Multicriteria order acceptance decision support in over-demanded job shops: A neural network approach

Order acceptance is an important issue in job shop production systems where demand exceeds capacity. In this paper, a neural network approach is developed for order acceptance decision support in job shops with machine and manpower capacity constraints. First, the order acceptance decision problem is formulated as a sequential multiple criteria decision problem. Then a neural network based preference model for order prioritization is described. The neural network based preference model is trained using preferential data derived from pairwise comparisons of a number of representative orders. An order acceptance decision rule based on the preference model is proposed. Finally, a numerical example is discussed to illustrate the use of the proposed neural network approach. The proposed neural network approach is shown to be a viable method for multicriteria order acceptance decision support in over-demanded job shops.     

An efficient algorithm for a job shop problem

We study the problem of minimizing makespan in a two-machine job shop with unit processing time operations. An efficient algorithm with respect to a succinct encoding of the problem instances is proposed. The algorithm is an improvement of earlier algorithms proposed for the problem by Brucker [1,2], Hefetz and Adiri [7], and Timkovskiy [15]. The idea behind the algorithm has the potential of extension to job shops with parallel machines.This research is supported in part by NSERC Grants A4619, OGP0105675, OGP0104900, General Motors of Canada, and the Manufacturing Research Corporation of Ontario.     

Multi-population interactive coevolutionary algorithm for flexible job shop scheduling problems

In this paper, it proposes a multi-population interactive coevolutionary algorithm for the flexible job shop scheduling problems. In the proposed algorithm, both the ant colony optimization and genetic algorithm with different configurations were applied to evolve each population independently. By the interaction, competition and sharing mechanism among populations, the computing resource is utilized more efficiently, and the quality of populations is improved effectively. The performance of our proposed approach was evaluated by a lot of benchmark instances taken from literature. The experimental results have shown that the proposed algorithm is a feasible and effective approach for the flexible job shop scheduling problem.     

Routing and scheduling in a flexible job shop by tabu search

A hierarchical algorithm for the flexible job shop scheduling problem is described, based on the tabu search metaheuristic. Hierarchical strategies have been proposed in the literature for complex scheduling problems, and the tabu search metaheuristic, being able to cope with different memory levels, provides a natural background for the development of a hierarchical algorithm. For the case considered, a two level approach has been devised, based on the decomposition in a routing and a job shop scheduling subproblem, which is obtained by assigning each operation of each job to one among the equivalent machines. Both problems are tackled by tabu search. Coordination issues between the two hierarchical levels are considered. Unlike other hierarchical schemes, which are based on a one-way information flow, the one proposed here is based on a two-way information flow. This characteristic, together with the flexibility of local search strategies like tabu search, allows to adapt the same basic algorithm to different objective functions. Preliminary computational experience is reported.     

Minimizing the Range of Order Completion Times with Multiple Job Classes

A number of important contributions have been made toward the problem of minimizing the difference in ‘customer’ treatment on a single machine. However, so far, all the research has been to solve the problem of minimizing the ‘job’ difference. That is, it is assumed implicitly that each customer places only one job, and hence minimizing the difference in customer treatment is equivalent to minimizing the difference in job treatment. In many practical situations, a customer may place an order which consists of several jobs. The jobs usually can be grouped into different classes. Thus, the range, i.e. the difference between the maximum and the minimum, of order completion times becomes an appropriate performance measure for treating customers equally. In this paper, a dynamic programming (DP) algorithm is developed to provide the optimal solution. Due to the exponential time complexity of the DP algorithm, two heuristic methods are also proposed to solve large-sized problems. Computational results for the heuristics are provided.     

