The vehicle routing problem with multiple trips (VRPMT) is a variant of the classical vehicle routing problem in which each vehicle may be assigned several routes within a working time period. This problem is classified into two versions: symmetric and asymmetric. The symmetric version arises when the travel distance between customers is the same in both directions, whereas the asymmetric one arises when this assumption does not hold. In practical applications, the travel distance between customers is often asymmetric; however little attention has been paid to the asymmetric version of the VRPMT, which we refer to as asymmetric VPRMT (AVRPMT). In this paper, we consider the AVRPMT, whose objective function is to minimize the total distance traveled by vehicles. Then we propose a near-optimal solution for this problem based on the Lagrangian heuristic. To do this, we first formulate the problem as an integer programming problem, and present a method to determine the lower bound of the problem by solving the minimum r-spanning arborescence problem. Next, we propose a method to determine a near-optimal solution for the problem by successively decreasing the difference between the upper and lower bounds. Finally, we verify the effectiveness of the proposed method through computational experiments.

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In modern automobile assembly lines, kanban cards or e-kanban cards are used for parts supply. If a worker on the production line makes a mistake in the assembly of parts to the car body, an inferior product will be sent to the following production process. Although these inferior products will be detected in the inspection process, the production line may be suspended. We call this inferior product loss. In this paper, we propose a lossdetection model for a work station where a worker installs parts to a car body. We use kanban cards to measure the number of parts used at the station. The relationship between the number of conveyed car bodies and parts used is compared to detect the loss. We present mathematical models to detect losses and some numerical examples to show the stochastic performance of the proposed loss-detection model.

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Backaches, stiff shoulders, sore muscles and other health problems caused by bad posture at work have received a great deal of attention. The rapidly aging workforce in Japan and increase in the number of working women are contributing factors. In response, many work posture evaluation methods have been proposed. Most of these methods involve visual observation/manual evaluation of workers' posture. However, to apply these methods, a high degree of skill is required when evaluating, and differences in evaluation depending on the observer may arise. In this study, we therefore propose a work posture evaluation system based on OWAS using image processing. The proposed system can perform evaluations automatically, and applies "boosting," a learning algorithm that detects posture without the use of markers or sensors. We aimed to improve accuracy using the two phases of "boosting," the direction of the body and work posture. In the evaluation experiments, we measured the accuracy of each "boosting" phase and the final work posture evaluation. The experimental results showed that the accuracy of both "boosting" phases was approximately 70%, and the final work posture evaluation accuracy was 72%. We conclude that these results are sufficiently accurate for the initial validation of the proposed work posture evaluation system.

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While increasing efforts are being made to address work-life balance (henceforth abbreviated as "WLB") in industries, occupational stress is considered as one of causes that impede the achievement of WLB. This paper attempts to investigate the causal relation between them by representing (1) The job strain model incorporating factors of job demand and control, (2) occupational stress, and (3) WLB cognition, in a single structural equation model. Model estimation through verification by samples resulted in the following goodness of fit of the model: CFI=0.95 and RMSEA=0.09. How occupational stress influences WLB consciousness is thus successfully represented by the "model for an influence exerted by occupational stress on WLB consciousness" in the present study which has three submodels of job strain, occupational stress, and WLB consciousness.

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