of alternative non-dominated solutions, three multiobjective optimization approaches have been implemented and tested within the context of h-NSDE: including a weighted-sum based approach, a fuzzy-measures based approach which takes into account the interaction among the criteria as well as a Pareto-based approach. Experiments conducted on existing data set benchmarks problems show the effect of these approaches on the performance of the h-NSDE algorithm. Moreover, comparative results between h-NSDE and some of the most popular multiobjective metaheuristics including SPEA2 and NSGA-II show clear superiority for h-NSDE in terms of both solution quality and solution diversity.     

A time–space network based exact optimization model for multi-depot bus scheduling

The vehicle scheduling problem, arising in public transport bus companies, addresses the task of assigning buses to cover a given set of timetabled trips with consideration of practical requirements, such as multiple depots and vehicle types as well as depot capacities. An optimal schedule is characterized by minimal fleet size and minimal operational costs including costs for unloaded trips and waiting time. This paper discusses the multi-depot, multi-vehicle-type bus scheduling problem (MDVSP), involving multiple depots for vehicles and different vehicle types for timetabled trips. We use time–space-based instead of connection-based networks for MDVSP modeling. This leads to a crucial size reduction of the corresponding mathematical models compared to well-known connection-based network flow or set partitioning models. The proposed modeling approach enables us to solve real-world problem instances with thousands of scheduled trips by direct application of standard optimization software. To our knowledge, the largest problems that we solved to optimality could not be solved by any existing exact approach. The presented research results have been developed in co-operation with the provider of transportation planning software PTV AG. A software component to support planners in public transport was designed and implemented in context of this co-operation as well.     

A branch-and-bound algorithm with fuzzy inference for a permutation flowshop scheduling problem

This paper considers an m-machine permutation flowshop scheduling problem of minimizing the makespan. This classical scheduling problem is still important in modern manufacturing systems, and is well known to be intractable (i.e., NP-hard). In fact branch-and-bound algorithms developed so far for this problem have not come to solve large scale problem instances with over a hundred jobs. In order to improve the performance of branch-and-bound algorithms this paper proposes a new dominance relation by which the search load could be reduced, and notices that it is based on a sufficient precondition. This suggests that the dominance relation holds with high possibility even if the precondition approximately holds, thus being more realistic. The branch-and-bound algorithm proposed here takes advantage of this possibility for obtaining an optimal solution as early as possible in the branch-and-bound search. For this purpose this paper utilizes membership functions in the context of the fuzzy inference. Extensive numerical experiments that were executed through Monte Carlo simulations and benchmark tests show that the developed branch-and-bound algorithm can solve 3-machine problem instances with up to 1000 jobs with probability of over 99%, and 4-machine ones with up to 900 jobs with over 97%.