We consider the optimization problem of safety stock placement in a supply chain, as formulated in [1]. We prove that this problem is NP-Hard for supply chains modeled as general acyclic networks. Thus, we do not expect to find a polynomial-time algorithm for safety stock placement for a general-network supply chain. / Singapore-MIT Alliance (SMA)

In this thesis, we focus on integration issue of manufacturing and sales functions from the perspective of aggregate production planning. The manufacturing function and sales function are performed by separate affiliated companies of the same business group, which operate as an integrated supplier-buyer system. In particular, this study provides theoretical and practical insight into the use of forecast volatility measure to better match supply with demand so as to reduce the costs of inventory and stock-outs in the manufacturer-buyer relationship under described master production-scheduling environment. Nature of forecast modifications provided by the buyer lays the foundation for the study. We modify the existing aggregate production planning model to accommodate a measure of historical forecast evolution. The overall objective of the thesis is to provide management with aforecast evolution-modeling framework to examine performance characteristics of the manufacturer-buyer interaction.

[pt] Nesta dissertação são apresentados dois modelos de estoque aplicados ao sistema de controle de estoques (Q, R), que envolve a definição do tamanho de lote a ser encomendado a cada vez e a ocasião de encomendar. Esses modelos têm como objetivo a minimização do custo total anual formado pelo custo de encomendar, de manter e de falta de estoque. Os modelos são testados na sua forma completa e com aproximações sugeridas por diversos autores e, em seguida, os resultados são comparados. Além disso, é desenvolvida uma formulação que busca simplificar a identificação dos casos reais que podem utilizar as aproximações sugeridas para estes modelos. Um dos modelos é utilizado para definir níveis ótimos de estoque de derivados de petróleo em uma refinaria da Petrobras e os resultados são comparados com níveis de estoque praticados hoje pela empresa. / [en] This dissertation presents two inventory models applied to the continuous review, order-point, order-quantity (Q, R), that define a fixed quantity to be ordered and the occasion to order. The objective is to minimize the total annual cost comprised by setup, backorder/stockout and holding costs. First, these models are tested with their complete formulation and compared with approximations proposed by many authors. Second, it is developed a formulation to facilitate the identification of real cases where approximation is recommended. Finally one of these models is applied to define optimum inventory levels of oil products in a Petrobras` refinery and results are compared with the level of inventory the company now holds.

A high level of delivery precision from a focal firm to their customers has the potential to provide competitive advantage amongst competing businesses. This report will detail the subject of inventory management and utilize theories on the subject in order to provide recommendations to a multinational company that wishes to increase their delivery precision. The results of the work conducted are presented and recommendations given in the form of firstly analyzing inventory and segregating the product range where applicable. This should be treated as the first priority to gain an insight into where potential problem areas lie and to determine the products that are the biggest contributors to the overall value of goods sold. As a secondary measure, managing supplier relations carefully and the strategic sourcing of materials are strategies that will help to effectively reduce problems through increased visibility of information in communication channels. An accurate demand forecasting model will predict demand ahead of time, ensuring that the correct products are being held as inventory for no longer than is strictly needed, with a safety stock system being used as a safety net for those products that are suitable. A theoretical implementation of exponential II smoothing based forecasting coupled with standard deviation based safety stock calculations, yields results that effectively raises delivery precision. By forecasting demand for individual months and using calculated safety stock levels, the model is able to adjust for the shortfall between forecasted demand and actual demand.

[pt] Esta dissertação aborda a evolução da malha ferroviária brasileira e o impacto deste modal de transporte nos estoques de Diesel e Gasolina das Bases de Distribuição localizadas no Sul do Brasil, pertencentes a uma importante distribuidora de derivados de petróleo. A relevância do estudo realizado deve-se à aprovação da Lei 9.478 - Lei do Petróleo - que quebrou o monopólio da Petrobras neste setor, transferindo para as distribuidoras o gerenciamento espacial e volumétrico de seus estoques. Por outro lado, o estudo contribui para o conhecimento da incipiente malha ferroviária brasileira, a partir da privatização ocorrida em 1996, e tornada importante diante da crescente necessidade de se agregar valor, eficiência e segurança ao transporte de combustíveis. O objetivo deste estudo é abordar a evolução da malha ferroviária brasileira e o impacto deste modal de transporte nos estoques de segurança de Diesel e Gasolina de uma grande Distribuidora de derivados de petróleo e o relacionamento dos custos de transporte atrelados aos riscos e impontualidade ainda prevalecentes no sistema ferroviário. / [en] This thesis approaches the evolution of the Brazilian railroad mesh and the impact of this modal of transportation to an important company in the supplies of Diesel and Gasoline to the Bases of Distribution located in the South of Brazil. The relevance of this study is justified due to the approval of Law 9.478 - Law of the Oil - that broke the monopoly of Petrobras in this sector, transferring to oil companies the spatial and volumetric management of their oil inventories. On the other hand, the study contributes for the knowledge of the incipient Brazilian railroad mesh, privatized in 1996, and becoming increasingly important giving the necessity of adding value, efficiency and security to the fuel transportation. The objective of the present study is the evolution of railroad mesh and the impact of this transportation modal on Gasoline and Diesel safety stocks handled by an important oil company and its relationship to the costs of transportation related to the risks and unpunctuality still prevailing in the railroad system.

