Abstract:We propose local search algorithms for the vehicle routing problem with soft time window constraints. The time window constraint for each customer is treated as a penalty function, which is very general in the sense that it can be non-convex and discontinuous as long as it is piecewise linear. In our algorithm, we use local search to assign customers to vehicles and to find orders of customers for vehicles to visit. It employs an advanced neighborhood, called the cyclic exchange neighborhood, in addition to standard neighborhoods for the vehicle routing problem. After fixing the order of customers for a vehicle to visit, we must determine the optimal start times of processing at customers so that the total penalty is minimized. We show that this problem can be efficiently solved by using dynamic programming, which is then incorporated in our algorithm. We then report computational results for various benchmark instances of the vehicle routing problem. The generality of time window constraints allows us to handle a wide variety of scheduling problems. As such an example, we mention in this paper an application to a production scheduling problem with inventory cost, and report computational results for real world instances.

No abstract

No abstract

Simple and accurate prediction methods of gear unit noise have been desired. This paper offers a new prediction equation for spur and helical gears under speed reduction service. A semi-empirical equation was developed by means of the addition of a dynamics term to Kato’s equation which represented the overall noise level by using gear’s specification data. As the proposed method takes into account the gear error characteristics in the vibration analysis of gear pairs, it can calculate the noise levels considering the influence of the tooth flank finishing method. It is shown that the predicted values agree with the measured values in an experiment within a range of approximately 5dB, under almost all the operating conditions and for all test gears having different finishing methods such as hobbing, Niles-type grinding and Maag-type grinding. Moreover, good agreement with data of some actual gear units indicates that the developed method may be used for general application.

No abstract