We analyse a dynamic variant of the vehicle routing problem with soft time windows in which an average punctuality must be guaranteed (e.g. lateness is allowed at some customer sites). The existing objective function does not support both the aspiration for punctuality and least cost so that additional efforts are necessary to achieve an acceptable punctuality level at least possible costs. Wit...

Column generation techniques have become a widely used technique to successfully solve large (integer) linear programs. One of the keys to obtaining a practically efficient algorithm is to have a fast method to limit the pricing of new columns to a small set. We study a large scale real-world vehicle dispatching problem with soft time windows which can be modeled as an integer linear program of...

In this paper, we introduce a model  to optimization of milk run system that is one of VRP problem with time window and uncertainty in inventory. This approach led to the routes with minimum cost of transportation while satisfying all inventory in a given bounded set of uncertainty .The problem is formulated as a robust optimization problem. Since the resulted problem illustrates that grows up ...

Abstract This paper studies a generalization of the shortest path tour problem with time windows ( GSPTPTW ). The aim is to find single-origin single-destination path, which has pass through an ordered sequence not necessarily disjoint node-subsets. Each node window for each node-subset it belongs. We investigate theoretical properties and propose dynamic programming approach solve it. Numerica...

Summary Lag windows are commonly used in time series analysis, econometrics, steady-state simulation and Markov chain Monte Carlo to estimate time-average covariance matrices. In the presence of positive correlation underlying process, estimators this matrix almost always exhibit significant negative bias, leading undesirable finite-sample properties. We propose a new family lag specifically de...

this paper discusses the multi-depot vehicle routing problem of heterogeneous fleet of vehicles with time windows for perishable commodities. the objective of the problem is to minimize the total time required for servicing all customers that is equivalent to the total cost. commodities are delivered to the customers with defined time windows by a fleet of heterogeneous vehicles, which have lim...