Exact Methods for Multi-echelon Inventory Control : Incorporating Shipment Decisions and Detailed Demand Information

Recent advances in information technologies and an increased environmental awareness have altered the prerequisites for successful logistics. For companies operating on a global market, inventory control of distribution systems is often an essential part of their logistics planning. In this context, the research objective of this thesis is: To develop exact methods for stochastic inventory control of multi-echelon distribution systems incorporating shipment decisions and/or detailed demand information.The thesis consists of five scientific papers (Paper I, II, III, IV and V) preceded by a summarizing introduction. All papers study systems with a central warehouse supplying a number of non-identical local warehouses (retailers) facing stochastic demand. For given replenishment policies, the papers provide exact expressions for evaluating the expected long-run system behavior (e.g., distributions of backorders, inventory levels, shipment sizes and expected costs) and present optimization procedures for the control variables. Paper I and II consider systems where shipments from the central warehouse are consolidated to groups of retailers and dispatched periodically. By doing so, economies of scale for the transports can be reached, reducing both transportation costs and emissions. Paper I assumes Poisson customer demand and considers volume-dependent transportation costs and emissions. The model involves the possibility to reserve intermodal (train) capacity in combination with truck transports available on demand. For this system, the expected inventory costs, the expected transportation costs and the expected transport emissions are determined. Joint optimization procedures for the shipment intervals, the capacity reservation quantities, the reorder points and order-up-to levels in the system are provided, with or without emission considerations. Paper II analyses the expected costs of the same system for compound Poisson demand (where customer demand sizes may vary), but with only one transportation mode and fixed transportation costs per shipment. It also shows how to handle fill rate constraints. Paper III studies a system where all stock points use installation stock (R,Q) ordering policies (batch ordering). This implies that situations can occur when only part of a requested retailer order is available at the central warehouse. In these situations, the models in existing literature predominantly assume that available units are shipped immediately (partial delivery). An alternative is to wait until the entire order is available before dispatching (complete delivery). The paper introduces a cost for splitting the order and evaluates a system where optimal choices between partial and complete deliveries are made for all orders. In a numerical study it is shown that significant savings can be made by using this policy compared to systems which exclusively use either partial or complete deliveries. Paper IV shows how companies can benefit from detailed information about their customer demand. In a continuous review base stock system, the customer demand is modeled with independent compound renewal processes at the retailers. This means that the customer inter-arrival times may follow any continuous distribution and the demand sizes may follow any discrete distribution. A numerical study shows that this model can achieve substantial savings compared to models using the common assumption of exponential customer inter-arrival times. Paper V is a short technical note that extends the scope of analysis for several existing stochastic multi-echelon inventory models. These models analyze the expected costs without first determining the inventory level distribution. By showing how these distributions can be obtained from the expected cost functions, this note facilitates the analysis of several service measures, including the ready rate and the fill rate

Metodologia de definição de rede de suprimentos para armazenagem de commodities agrícolas