Supply chain scheduling with receiving deadlines and non-linear penalty

We study the operations scheduling problem with delivery deadlines in a three-stage supply chain process consisting of (1) heterogeneous suppliers, (2) capacitated processing centres (PCs), and (3) a network of business customers. The suppliers make and ship semi-finished products to the PCs where products are finalized and packaged before they are shipped to customers. Each business customer has an order quantity to fulfil and a specified delivery date, and the customer network has a required service level so that if the total quantity delivered to the network falls below a given targeted fill rate, a non-linear penalty will apply. Since the PCs are capacitated and both shipping and production operations are non-instantaneous, not all the customer orders may be fulfilled on time. The optimization problem is therefore to select a subset of customers whose orders can be fulfilled on time and a subset of suppliers to ensure the supplies to minimize the total cost, which includes processing cost, shipping cost, cost of unfilled orders (if any), and a non-linear penalty if the target service level is not met. The general version of this problem is difficult because of its combinatorial nature. In this paper, we solve a special case of this problem when the number of PCs equals one, and develop a dynamic programming-based algorithm that identifies the optimal subset of customer orders to be fulfilled under each given utilization level of the PC capacity. We then construct a cost function of a recursive form, and prove that the resulting search algorithm always converges to the optimal solution within pseudo-polynomial time. Two numerical examples are presented to test the computational performance of the proposed algorithm.     

Heuristics for a coupled-operation scheduling problem

In this paper, we study a strongly NP-hard single machine scheduling problem in which each job consists of two operations that are separated by a time delay which lies within a specified range. The objective is to minimize the makespan. Determining the feasibility and, if applicable, makespan of any proposed permutation of the operations is non-trivial, requiring a longest path algorithm with O(n²) complexity for each permutation. Several heuristic algorithms are proposed: a deterministic and randomized construction algorithm, three descent algorithms and two reactive tabu search algorithms. The local search algorithms use a first improvement neighbourhood and mainly visit only feasible solutions within the search space. Results of extensive computational tests are reported, showing that the heavy computational burden of testing potential solutions renders the local search algorithms uncompetitive in comparison to the construction algorithms. The iterated descent algorithm performs least well.     

A facility neighborhood search heuristic for capacitated facility location with single-source constraints and flexible demand

We consider a generalization of the well-known capacitated facility location problem with single source constraints in which customer demand contains a flexible dimension. This work focuses on providing fast and practically implementable optimization-based heuristic solution methods for very large scale problem instances. We offer a unique approach that utilizes a high-quality efficient heuristic within a neighborhood search to address the combined assignment and fixed-charge structure of the underlying optimization problem. We also study the potential benefits of combining our approach with a so-called very large-scale neighborhood search (VLSN) method. As our computational test results indicate, our work offers an attractive solution approach that can be tailored to successfully solve a broad class of problem instances for facility location and similar fixed-charge problems.     

A polynomial time heuristic for the two-machine flowshop scheduling problem with setup times and random processing times

The two-machine flowshop scheduling problem to minimize makespan is addressed. Jobs have random processing times which are bounded within certain intervals. The distributions of job processing times are not known. This problem has been addressed in the literature with the assumption that setup times are included in processing times or are zero. In this paper, we relax this assumption and treat setup times as separate from processing times. We propose a polynomial time heuristic algorithm. Both Johnson algorithm and Yoshida and Hitomi algorithm, both of which developed for the deterministic problem, are special cases of the proposed algorithm. The heuristic algorithm uses a weighted average of lower and upper bounds for processing times. For different weights, the results of the proposed algorithm are compared based on randomly generated data. The computational analysis has shown that the proposed algorithm, with equal weights given to the lower and upper bounds, performs considerably well with an overall average error of 0.36%. The analysis has also shown that the proposed algorithm can safely be used regardless of processing time distributions and the range between lower and upper bounds.     

An approach for solving competitive location problems with variable demand using multicore systems

A planar competitive location and design problem with variable demand is considered. The assumption that the demand may vary depending on the conditions of the market makes the problem more realistic, but it also increases its complexity, and therefore, the computational effort needed to solve it. In this paper, a modification of a heuristic recently proposed to cope with the problem is presented, which allows, on the one hand, to obtain the same solutions as the original heuristic more quickly and, on the other hand, to handle larger size problems. Furthermore, a parallel version of the algorithm, suitable for being run in most of today’s personal computers, has also been proposed. The parallel algorithm has been implemented using the OpenMP library and the results show an ideal efficiency up to at least eight processors (the largest number of available processing elements). The effectiveness of the parallel algorithm has also been measured. From the computational results, it can be inferred that the proposed parallelization is robust.     

