A bicriteria flowshop scheduling with a learning effect

In many situations, a worker’s ability improves as a result of repeating the same or similar tasks; this phenomenon is known as the learning effect. In this paper the learning effect is considered in a two-machine flowshop. The objective is to find a sequence that minimizes a weighted sum of total completion time and makespan. Total completion time and makespan are widely used performance measures in scheduling literature. To solve this scheduling problem, an integer programming model with n² + 6n variables and 7n constraints where n is the number of jobs is formulated. Because of the lengthy computing time and high computing complexity of the integer programming model, the problem with up to 30 jobs can be solved. A heuristic algorithm and a tabu search based heuristic algorithm are presented to solve large size problems. Experimental results show that the proposed heuristic methods can solve this problem with up to 300 jobs rapidly. According to the best of our knowledge, no work exists on the bicriteria flowshop with a learning effect.     

A column generation approach for an employee scheduling problem with multiple shifts and work locations

This paper is concerned with the problem of assigning employees to a number of work centres taking into account employees' expressed preferences for specific shifts, off-days, and work centres. This particular problem is faced by the Kuwait National Petroleum Corporation that hires a firm to prepare schedules for assigning employees to about 86 stations distributed all over Kuwait. The number of variables in a mixed-integer programming model formulated for this problem is overwhelming, and hence, a direct solution to even the continuous relaxation of this model for relatively large-scale instances is inconceivable. However, we demonstrate that a column generation method, which exploits the special structures of the model, can readily solve the continuous relaxation of the model. Based on this column generation construct, we develop an effective heuristic to solve the problem. Computational results indicate that the proposed approach can facilitate the generation of good-quality schedules for even large-scale problem instances in a reasonable time.     

A Genetic Algorithm for Solving a Capacitated p-Median Problem

Facility-location problems have several applications, such as telecommunications, industrial transportation and distribution. One of the most well-known facility-location problems is the p-median problem. This work addresses an application of the capacitated p-median problem to a real-world problem. We propose a genetic algorithm (GA) to solve the capacitated p-median problem. The proposed GA uses not only conventional genetic operators, but also a new heuristic “hypermutation” operator suggested in this work. The proposed GA is compared with a tabu search algorithm.     

Hybrid simulated annealing and MIP-based heuristics for stochastic lot-sizing and scheduling problem in capacitated multi-stage production system

This paper addresses lot sizing and scheduling problem of a flow shop system with capacity constraints, sequence-dependent setups, uncertain processing times and uncertain multi-product and multi-period demand. The evolution of the uncertain parameters is modeled by means of probability distributions and chance-constrained programming (CCP) theory. A new mixed-integer programming (MIP) model with big bucket time approach is proposed to formulate the problem. Due to the complexity of problem, two MIP-based heuristics with rolling horizon framework named non-permutation heuristic (NPH) and permutation heuristic (PH) have been performed to solve this model. Also, a hybrid meta-heuristic based on a combination of simulated annealing, firefly algorithm and proposed heuristic for scheduling is developed to solve the problem. Additionally, Taguchi method is conducted to calibrate the parameters of the meta-heuristic and select the optimal levels of the algorithm’s performance influential factors. Computational results on a set of randomly generated instances show the efficiency of the hybrid meta-heuristic against exact solution algorithm and heuristics.     

An exact algorithm for the sequential ordering problem and its application to switching energy minimization in compilers

This article presents an exact algorithm for the precedence-constrained traveling salesman problem, which is also known as the sequential ordering problem. This NP-hard problem has applications in various domains, including operational research and compilers. In this article, the problem is presented and solved in the context of minimizing switching energy in compilers. Most previous work on minimizing switching energy in the compiler domain has been limited to simple heuristics that are not guaranteed to give an optimal solution. In this work, we present an exact algorithm for solving the switching energy minimization problem using a branch-and-bound approach. The proposed algorithm is simple and intuitive, yet powerful. It is the first exact algorithm for the switching energy problem that is shown to solve real instances of the problem within a few seconds per instance. Compared to previous work in the operational research domain, the proposed algorithm is believed to be the most powerful exact algorithm that does not require a linear programming formulation. The proposed algorithm is experimentally evaluated using instances taken from a production compiler. The results show that with a time limit of 10 ms per node, the proposed algorithm optimally solves 99.8 % of the instances. It optimally solves instances with up to 598 nodes within a few seconds. The resulting switching cost is 16 % less than that produced without energy awareness and 5 % less than that produced by a commonly used heuristic.     

