Optimal downlink rate allocation in multicell CDMA networks

We study downlink rate allocation for a three cells CDMA system. Based on the discretized cell model, the rate optimization problem that maximizes the total downlink rate allocation is formulated. We propose an approximation procedure for obtaining a rate allocation in three cells case. Via numerical examples, we show that this procedure gives a good approximation of the optimal downlink rate allocation

The Vehicle Rescheduling Problem

The capacitated vehicle routing problem is to find a routing schedule describing the order in which geographically dispersed customers are visited to satisfy demand by supplying goods stored at the depot, such that the traveling costs are minimized. In many practical applications, a long term routing schedule has to be made for operational purposes, often based on average demand estimates. When demand substantially differs, constructing a new schedule is beneficial. The vehicle rescheduling problem is to find a new schedule that not only minimizes the total traveling costs but also minimizes the costs of deviating from the original schedule. In this paper two mathematical programming formulations of the rescheduling problem are presented as well as two heuristic methods, a two-phase heuristic and a modified savings heuristic. Computational and analytical results show that for sufficiently high deviation costs, the two-phase heuristic generates a schedule that is on average close to optimal or even guaranteed optimal, for all considered problem instances. The modified savings heuristic generates schedules of constant quality, however the two-phase heuristic produces schedules that are on average closer to the optimum.vehicle routing;operational planning;vehicle rescheduling problem

A Local Search Algorithm for Clustering in Software as a Service Networks

In this paper we present and analyze a model for clustering in networks that offer Software as a Service (SaaS). In this problem, organizations requesting a set of applications have to be assigned to clusters such that the costs of opening clusters and installing the necessary applications in clusters are minimized. We prove that this problem is NP-hard, and model it as an Integer Program with symmetry breaking constraints. We then propose a Tabu search heuristic for situations where good solutions are desired in a short computation time. Extensive computational experiments are conducted for evaluating the quality of the solutions obtained by the IP model and the Tabu Search heuristic. Experimental results indicate that the proposed Tabu Search is promising.integer programming;complexity theory;Tabu Search;software as a service

The Time Window Assignment Vehicle Routing Problem

In many distribution networks, it is vital that time windows in which deliveries are made are assigned to customers for the long term. However, at the moment of assigning time windows demand is not known. In this paper we introduce the time window assignment vehicle routing problem, the TWAVRP. In this problem time windows have to be assigned before demand is known. Next the realization of demand is revealed and an optimal vehicle routing schedule has to be made that satisfies the time window constraints. We assume that different scenarios of demand realizations are known, as well as their probability distribution. The TWAVRP is the problem of assigning time windows such that the expected traveling costs are minimized. We propose a formulation of the TWAVRP and develop two variants of a column generation algorithm to solve the LP relaxation of this formulation. Numerical experiments show that these algorithms provide us with very tight LP-bounds to instances of moderate size in reasonable computation time. We incorporate the column generation algorithm in a branch and price algorithm and find optimal integer solutions to small instances of the TWAVRP. In our numerical experiments, the branch and price algorithm typically finds the optimal solution very early in the branching procedure and spends most time on proving optimality

The Vehicle Rescheduling Problem

The capacitated vehicle routing problem is to find a routing schedule describing the order in which geographically dispersed customers are visited to satisfy demand by supplying goods stored at the depot, such that the traveling costs are minimized. In many practical applications, a long term routing schedule has to be made for operational purposes, often based on average demand estimates. When demand substantially differs, constructing a new schedule is beneficial. The vehicle rescheduling problem is to find a new schedule that not only minimizes the total traveling costs but also minimizes the costs of deviating from the original schedule. In this paper two mathematical programming formulations of the rescheduling problem are presented as well as two heuristic methods, a two-phase heuristic and a modified savings heuristic. Computational and analytical results show that for sufficiently high deviation costs, the two-phase heuristic generates a schedule that is on average close to o

Comparison of two methods for customer differentiation

In response to customer specific time guarantee requirements, service providers can offer differentiated ser- vices. However, conventional customer differentiation methods often lead to high holding costs and may have some practical drawbacks. We compare two customer differentiation policies: stock reservation and pipeline stock priority for high priority customers. We derive exact analytical expressions of the waiting time distri- bution of both types of customers for a stock reservation policy. We then provide accurate approximation methods for a pipeline stock priority policy. By comparison, we offer insights concerning which method should be used under different service level requirements

Approximate Order-up-to Policies for Inventory Systems with Binomial Yield

This paper studies an inventory policy for a retailer who orders his products from a supplier whose deliveries only partially satisfy the quality require- ments. We model this situation by an infinite-horizon periodic-review model with binomial random yield and positive lead time. We propose an order- up-to policy based on approximating the inventory model with unreliable supplier by a model with a reliable supplier and suitably modified demand distribution. The performance of the order-up-to policy is verified by com- paring it with both the optimal policy and the safety stock policy proposed in Inderfurth & Vogelgesang (2013). Further, we extend our approximation to a dual-sourcing model with two suppliers: the first slow and unreliable, and the other fast and fully reliable. Compared to the dual-index order- up-to policy for the model with full information on the yield, the proposed approximation gives promising results

Waiting times in classical priority queues via elementary lattice path counting

In this paper we describe an elementary combinatorial approach for deriving the waiting and response time distributions in a few classical priority queueing models. By making use of lattice paths that are linked in a natural way to the stochastic processes analysed, the proposed method offers new insights and complements the results previously obtained by inverting the associated Laplace Transforms

Scheduling deliveries under uncertainty

Quite often transportation companies face two types of jobs, ones which they can plan themselves and ones which have to be done on call. In this paper we study the scheduling of these jobs, while we assume that job durations are known beforehand as well as windows in which the jobs need to be done. We develop several heuristics to solve the problem at hand. The most successful are based on defining an appropriate buffer. The methods are assessed in extensive experiments on two aspects, viz. efficiency, in the sense that they carry out many jobs and certainty, in the sense that they provide information beforehand about which jobs they will execute

Enabling customer satisfaction and stock reduction through service differentiation with response time guarantees

In response to customer specific service time guarantee requirements, service providers can offer differentiated services. However, conventional customer differentiation models based on fill rate constraints do not take full advantage of the stock reduction that can be achieved by differentiating customers based on agreed response times. In this paper we focus on the (S − 1, S, K) model with two customer classes, in which low priority customers are served only if the inventory level is above K. We employ lattice paths combinatorics to derive the exact distribution of the response time (within leadtime) for the lower priority class and provide a simple and accurate approximation for the response time of the high priority class. We show that the stock levels chosen based on agreed response times can be significantly lower than the ones chosen based on fillrates. This indicates that response time guarantees are an efficient tool in negotiating after-sale contracts, as they improve customer satisfaction and reduce investment costs