This paper discusses properties of a preventive maintenance policy in multiple part preventive maintenance problems theoretically and numerically. A product such as a machine or an engine consists of multiple important identical parts. Parts are periodically inspected and if a part has a crack then it is either repaired or replaced with new one. If crack of a part is over the critical level then it must be replaced, because it leads to machine’s breakdown and a serious problem. In some kinds of machines, using repaired parts will incur an additional operating cost, because of decrease of its performance. Repair and operation costs are also needed for maintenance. In this paper, an optimal part repair and replacement policy is developed theoretically and numerically. The model is described and formulated as a Markov decision process. For no fixed repair cost it is divided into identical single part maintenance problems, and sufficient conditions under which a threshold type policy is optimal are presented theoretically. Then the cases that optimal policies are not of threshold type are illustrated by numerical experiments.
We propose an application of a two-phase decomposition algorithm for a practical airline crew rostering problem for fair working time. The problem is to find an optimal assignment of duties to individual crew members such that various hard constraints such as rest days, rules and regulations are satisfied. The objective is to minimize the total deviation of the average working time from the standard working time for crew members. A two-phase decomposition algorithm is successfully applied to solve the problem. The proposed method decomposes the original problem into the master problem and the subproblem. The master problem is solved by an exact algorithm with a generalized set partitioning formulation if all possible rosters are enumerated by an efficient enumeration algorithm. The upper bound is improved by a metaheuristic algorithm. The effectiveness of the proposed method for a large scale rostering problem is shown from computational experiments.
This paper considers fair home-away tables in sports scheduling. A home-away table defines where each match is held in a round-robin tournament, and the quality of the tournament schedule strongly depends on the home-away table. Although some home-away tables considering fairness have been proposed, some unfair aspects remain in them. We propose three kinds of home-away tables, an even-breaks table, a consecutive-breaks table, and a k-interval table, which are fairer than the previously proposed home-away tables. To find consecutive-breaks and k-interval home-away tables consistent with a given timetable, we propose algorithms based on 2-satisfiability. We also introduce a necessary condition on the number of teams where consecutive-breaks and k-interval home-away tables exist.
Wavelength division multiplexing (WDM) technology transmits multiple optical communication channels in an optical fiber. Routing and wavelength assignment (RWA) problems on WDM network have widely attracted interest of many researchers. Recently, so called sub-wavelength paths which are smaller granular paths than the wavelength-paths are discussed. In this paper, we deal with the RWA problem with considering sub-wavelength assignment on optical networks. One of the purpose of our study is to investigate active rates for optical networks. We formulate a sub-wavelength path assignment problem maximizing accommodated traffic demands by integer programming and solve it by a cutting plane algorithm. Since, in actuality, RWA is done individually for each demand on the time when the demand occurs, we consider a greedy type on-line algorithm. Numerical experiments show the efficiency of our algorithms and give some observation for active rates. Moreover, we verify the efficiency of our greedy-type algorithm on realistic situations which follow 10/40/100 Gbps system used for the current communication on optical networks. Our experimental results conclude that the active rates are depending on the configurations of the underlying graphs, and that our greedy-type algorithm is efficient for several kinds of instances.
In this paper, we study an operational planning and scheduling problem in an automatic picking system. This problem was introduced as a practical benchmark problem arising in logistics and involves assignment and scheduling tasks. We first show the NP-hardness of the problem. We then propose a graph-based heuristic algorithm for computing a good schedule of requests for a given assignment of products. The computational results for benchmark instances show that good schedules of requests are obtained in short computation time.
In this paper, we consider the crew pairing problem in airline scheduling that calls for assigning crew members in order to cover all flights with the minimum total person-days under the constraints that the schedule of each crew member does not violate given constraints on the total working time, flying time, and the number of landings. In practical applications, it is difficult to create an efficient schedule satisfying all the constraints. We formulate the problem as a set covering problem and apply an LP-based column generation approach to generate a candidate set of schedules. We propose a branch-and-bound method based upon a resource constrained dynamic programming for the column generation procedure. Computational results are given for a number of large-scale instances with up to 10,000 flights.
In this paper, we propose a heuristic algorithm for a container loading problem for logistic platforms, which is the problem for the Challenge Renault/ESICUP 2015. The three-dimensional container loading problem involves packing a set of cuboid items into bins so as to minimize the total volume used. In this paper, we propose an effective approach to solve this problem based on a greedy strategy. We first generate high-quality stacks that consist of some items and then pack these stacks on the floor of bins, considering the resulting problem as a two-dimensional bin packing problem. The proposed algorithm is tested on a series of instances provided for the challenge. The computational results show that the proposed algorithm performs well on these instances.