<p>GNT Group is a Nordic/Baltic wholesaler that distributes products in the IT, entertainment and home electronics sector. GNT is facing problems with inaccurate inventory levels which can lead to unnecessarily high inventory carrying costs or lost sales. Currently the decisions about when and how many to order are made somewhat arbitrarily by the responsible personnel. Their decisions are based only on some brief sales history and on experience. </p><p>GNT wants to develop its ERP system to be able to support the purchaser in these and other related decisions. The purpose of this thesis is to give suggestions to what decisions the ERP system should support and how these decisions can be made. </p><p>The three main tasks in this thesis are to suggest how to calculate the optimal order quantity, how to calculate the optimal ordering point and how to decide whether it can be profitable to store an article in only one of GNT’s warehouses. </p><p>The suggested solution is based on a volume value/demand frequency classification which also takes an item’s life cycle characteristics into consideration. For the different classes suitable calculations and decisions are suggested concerning the three main tasks and issues related to them.</p>

In this paper, we study the stochastic transportation-inventory network design problem involving one supplier and multiple retailers. Each retailer faces some uncertain demand. Due to this uncertainty, some amount of safety stock must be maintained to achieve suitable service levels. However, risk-pooling benefits may be achieved by allowing some retailers to serve as distribution centers (and therefore inventory storage locations) for other retailers. The problem is to determine which retailers should serve as distribution centers and how to allocate the other retailers to the distribution centers. Shen et al. (2000) and Daskin et al. (2001) formulated this problem as a set-covering integer-programming model. The pricing subproblem that arises from the column generation algorithm gives rise to a new class of submodular function minimization problem. They only provided efficient algorithms for two special cases, and assort to ellipsoid method to solve the general pricing problem, which run in O(n⁷ log(n)) time, where n is the number of retailers. In this paper, we show that by exploiting the special structures of the pricing problem, we can solve it in O(n² log n) time. Our approach implicitly utilizes the fact that the set of all lines in 2-D plane has low VC-dimension. Computational results show that moderate size transportation-inventory network design problem can be solved efficiently via this approach. / Singapore-MIT Alliance (SMA)

GNT Group is a Nordic/Baltic wholesaler that distributes products in the IT, entertainment and home electronics sector. GNT is facing problems with inaccurate inventory levels which can lead to unnecessarily high inventory carrying costs or lost sales. Currently the decisions about when and how many to order are made somewhat arbitrarily by the responsible personnel. Their decisions are based only on some brief sales history and on experience. GNT wants to develop its ERP system to be able to support the purchaser in these and other related decisions. The purpose of this thesis is to give suggestions to what decisions the ERP system should support and how these decisions can be made. The three main tasks in this thesis are to suggest how to calculate the optimal order quantity, how to calculate the optimal ordering point and how to decide whether it can be profitable to store an article in only one of GNT’s warehouses. The suggested solution is based on a volume value/demand frequency classification which also takes an item’s life cycle characteristics into consideration. For the different classes suitable calculations and decisions are suggested concerning the three main tasks and issues related to them.

