This thesis studies the allocation of stock in a two-level inventory system with stochastic demand. The system consists of one central warehouse which supplies N non-identical retailers with one single product. Customer demand occurs solely at the retailers and follows independent Poisson processes. The purpose is to investigate the value of using a more advanced allocation policy than First Come-First Serve at the central warehouse. The focus is on evaluating how well the simple First Come-First Serve assumption works in a system where the warehouse has access to real-time point-of-sale data, and where shipments are time based and consolidated for all retailers. The considered allocation policy is a myopic policy where the solution to a minimization problem, formulated as a constrained newsvendor problem, determines how the warehouse allocates its stock to the retailers. The minimization problem is solved using (a heuristic method based on) Lagrangian relaxation, and simulation is used to evaluate the average inventory holding costs and backorder costs per time unit when using the considered policy. The simulation study shows that cost savings around 1-4 percent can be expected for most system configurations. However, there were cases where savings were as high as 5 percent, as well as cases where the policy performed worse than First Come-First Serve. The study also shows that the highest cost savings are found in systems with relatively low demand, few retailers, short transportation times and a short time interval between shipments.

<p>This thesis studies the allocation of stock in a two-level inventory system with stochastic demand. The system consists of one central warehouse which supplies N non-identical retailers with one single product. Customer demand occurs solely at the retailers and follows independent Poisson processes. The purpose is to investigate the value of using a more advanced allocation policy than First Come-First Serve at the central warehouse. The focus is on evaluating how well the simple First Come-First Serve assumption works in a system where the warehouse has access to real-time point-of-sale data, and where shipments are time based and consolidated for all retailers. The considered allocation policy is a myopic policy where the solution to a minimization problem, formulated as a constrained newsvendor problem, determines how the warehouse allocates its stock to the retailers. The minimization problem is solved using (a heuristic method based on) Lagrangian relaxation, and simulation is used to evaluate the average inventory holding costs and backorder costs per time unit when using the considered policy. The simulation study shows that cost savings around 1-4 percent can be expected for most system configurations. However, there were cases where savings were as high as 5 percent, as well as cases where the policy performed worse than First Come-First Serve. The study also shows that the highest cost savings are found in systems with relatively low demand, few retailers, short transportation times and a short time interval between shipments.</p>

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Nesta dissertaÃÃo, nosso principal objetivo foi desenvolver uma tÃcnica de resoluÃÃo para um problema na Ãrea de telecomunicaÃÃes. O problema em questÃo à chamado de problema de PonderaÃÃo de Rodadas (PR) e foi inicialmente proposto em [Klasing,Morales,Perennes, 2008]. O contexto do problema envolve uma rede sem fio, onde as comunicaÃÃes sÃo realizadas via ondas de rÃdio e a rede funciona atravÃs de uma operaÃÃo da rede que satisfaz certas restriÃÃes. Inicialmente, explicamos como à formada uma rede de rÃdio e descrevemos a forma de operaÃÃo da rede de rÃdio junto Ãs restriÃÃes usando um modelo matemÃtico. Em seguida, formalizamos o problema PR como um problema de otimizaÃÃo, especificando suas restriÃÃes, correspondente à geraÃÃo do conjunto de possÃveis operaÃÃes da rede, e critÃrio de otimizaÃÃo, referente ao uso dos recursos da rede. Posteriormente, mostramos um estudo preliminar do problema de ColoraÃÃo FracionÃria (CF) e apresentamos uma tÃcnica de resoluÃÃo deste problema atravÃs do uso de uma heurÃstica lagrangeana baseada em uma relaxaÃÃo lagrangeana de uma formulaÃÃo de programaÃÃo inteira do problema. Essa tÃcnica de resoluÃÃo à entÃo adaptada para o problema PR, consistindo na principal contribuiÃÃo de nossa pesquisa. Por fim, mostramos os resultados computacionais e anÃlises das nossas implementaÃÃes para os problemas CF e PR. / In this dissertation, our main objective was to develop a technique for resolution to a problem in the area of telecommunications. The problem in question is called Round Weighting Problem (RWP) and was originally proposed in (KLASING; MORALES; PeRENNES, 2008). The context of the problem involves a wireless network where communications are performed by radio waves and the network operates through a network operation that satises the constraints of the problem. Initially, we explain how a radio network is formed and describe the mode of operation of the radio network with restrictions using a mathematical model. Then, we formalize the RWP as an optimization problem, specifying their restrictions, corresponding to the generation of the set of possible network operations, and optimization criterion, regarding the use of network resources. Subsequently, we show a preliminary study of the Fractional Coloring problem (FC problem) and present a technique to solve this problem through the use of a lagrangian heuristic based on a lagrangian relaxation of an integer programming formulation of the problem. This resolution technique is then adapted to the RWP, consisting in the main contribution of our research. Finally, we show the computational results and analyzes of our implementations for the Fractional Coloring problem and RWP.