Using Lagrangian dual information to generate degree constrained spanning trees

In this paper, a Lagrangian-based heuristic is proposed for the degree constrained minimum spanning tree problem. The heuristic uses Lagrangian relaxation information to guide the construction of feasible solutions to the problem. The scheme operates, within a Lagrangian relaxation framework, with calls to a greedy construction heuristic, followed by a heuristic improvement procedure. A look ahead infeasibility prevention mechanism, introduced into the greedy heuristic, allowed us to solve instances of the problem where some of the vertices are restricted to having degrees 1 or 2. Furthermore, in order to cut down on CPU time, a restricted version of the original problem is formulated and used to generate feasible solutions. Extensive computational experiments were conducted and indicate that the proposed heuristic is competitive with the best heuristics and metaheuristics in the literature.     

Scheduling linear deteriorating jobs to minimize the number of tardy jobs

In this paper a problem of scheduling a single machine under linear deterioration which aims at minimizing the number of tardy jobs is considered. According to our assumption, processing time of each job is dependent on its starting time based on a linear function where all the jobs have the same deterioration rate. It is proved that the problem is NP-hard; hence a branch and bound procedure and a heuristic algorithm with O(n ²) is proposed where the heuristic one is utilized for obtaining the upper bound of the B&B procedure. Computational results for 1,800 sample problems demonstrate that the B&B method can solve problems with 28 jobs quickly and in some other groups larger problems are also solved. Generally, B&B method can optimally solve 85% of the samples which shows high performance of the proposed method. Also it is shown that the average value of the ratio of optimal solution to the heuristic algorithm result with the objective ??(1 ? Ui) is at most 1.11 which is more efficient in comparison to other proposed algorithms in related studies in the literature.     

A compromised large-scale neighborhood search heuristic for capacitated air cargo loading planning

Cost effectiveness is central to the air freight forwarders. In this work, we study how an air freight forwarder should plan its cargo loading in order to minimize the total freight cost given a limited number of rented containers. To solve the problem efficiently for practical implementation, we propose a new large-scale neighborhood search heuristic. The proposed large-scale neighborhood relaxes the subset-disjoint restriction made in the existing literature; the relaxation risks a possibility of infeasible exchanges while at the same time it avoids the potentially large amount of checking effort required to enforce the subset-disjoint restriction. An efficient procedure is then used to search for improvement in the neighborhood. We have also proposed a subproblem to address the difficulties caused by the fixed charges. The compromised large-scale neighborhood (CLSN) search heuristic has shown stably superior performance when compared with the traditional large-scale neighborhood search and the mixed integer programming model.     

Simulated annealing and tabu search for multi-mode project payment scheduling

This paper involves the multi-mode project payment scheduling problem where the activities can be performed with one of several discrete modes and the objective is to assign activities’ modes and progress payments so as to maximize the net present value of the contractor under the constraint of project deadline. Using the event-based method the basic model of the problem is constructed and in terms of the different payment rules it is extended as the progress based, expense based, and time based models further. For the strong NP-hardness of the problem which is proven by simplifying it to the deadline subproblem of the discrete time–cost tradeoff problem, we develop two heuristic algorithms, namely simulated annealing and tabu search, to solve the problem. The two heuristic algorithms are compared with the multi-start iterative improvement method as well as random sampling on the basis of a computational experiment performed on a data set constructed by ProGen project generator. The results show that the proposed simulated annealing heuristic algorithm seems to be the most promising algorithm for solving the defined problem especially when the instances become larger. In addition, the effects of several key parameters on the net present value of the contractor are analyzed and some conclusions are given based on the results of the computational experiment.     