The present paper discusses the integration of product design and manufacturing by means of information sharing through due-date estimation and scheduling systems. The present author and other researchers have investigated a due-date estimation method in a make-to-order context. We analyzed and considered several manufacturing problems using the due-date estimation method. Among the problems researched were the following two: the first is the problem of optimizing the allocation of module inventories on semi-finished products and processed parts, and the second is the due-date estimation and production scheduling for customer orders with unfixed specification. In conducting our research, we realized that these problems are closely related with the integration of product design and manufacturing. In the present paper, we discuss the concrete examples found in these two problems and verify that the information sharing between the product design section and the manufacturing division is necessary in order to meet the increasingly strict requirements of customers and achieve more efficient manufacturing.
We consider the allocation of a running time supplement to a railway timetable. Previously, Vekas et al. examined the optimal way to allocate the running time supplement. The uncertain disturbances in a railway were modeled using random variables. In their model, it was assumed that there was an upper limit to the total supplement, but its allocation was not restricted. In this paper, we suggest an improvement to the previous model and present a new stochastic programming model in which there is a constraint on the running time supplement allocated to each trip to minimize the expected delay. Then a solution algorithm to solve the problem is developed. In the previous model, allocation of the running time supplement was biased because it was not allocated to all trips. We balance the amounts of supplements for trips by adding upper and lower bounds. The uctuations of the supplements for trips become small, and the probability of a delay decreases using our new model. Then the calculation times using the L-shaped algorithm and the former method solving a deterministic equivalent of large-scale problems are compared. It is shown that the large-scale problems can be solved effectively by using the L-shaped method.
This paper extends the maximum flow-covering location and service start time problem (MFCLSTP) by additionally imposing a minimum stay at a facility before the service can be used. The original formulation determines the locations of facilities and the start times of fixed-duration services so as to maximally cover flows of commuters who access services on the way home from work. In MFCLSTP, commuters must stay at a facility from the start of the service until the end of the service in order to consume it. Examples of such services include movies, lectures, and baseball games. There are, however, many on-demand services, which can be consumed by commuters who access the providing facility for a fixed continuous duration of a hours during any of c (≥ a) open hours of the facility. To deal with this situation, we extend the definition of coverage in the original model and provide an integer programming formulation of the proposed problem. The model is applied to the Tokyo metropolitan railway network, using census data of commuter traffic for railway users in this area. Exact optimal solutions are obtained by using a mathematical optimization solver with both the original and extended problems, and the characteristics of the solutions are compared. The results show that the optimal solutions for the extended problem allow a much larger flow than the optimal solutions for the original problem do, even when a is very close to c. The locations selected for the optimal solutions of the proposed problem are seen to be much more spatially dispersed than those chosen for the original problem.
Given a family of m + 1 sets of n vertices in a metric space, a bi-level optimization problem to be considered in this paper asks to find a minimum cost repetitive walk with a prescribed terminal vertex. The bi-level optimization problem is inspired by an industrial application in the printed circuit board production. When a total order of the vertex sets is fixed, two consecutive vertex sets A and B give rise to a lower-level problem of finding a minimum cost Hamiltonian path that alternately visits the two sides, A and B, and has the prescribed terminal in the vertex set A, in the induced complete bipartite graph. The cost of a travel from side A to side B is multiplied by a factor β ≥ 1, called a bias, whereas the cost of a travel from B to A simply takes a metric weight. The upper-level problem asks to find a total order of the vertex sets so that the cost of the repetitive walk, that is, the total cost of the m alternating Hamiltonian paths between every two consecutive vertex sets, is minimized. In this paper, a 1.5(1+β)2/(1+β2)-approximation algorithm is presented to the bi-level optimization problem. The approximation ratio is always bounded by 3, and it also approaches 1.5 as the bias β tends to infinity.
This paper proposes two mathematical programming models to deal with a scheduling problem on the renovation of several roads that need to be repaired by a certain date. A typical example of the scheduling problem is the one for aging and deteriorating bridges in Japan. Our idea behind the formulation of the models is that, if one optimizes a set of roads simultaneously under repair, then the influence on traffic can be minimized. The first model turns out to be easy to solve since it can be rewritten as a linear 0-1 integer programming problem; however it would be too simple. The second model is designed to be realistic while its computation is a difficult task in general. This paper describes how to reduce its computational cost. In addition, we compare the results for the two models to grasp their features.
In this paper, we consider a multi-hop sensor network, where the network topology is a tree, TDMA (time division multiple access) is employed as medium access control, and all data generated at sensor nodes are delivered to a sink node (the base station) located on the root of the tree through the network. It is reported that if a transmission schedule that avoids interference between sensor nodes completely can be computed, TDMA is preferable to CSMA/CA (carrier sense multiple access with collision avoidance) in performance. In general, the TDMA scheduling problem to find the shortest schedule is formulated as a combinatorial optimization problem, where each combination corresponds to a schedule. However, solving such a combinatorial optimization problem is difficult, especially for large-scale multi-hop sensor networks. The reason of the difficulty is that the number of the combinations increases exponentially with the increase of the number of nodes. In this paper, to formulate the TDMA scheduling problem, we propose a min-max model and a min-sum model. The min-max model yields the shortest schedule, but it is difficult to solve large-scale problems. The min-sum model does not guarantee providing the shortest schedule; however, it may give us good schedules over a short amount of computation time, compared to the min-max model. Numerical examples show that the min-sum model can provide good schedules in a reasonable CPU time, even when the min-max model fails to compute the shortest schedule in a reasonable CPU time.