Efficient algorithms for machine scheduling problems with earliness and tardiness penalties

In this paper, we study the multi-machine scheduling problem with earliness and tardiness penalties and sequence dependent setup times. This problem can be decomposed into two subproblems—sequencing and timetabling. Sequencing focuses on assigning each job to a fixed machine and determine the job sequence on each machine. We call such assignment a semi-schedule. Timetabling focuses on finding an executable schedule from the semi-schedule via idle-time insertion. Sequencing is strongly NP-hard in general. Although timetabling is polynomial-time solvable, it can become a computational bottleneck if the procedure is executed many times within a larger framework. This paper makes two contributions. We first propose a quantum improvement to the computational efficiency of the timetabling algorithm. We then apply it within a squeaky wheel optimization framework to solve the sequencing and overall problem. Finally, we demonstrate the strength of our proposed algorithms by experiments.     

Robust vehicle routing problem with deadlines and travel time/demand uncertainty

In this article, we investigate the vehicle routing problem with deadlines, whose goal is to satisfy the requirements of a given number of customers with minimum travel distances while respecting both of the deadlines of the customers and vehicle capacity. It is assumed that the travel time between any two customers and the demands of the customer are uncertain. Two types of uncertainty sets with adjustable parameters are considered for the possible realizations of travel time and demand. The robustness of a solution against the uncertain data can be achieved by making the solution feasible for any travel time and demand defined in the uncertainty sets. We propose a Dantzig-Wolfe decomposition approach, which enables the uncertainty of the data to be encapsulated in the column generation subproblem. A dynamic programming algorithm is proposed to solve the subproblem with data uncertainty. The results of computational experiments involving two well-known test problems show that the robustness of the solution can be greatly improved.     

Accessing feasible space in a generalized job shop scheduling problem with the fuzzy processing times: a fuzzy-neural approach

This paper presents a fuzzy-neural approach for constraint satisfaction of a generalized job shop scheduling problem (GJSSP) fuzzy processing times. Our study is an extension of recently developed research in a GJSSP where the processing time of operations was constant. Our paper assumes that the processing time of jobs is uncertain. The proposed fuzzy-neural approach can be adaptively adjusted with weights of connections based on sequence resource and uncertain processing time constraints of the GJSSP during its processing. The computational results show that the proposed neural approach is able to find good solutions in reasonable time.     

A dynamic vehicle routing problem with multiple delivery routes

This paper considers a vehicle routing problem where each vehicle performs delivery operations over multiple routes during its workday and where new customer requests occur dynamically. The proposed methodology for addressing the problem is based on an adaptive large neighborhood search heuristic, previously developed for the static version of the problem. In the dynamic case, multiple possible scenarios for the occurrence of future requests are considered to decide about the opportunity to include a new request into the current solution. It is worth noting that the real-time decision is about the acceptance of the new request, not about its service which can only take place in some future routes (a delivery route being closed as soon as a vehicle departs from the depot). In the computational results, a comparison is provided with a myopic approach which does not consider scenarios of future requests.     

Economies of scale,competitiveness, and trade patterns within the European community: Clarendon Press,Oxford, 1983, 193 pages, £20.00

We consider two queues in series with input to each queue, which can be controlled by accepting or rejecting arriving customers. The objective is to maximize the discounted or average expected net benefit over a finite or infinite horizon, where net benefit is composed of (random) rewards for entering customers minus holding costs assessed against the customers at each queue. Provided that it costs more to hold a customer at the first queue than at the second, we show that an optimal policy is monotonic in the following senses: Adding a customer to either queue makes it less likely that we will accept a new customer into either queue; moreover moving a customer from the first queue to the second makes it more (less) likely that we will accept a new customer into the first (second) queue. Our model has policy implications for flow control in communication systems, industrial job shops, and traffic-flow systems. We comment on the relation between the control policies implied by our model and those proposed in the communicationa literature.     

