In this paper, we consider a repair-cost limit replacement problem and develop a graphical method to determine the optimal repair-cost limit which minimizes the expected cost per unit time in the steady-state, using the Lorenz transform of the underlying repair-cost distribution function. The method proposed can be applied to an estimation problem of the optimal repair-cost limit from empirical repair-cost data. Numerical examples are devoted to examine asymptotic properties of the non-parametric estimator for the optimal repair-cost limit.

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In this paper, multi-source possibilistic information is represented by a set of possibilistic constraints to characterize decision variables from different information aspects. Possibilistic linear programming is used to integrate multi-source possibilistic information into the upper and the lower possibility distributions of decision vector.

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This paper presents a new method for generating the optimal development of a thin-walled object. The design of developments of thin-walld objects such as ventilation pipes is very important in the industry, where many complex development patterns are required. Although many CAD systems have been developed for this purpose, none to date has been able to satisfy this sort of practical demands because they are only applicable to limited patterns. For example, researches based on the flatting technique applicable to some developable figures have been reported. This may be the first report with respect to the optimal selection of bending lines for the development of an object. In this work, GA is adopted, where a new coding method and a fitness function are introduced that pool the experience of experts in the field and take into account all physical aspects of this domain. Additional conditions for generating only feasible developments are also considered. The phenotype of each solution is expressed in the form of a 0-1 matrix, which describes the conditions mentioned above, and the genotype is expressed as a starting point and a zigzag (right and down) path in the matrix. In addition, an "Alternative path representation" is proposed for the coding of GA. The fitness function is made up of two objective functions, the first of which describes the total length of bending lines that link two sample points surrounding the entrance and the exit, respectively ; the second of which describes the smoothness of changes in directions of normal vectors of the generated side surface. The coding method of "Alternative path representation" is effective enough for speeding up the calculation. It has been confirmed through several experiments that the method presented here is sufficiently applicable to the generation of a variety of development-patterns required by the industry.

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This paper is concerned with an efficient algorithm for solving a large-scale dense non-factorable quadratic programming problem arising in portfolio optimization consisting of a large number of assets. A number of algorithms for quadratic programming problems have been proposed in the past. However, these methods tend to become less efficient as the rank of the covariance matrix increases. The algorithm proposed in this paper is a combination of projected steepest descent algorithm and projected variable metric algorithm. Subproblems to be solved in each step are simple linear programs which can be solved very fast, contrary to other quadratic programming algorithms which require the manipulation of large dense matrix. Computational experiment shows that this algorithm outperforms renowned softwares when the number of assets is over one thousand.

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A Home Care Service Scheduling Problem (HCSSP) is a real world (large-scale) and multi-objective combinatorial optimization problem. To plan the schedule, we need to satisfy requests of all dependents and constraints at the number of helpers who each provider can dispatch to them. It takes a lot of time to get the optimal schedule of HCSSP. From the practical point of view, we should not wait for hours to get the optimal schedule but use quasi-optimal schedules. In order to obtain a quasi-optimal schedule quickly, we solve HCSSP by meta-heuristic methods. In this paper we show and compare two methods to solve HCSSP. One is Genetic Algorithm (GA) method, another is Tabu Search (TS) method. Comparison in our case shows that TS is superior to GA.

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In this paper, we develop an urban space model that describes travel demand as well as distributions of residential area and transportation area. The area considered is a square consisting of square zones laid on a grid pattern. In each zone i, land is allocated to residential area and transportation area, and only one building is built on the residential area. The population density is assumed to be constant so that the size of the building is proportional to the number of residents x_i in zone i. The principle that plays an important role in this model is that the transportation area must have sufficient capacity to manage the traffic passing there. Therefore, if the traffic volume in a zone is large, the area available for the site of a building becomes small. In this case, the population in that zone should be small, or the building should be high to accommodate large population and this leads to increase the travel time in the building. Trip generation and trip distribution in our model are performed very simply in the sense that for each pair of residents, one trip is made in unit time with constant probability b. The residents in each zone are aggregated so that the number trips originates in zone i and terminates in zone j is bx_ix_j. A route followed by a trip consists of three parts. One starts a trip at his or her location and goes down to the ground, then follows one of the alternative route on land and finally goes up to the location of the other. We consider two alternative routes on land, both are the shortest distance routes with respect to L_1 metric, one route contains only one left-turn, and the other contains only one right-turn. In order to determine the necesary transportation area in each zone in terms of the traffic volume passing through it, we introduce the transportation capacity of unit area of road and define it as a function of vehicle speed. We also introduce the congestion phenomena in such a way that capacity increases linearly from in light traffic condition to heavy traffic condition as vehicle speed decreases. The system principle of our model is to minimize the total travel time of trips between the residents' locations. We define the minimization problem whose variables are the population x_i in each zone i and the route choice probability between each pair of zones. We solve some numerical examples using three slightly different models. The first one is the least flexible one, the capacity and the speed are fixed and the route between origin and destination is specified to one left-turn only. In this case, as the population of the whole area becomes large, the traffic volume passing through the central district increases so that the height of the buildings as well as the travel time consumed there grows rapidly. The second one adopts the functional relation such that the capacity of unit transportation area can be increased in the cost of decrease in vehicle speed. This moderates the rapid increase in the proportion of transportation area especially in the central district. In the last one, trips between each OD zones can be assigned to each one of the alternative routes. This brings to a solution such remarkable feature that the proportion of transportation area in the central district is lower than that in surrounding area.

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