In the sequencing problem in mixed-model assembly lines, the branch-and-bound method and heuristic method have thus far been developed for minimizing total incomplete working hours. However, these are developed based on the heuristic solution method of a single-station model. Therefore, the precision of the solution considerably changes with differences in processing time for each station. In this study, an effective search method for the sequencing problem in mixed-model assembly lines is proposed. In our method, an efficient search is performed by improving the updating conditions of the solution using the simulated annealing method, and a high precision is achieved without depending on numerical examples.
Although assembly line is widely used for several decades since it appears during the Industrial Revolution, nowadays, it still has the vitality, especially in the developing countries such as China, where labor-intensive enterprise is still the mainstay industry. Assembly line has its advantages for reducing costs and production time. However, laborer is the main factor of production speed in such a labor-intensive enterprise. Because of the various working capacity of worker, one work process may delay or idle, and this will influence processes. This unforeseeable consecutive delay of process may lead to the postponing of whole manufacturing production. In order to minimize the risk, the assignment of the workers, especially untrained worker is focused on. In previous researches, rules of optimal worker assignment with two kinds of workers, which are distinguished by the capacity of processing, were proposed when minor untrained workers are less than four people. In this paper, we deal with the rules under this LCMwMP (limited-cycled model with multiple periods) model without concerning the number of minor untrained workers. Additionally, some rules of minor well-trained workers assignment optimization are researched by numerical analyses.
Optimization of daily vehicle routes with deliveries and pickups as well as multiple use of vehicles for a rental business is considered. The problem is formulated as a variant of generalized set covering problems in which variables correspond to workdays of vehicles. Two variants of column generation heuristic algorithms are developed: one to obtain near-optimal solutions with moderate amount of CPU time together with the associated lower bound, and the other to get solutions with maximum of 8% GAP within 30 CPU seconds. The speed-up of the algorithm is achieved by approximately solving subproblems which exploits information of optimal dual prices associated with the restricted LP master problem. The column generation heuristic algorithms are applied successfully not only to single-depot problems but also to multi-depot problems.
This study proposes a new method for reactive project scheduling that enhances a smooth progress of a project, which is referred to as a “degree of project progress (DPP).” The proposed method generates a so called revision plan for the rest of a current project baseline schedule at each inspection point in time based on a project delay which can be obtained from the deviation between the planned and actual starting times of activities. Revision planning indicates a series of decisions whether an existing baseline schedule should be revised or not. Then the project goes on in accordance with the revision plan. Numerical experiment derives the effectiveness of the proposed method and demonstrates the applicability of our method as an efficient reactive schedule revision in project time management.
For green supply chains, it is essential to disassemble and recycle end-of-life (EOL) assembled products for material circulation. In order to establish disassembly plants environmentally friendly and economical manner, a disassembly parts selection is often carried out. Each part has a different recycling rate and cost, and all parts have precedence relationships among disassembly tasks. Igarashi et al. (2014) [International Journal of Industrial Engineering and Management Systems, Vol.13, No.1, pp.52-66] proposed a disassembly parts selection method that is carried out in an environmentally friendly and economical manner with non-destructive or destructive disassembly with integer programming with ε constraint. However, calculated efforts are required to achieve optimum solutions for the ε constraint method. On the other hand, goal programming is well known as an effective way to solve multi-criteria decision-making problems. This study proposes a bi-objective disassembly parts selection with recycling rate and cost using goal programming, and analyzes multiple types of EOL assembled products and disassembly parts selection. First, an environmentally friendly and economical disassembly parts selection is addressed using a 3D-CAD and Recyclability Evaluation Method (REM) developed by Hitachi Ltd. Next, the environmentally friendly and economical disassembly parts selection is formulated with goal programming. Finally, a case study is quantitatively discussed by comparing different types of assembled products and goal programming parameters. It is demonstrated that the proposal method by goal programming in this study finds the same solutions with the lower number of numerical experiments as that with the ε constraint method.
Many practical problems with uncertainties can be formulated as stochastic programming problems, and their optimal solutions are useful for decision-making. However, solving problems is generally difficult, and feasible methods for finding analytical solutions are needed. The purpose of this study is to propose a hybrid method that combines pseudo particle swarm optimization in an uncertain environment (PPSOUCE) and the Monte Carlo (MC) method for solving a stochastic programming problem. As an example, we used the proposed hybrid method to solve a stochastic job-shop scheduling problem (SJSSP). We compared our proposed PPSOUCE with the MC method to a hybrid method of a genetic algorithm in an uncertain environment (GAUCE) with the MC method. Numerical experiments illustrate that our method provides better solutions with shorter CPU times than those of the method that combines the GAUCE and the MC method.