Freight car dispatching with generalized flows

In the freight car dispatching problem empty freight cars have to be assigned to known demands respecting a given time horizon and certain constraints. The goal is to minimize the resulting transportation costs. One of the constraints is that customers can specify the type of cars they want. It is possible, however, that cars of certain types can be substituted by other cars, either in a 1-to-1 fashion or at different exchange rates. We show that these substitutions make the dispatching problem hard to solve and hard to approximate. We model the dispatching problem as an integral generalized transportation problem on a bipartite graph. Using rounding techniques, the LP-relaxation can be transformed to a transportation schedule violating some of the constraints slightly. Under an additional assumption on the cost function we fix this violation and derive a $4$-approximation of the problem

Low volume store planning for workload balancing and truckload

Okutkan, Caner (Dogus Author) -- Çelepçıkay, Ömer (Dogus Author) -- Çimen, Egemen Berki (Dogus Author)In this study, it is aimed to decrease the number of days planned to be shipped in stores with low sales volume, to create a balanced work load and to increase vehicle occupancy capacity . Particularly, Less than Truckload problem is analyzed and model in this study. The techniques used in this study showed that adaptability can be achieved with shipment and store planning as well as green supply chain environment to minimize Less than Truckload (LTL) as well as gas consumption. A mathematical model was created in the direction of multi objective problem and solved in the GAMS environment. Moreover, scenario analyzes were made and the study was tested on five specially identified regions on Turkey

Freight car dispatching with generalized flows

In the freight car dispatching problem, empty freight cars have to be assigned to known demands respecting a given time horizon and certain constraints. The goal is to minimize the resulting transportation costs. One of the constraints is that customers can specify the type of cars they want. It is possible, however, that cars of certain types can be substituted by other cars, either in a 1-to-1 fashion or at different exchange rates. We show that these substitutions make the dispatching problem hard to solve and hard to approximate. We model the dispatching problem as an integral generalized transportation problem on a bipartite graph. Using rounding techniques, the LP-relaxation can be transformed to a transportation schedule violating some of the constraints slightly. Under an additional assumption on the cost function, we fix this violation and derive a 4-approximation of the problem. (c) 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 66(1), 33-39 201