Sammanfattning Syfte - Syftet med denna studie är att bidra till ökad förståelse för hur lager kan styras när varierad efterfrågan förekommer. För att uppnå syftet är målet med studien att sammanställa processer som underlättar för lagerstyrning vid varierad efterfrågan. Detta möjliggörs genom att besvara följande frågeställningar: 1. Vilka metoder för säkerhetslagerberäkning och lagerstyrning är lämpliga när hänsyn bör tas till varierad efterfrågan? 2. Hur påverkas lagerförings- och ordersärkostnader av olika sätt att styra lager vid varierad efterfrågan? Metod - Teorier angående lagerstyrning vid varierad efterfrågan samlades in via litteraturstudier. En fallstudie genomfördes för att applicera det teoretiska ramverket på empiri från fallföretaget. Empiri samlades in via intervjuer och dokumentationsstudier och utgjorde en grund för beräkningar och vidare analys. Resultat - Lämplig säkerhetslagerberäkning vid varierad efterfrågan anses vara SERV2 som tar hänsyn till antalet bristtillfällen och ger ett bra mått på lagertillgängligheten över tid. De dynamiska lagerstyrningsmetoderna Silver &amp; Meal samt Wagner-Whitin kan i större utsträckning hantera stora variationer i efterfrågan gentemot beställningspunktssystem. Beräkningar resulterade i att Wagner-Whitin var den lagerstyrningsmetod som i majoriteten av fallen genererar lägst totalkostnad när hänsyn tas till lagerförings- och ordersärkostnader. En process för lagerstyrning vid varierad efterfrågan har kartlagts där indata i form av metod- och resursobjekt redogörs. Detta för att bidra till ökad förståelse för hur lager kan styras vid varierad efterfrågan. Implikationer - Inom denna studie framgår det att kostnaderna för lagerstyrningen vid varierad efterfrågan kan sänkas med hjälp av dynamiska lagerstyrningsmetoder. Det är dock viktigt med trovärdig indata för att generera tillförlitliga resultat. Begränsningar - Inom de dynamiska lagerstyrningsmetoderna vägs ordersärkostnad mot lagerföringskostnad och genererar det mest ekonomiska alternativet ur lagerstyrningens perspektiv. Det måste inte vara det bästa ur ett helhetsperspektiv då förändrade orderkvantiteter kan påverka andra delar av materialflödet. De processkartor som är upprättade utgår från den valda lösningen, detta begränsar tillämpningen till verksamheter som har liknande förutsättningar som fallföretaget. Nyckelord - Varierad efterfrågan, lagerstyrning, säkerhetslagerberäkning, lagerstyrningsmetod. / Abstract Purpose - The purpose of this thesis is to develop an understanding of how to control inventory when the demand varies. To achieve the purpose, the goal is to create a process that facilitates inventory management at varied demand. This is feasible by answering following questions: 1. Which methods of safety stock calculation and inventory control are appropriate and take varied demand in consideration? 2. How is the inventory carrying cost and ordering cost affected by different methods of controlling inventory when demand varies? Method - Information about controlling inventory at varied demand was gathered through literature studies. A case study was carried out to apply the theoretical framework on empirical data from the business case. The empirical data was collected through interviews and documentation studies, which provided a basis for calculation and further analysis. Findings - SERV2 is considered as an appropriate method for safety stock calculations since it takes the number of occasions for shortages into account and provides a good measurement of the stock availability over time. The dynamic inventory control methods Silver &amp; Meal and Wagner-Whitin can handle variations in demand better than order point systems. Calculations show that Wagner-Whitin generates the lowest total costs in the majority of cases. A process is established to facilitate inventory management at varied demand. Implications - Within this study it is shown that using dynamic inventory control methods can reduce inventory control costs when demand varies. Nonetheless it is important to have persuasive input to generate reliable results. Limitations - The dynamic inventory control methods balance order cost with inventory carrying costs to find the most economic option from an inventory control perspective. It is not always the best solution from a holistic perspective since changed order quantities can affect other parts of the material flow. The established process charts are based on chosen solution, which limits its application to businesses with similar conditions as the case study. Keywords - Varied demand, inventory control, safety stock calculation, inventory management

Optimizing supply chain is the most successful key for manufacturing systems to be competitive. Supply chain (SC) has gotten intensive research works at all levels: strategic, tactical, and operational levels. These levels, in some researches, have integrated with each other or integrated with other planning issues such as inventory. Optimizing inventory location and level of safety stock at all supply chain partners is essential in high competitive markets to manage uncertain demand and service level. Many works have been developed to optimize the location of safety stock along supply chain, which is important for fast response to fluctuation in demand. However, most of these studies focus on the design stage of a supply chain. Because demand at different horizon times may vary according to different reasons such as the entry of different competitors on market or seasonal demand, safety stock should be optimized accordingly. At the planning (tactical) level, safety stock can be controlled according to each planning horizon to satisfy customer demand at lower cost instead of being fixed by a decision taken at the strategic level. On the other hand, most studies that consider safety stock optimization are tied to a specific system structure such as serial, assembly, or distribution structure. This research focuses on formulating two different models. First, a multi- echelon safety stock optimization (MESSO) model for general supply chain topology is formulated. Then, it is converted into a robust form (RMESSO) which considers all possible fluctuation in demand and gives a solution that is valid under any circumstances. Second, the safety stock optimization model is integrated with tactical supply chain planning (SCP) for manufacturing systems. The integrated model is a multi-objective mixed integer non-linear programming (MINLP) model. This model aims to minimize the total cost and total time. A case study for each model is provided and the numerical results are analyzed.