飞机维修短期计划模型及其算法研究

目前对于飞机维修计划的研究,大都通过精确算法一次性完成周期内所有飞机的排班优化。本文在分析传统数学规划模型的基础上,以最大化利用两次维修之间的可用飞行时间为目标,构造了飞机维修计划优化模型。然后提出了求解此模型的启发式两阶段分解算法,第一阶段优先完成需维修飞机的任务指派,第二阶段再完成余下飞机的任务指派。利用航空公司真实数据进行的数值试验表明,两阶段分解算法能够显著提高模型的求解效率和质量,可以有效求解大规模飞机维修计划制定问题。     

Minimizing makespan in a two-machine flowshop scheduling with batching and release time

This paper studies two-machine flowshop scheduling with batching and release time, whose objective is to minimize the makespan. We formulate the scheduling problem as a mixed integer programming model and show that it is a strongly NP-hard problem. We derive a lower bound and develop dynamic programming-based heuristic algorithms to solve the scheduling problem. Computational experiments are carried out to evaluate the performance of the heuristic algorithms. The numerical results show that some of the heuristic algorithms can indeed find effective solutions for the scheduling problem.     

Robotic disassembly line balancing problem: A mathematical model and ant colony optimization approach

The use of robots is significantly increasing day by day in manufacturing systems, and especially improving the efficiency of the lines. Robots can be used to complete disassembly tasks, and each of the robots can need different operation times to perform the tasks. In this paper, the balancing of the robotic disassembly line problem has been studied to develop efficient solution techniques. Firstly, a mixed-integer linear mathematical model is proposed to determine and solve the problem optimally. A case study from literature is addressed to assess and show the efficiency and effectiveness of the model to minimize cycle time. Secondly, a heuristic algorithm based on ant colony optimization is also proposed to discover a solution for especially the large-size test problems due to the complexity of the problem. The performance of the proposed heuristic algorithm is verified and compared with the different heuristic on data sets. The computational results indicate that the proposed mathematical model and the algorithms are promising for the small and large-size test problems, respectively. Finally, it should be stated that robots have great potential to use in the area of disassembly line and useful solutions provide according to test results.     

A mathematical formulation and complexity considerations for the blocks relocation problem

The blocks relocation problem (BRP) may be defined as follows: given a set of homogeneous blocks stored in a two-dimensional stock, which relocations are necessary to retrieve the blocks from the stock in a predefined order while minimizing the number of those relocations? In this paper, we first prove NP-hardness of the BRP as well as a special case, closing open research questions. Moreover, we propose different solution approaches. First, a mathematical model is presented that provides optimal solutions to the general BRP in cases where instances are small. To overcome such limitation, some realistic assumption taken from the literature is introduced, leading to the definition of a binary linear programming model. In terms of computational time, this approach is reasonably fast to be used to solve medium-sized instances. In addition, we propose a simple heuristic based upon a set of relocation rules. This heuristic is used to generate “good” quality solutions for larger instances in very short computational time, and, consequently, is proposed for tackling problem instances where solutions are required (almost) immediately. Solution quality of the heuristic is measured against optimal solutions obtained using a state-of-the-art commercial solver and both of them are compared with reference results from literature.     

Single-machine total completion time scheduling with a time-dependent deterioration

In this paper, we consider the single-machine scheduling problems with a time-dependent deterioration. By the time-dependent deterioration, we mean that the processing time of a job is defined by an increasing function of total normal processing time of jobs in front of it in the sequence. The objective is to minimize the total completion time. We develop a mixed integer programming formulation for the problem. The complexity status of this problem remains open. Hence, we use the smallest normal processing time (SPT) first rule as a heuristic algorithm for the general cases and analyze its worst-case error bound. Two heuristic algorithms utilize the V-shaped property are also proposed to solve the problem. Computational results are presented to evaluate the performance of the proposed algorithms.     

A graph-pair representation and MIP-model-based heuristic for the unequal-area facility layout problem

Owing to its theoretical as well as practical significance, the facility layout problem with unequal-area departments has been studied for several decades, with a wide range of heuristic and a few exact solution procedures developed by numerous researchers. In one of the exact procedures, the facility layout problem is formulated as a mixed-integer programming (MIP) model in which binary (0/1) variables are used to prevent departments from overlapping with one another. Obtaining an optimal solution to the MIP model is difficult, and currently only problems with a limited number of departments can be solved to optimality. Motivated by this situation, we developed a heuristic procedure which uses a “graph pair” to determine and manipulate the relative location of the departments in the layout. The graph-pair representation technique essentially eliminates the binary variables in the MIP model, which allows the heuristic to solve a large number of linear programming models to construct and improve the layout in a comparatively short period of time. The search procedure to improve the layout is driven by a simulated annealing algorithm. The effectiveness of the proposed graph-pair heuristic is demonstrated by comparing the results with those reported in recent papers. Possible extensions to the graph-pair representation technique are discussed at the end of the paper.     