Fuzzy scheduling of job orders in a two-stage flowshop with batch-processing machines

In this paper, we present a mixed-integer fuzzy programming model and a genetic algorithm (GA) based solution approach to a scheduling problem of customer orders in a mass customizing furniture industry. Independent job orders are grouped into multiple classes based on similarity in style so that the required number of setups is minimized. The family of jobs can be partitioned into batches, where each batch consists of a set of consecutively processed jobs from the same class. If a batch is assigned to one of available parallel machines, a setup is required at the beginning of the first job in that batch. A schedule defines the way how the batches are created from the independent jobs and specifies the processing order of the batches and that of the jobs within the batches. A machine can only process one job at a time, and cannot perform any processing while undergoing a setup. The proposed formulation minimizes the total weighted flowtime while fulfilling due date requirements. The imprecision associated with estimation of setup and processing times are represented by fuzzy sets.     

A memetic algorithm for job shop scheduling using a critical-path-based local search heuristic

In this article, a new memetic algorithm has been proposed to solve job shop scheduling problems (JSSPs). The proposed method is a genetic-algorithm-based approach combined with a local search heuristic. The proposed local search heuristic is based on critical operations. It removes the critical operations and reassigns them to a new position to improve the fitness value of the schedule. Moreover, in this article, a new fitness function is introduced for JSSPs. The new fitness function called priority-based fitness function is defined in three priority levels to improve the selection procedure. To show the generality of our proposed method, we apply it to three different types of job scheduling problems including classical, flexible and multi-objective flexible JSSPs. The experiment results show the efficiency of the proposed fitness function. In addition, the results show that incorporating local search not only offers better solutions but also improves the convergence rate. Compared to the state-of-the-art algorithms, the proposed method outperforms the existing methods in classical JSSPs and offers competitive solutions in other types of scheduling problems.     

Approaches to Machine Load Balancing in Flexible Manufacturing Systems

The load balancing problem for a flexible manufacturing system concerns the allocation of operations to machines and of tools to magazines with limited capacity, while seeking to balance the workload on all machines. Previous attempts to tackle this problem have used integer programming and a specialized branch and bound procedure has been developed. A modified integer programming approach is proposed here. The problem has certain features which can be used advantageously for an approximate solution technique. The approximation technique is described and computational results presented. Extensions to the problem of pooling machines are also considered.     

Ensuring service levels in routing problems with time windows and stochastic travel times

In the stochastic variant of the vehicle routing problem with time windows, known as the SVRPTW, travel times are assumed to be stochastic. In our chance-constrained approach to the problem, restrictions are placed on the probability that individual time window constraints are violated, while the objective remains based on traditional routing costs. In this paper, we propose a way to offer this probability, or service level, for all customers. Our approach carefully considers how to compute the start-service time and arrival time distributions for each customer. These distributions are used to create a feasibility check that can be “plugged” into any algorithm for the VRPTW and thus be used to solve large problems fairly quickly. Our computational experiments show how the solutions change for some well-known data sets across different levels of customer service, two travel time distributions, and several parameter settings.     

考虑顾客便利半径和质量阈值的竞争设施选址问题

在竞争设施选址问题中,顾客选择行为是决定设施占领市场份额的重要因素,其描述了需求在设施之间的分配方式。为了贴近顾客真实的光顾行为,本文提出了一种考虑顾客便利半径和质量阈值的顾客选择规则,并研究了在该规则下市场中新进入公司的竞争设施选址问题。提出了一种基于排名的遗传算法(RGA)求解该问题,并将该算法与经典遗传算法(GA)和基于排名的离散优化算法(RDOA)进行了比较,结果说明了算法的有效性以及模型中质量阈值的重要性。