Minimizing total tardiness in a scheduling problem with a learning effect

Minimizing of total tardiness is one of the most studied topics on single machine problems. Researchers develop a number of optimizing and heuristic methods to solve this NP-hard problem. In this paper, the problem of minimizing total tardiness is examined in a learning effect situation. The concept of learning effects describes the reduction of processing times arising from process repetition. A 0–1 integer programming model is developed to solve the problem. Also, a random search, the tabu search and the simulated annealing-based methods are proposed for the problem and the solutions of the large size problems with up to 1000 jobs are found by these methods. To the best of our knowledge, no works exists on the total tardiness problem with a learning effect tackled in this paper.     

A bicriteria m-machine flowshop scheduling with sequence-dependent setup times

In this study, a bicriteria m-machine flowshop scheduling with sequence-dependent setup times is considered. The objective function of the problem is minimization of the weighted sum of total completion time and makespan. Only small size problems with up to 6 machines and 18 jobs can be solved by the proposed integer programming model. Also the model is tested on an example. We also proposed three heuristic approaches for solving large jobs problems. To solve the large sizes problems up to 100 jobs and 10 machines, special heuristics methods is used. Results of computational tests show that the proposed model is effective in solving problems.     

Using a Hybrid Evolutionary Algorithm to Minimize Variance in Response Time for Multimedia Object Requests

This research addresses the scheduling problem of multimedia object requests, which is an important problem in information systems, in particular, for World Wide Web applications. The performance measure considered is the variance of response time which is crucial as end users expect fair treatment to their service requests. This problem is known to be NP-hard. The literature survey indicates that two heuristics have been proposed to solve the problem. In this paper, we present a new heuristic, a hybrid evolutionary heuristic, which is shown to perform much better than the two existing ones, e.g., the overall average errors of the existing ones are 1.012 and 2.042 while the error of the proposed hybrid evolutionary heuristic is 0.154.     

A new branch and bound algorithm for cell formation problem

Cell formation (CF) is the first and the most important problem in designing cellular manufacturing systems. Due to its non-polynomial nature, various heuristic and metaheuristic algorithms have been proposed to solve CF problem. Despite the popularity of heuristic algorithms, few studies have attempted to develop exact algorithms, such as branch and bound (B&B) algorithms, for this problem. We develop three types of branch and bound algorithms to deal with the cell formation problem. The first algorithm uses a binary branching scheme based on the definitions provided for the decision variables. Unlike the first algorithm, which relies on the mathematical model, the second one is designed based on the structure of the cell formation problem. The last algorithm has a similar structure to the second one, except that it has the ability to eliminate duplicated nodes in branching trees. The proposed branch and bound algorithms and a hybrid genetic algorithm are compared through some numerical examples. The results demonstrate the effectiveness of the modified problem-oriented branch and bound algorithm in solving relatively large size cell formation problems.     

基于货物分类配送的电动汽车路径优化与换电策略研究

电动汽车参与的物流配送服务需要统筹协调车辆路径、配送对象与换电策略。本文提出了考虑货物分类需求的电动汽车路径优化与换电策略问题,并建立了该问题的整数规划数学模型。其次,提出了基于禁忌搜索-改进节约算法的两阶段混合启发式算法MCWTS和一种四阶段启发式算法IGALNS。通过多组小规模算例验证了算法的有效性。随后,分别从运营成本、路径距离、换电策略以及混合运输线路等方面比较并分析了货物分类对运营策略的影响。实验结果表明,该模型可以在配送距离略有增加的情况下避免将不适宜混合运输的货物指派给同一车辆,达到降低货物运输损失提高顾客满意度的目的。最后,通过多组较大规模算例对两种启发式算法的有效性进行了比较。