Tese (doutorado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Civil e Ambiental, 2020.A agricultura brasileira está entre as mais importantes do planeta, ocupando posição de destaque na exportação das commodities agrícolas de grãos como soja e milho. O fato das áreas de produção serem distantes dos portos e a sua velocidade de expansão territorial ser maior que a velocidade de instalação de novas estruturas de movimentação e armazenagem, emergem impactos negativos no sistema logístico. A ausência de um sistema logístico eficiente e com capacidade de armazenagem suficiente para todo o volume de colheita força os agricultores a venderem suas colheitas imediatamente, provocando uma redução de preços das commodities por excesso de oferta e a venda em um momento de preços em queda. Diante deste cenário, o presente estudo tem por objetivo principal desenvolver uma metodologia para definição de rede de suprimentos para armazenagem e escoamento de commodities agrícolas. Para alcançar tais objetivos foi desenvolvida uma metodologia composta de sete passos metodológicos que abrangem as etapas de execução da metodologia segundo um conjunto de restrições de definições teóricas para a aplicação do mesmo. De modo a validar a metodologia foi realizado um estudo de caso em que foram utilizados os mapas de estimativas das safras de soja e de milho do município de Nova Ubiratã no Estado do Mato Grosso – MT para determinar a configuração da rede suprimentos para o município que supra o déficit de capacidade estática por armazenagem para a safra 2017/2018 e que minimize o custo total da rede de suprimento. Para esse estudo de caso foram usados mapas da infraestrutura logística envolvida (rodovias e de armazenagem) para o escoamento destas safras, rede de suprimento e de localização p-mediana, linguagens de programação R e Python, e Sistemas de Informações Geográficas (SIG). Os resultados mostraram que a rede de suprimento com menor custo de transporte e armazenagem fora aquela que utilizou unidades de armazenamento de 162 mil toneladas de capacidade e com cobertura da produção de 120%. A metodologia possibilitou analisar a rede de suprimento atual sob a ótica de oferta-demanda e calcular as localizações e o número de instalações de facilidades logísticas necessárias para suprir o déficit da região do estudo de caso. Ademais, a metodologia demonstrou capacidade de tratar problemas de localização e otimização da rede de suprimentos em escala regional com agilidade e a eficiência preconizada.The Brazilian agriculture is one of the most important on the planet, with a prominent position in the agricultural commodities export of soybeans and corn. As the crop production areas are far from the ports and the speed of territorial expansion is greater than the speed of installation of new storage structures, important negative impacts on the logistics system emerge. The absence of an efficient logistical system with enough storage capacity for the entire harvest season forces farmers to sell their crops immediately after the harvest, causing a reduction in commodity prices due to oversupply and with sales at a time of falling prices. In this scenario, the main objective of this thesis was to develop a methodology for defining the supply network for the storage and flow of agricultural commodities. To achieve those objectives, the methodology developed consist of seven methodological steps that encompass the stages of the modeling execution according to a set of restrictions and definitions for its application. In order to validate the methodology, a study case was carried out using crop estimatives maps for soybean and corn in the municipality of Nova Ubiratã in the State of Mato Grosso – MT, Brazil. This maps to determine the configuration of the supply network for the municipality that overcomes the shortage of static storage capacity for the harvest of 2017/2018 and minimizes the total cost of the supply chain. For this case study, maps of the logistics infrastructure involved (highways and storage) were used for the flow of these crops, network model and p-median location, programming languages R and Python, and Geographic Information Systems (GIS). The results showed that the supply network with the lowest transport and storage cost was that one with storage units of 162 thousand tons of capacity and with production coverage of 120%. The model made it possible to analyze the current supply network from the perspective of supply-demand and calculate the locations and the number of logistical facilities necessary to supply the deficit of the region of the study case. In addition, the methodology demonstrated the ability to address problems of localization and optimization of the supply network on a regional scale with agility and the expected efficiency

Analysing service level agreements with multiple customers.

Within numerous production and distribution environments, maintenance of effective customer service is central to securing competitive benefits. Globalised industries are becoming more commonplace as well, further increasing the competitive pressure. Companies, as a result, are forced to expand product availability and deliver to the demand on schedule. As part of a supply chain, service levels are an important measure of performance in operations management and are widely used to evaluate and manage supplier performance. This thesis examines the SLA for the supplier under two types of contracts to guarantee the agreed customer service level. Specifically, this dissertation will shed light on the two most important (SLA) measurements for inventory systems: fill rate and ready rate. Both SLA measurements are commonly used as performance measures in SLAs between customers and suppliers. Throughout this thesis, we examine performance-based contracts in which the supplier has either: a single customer with a large demand, or multiple customers with a smaller demand. Our experiments were designed so that the demand distribution for the single customer case was similar to the aggregated demand distribution in the multiple customer case. The thesis primarily focused on four main questions, with each question being examined in its own chapter. The first research problem is addressed in Chapter 3. Earlier studies of finite horizon fill rate only consider the situation in which there is a single customer in the supply chain. In Chapter 3, we develop a model to analyse the fill rate distributions for a supplier that has multiple customers, each with its own SLA. In particular, we examine the impacts of performance review period length and the correlation between customer demands on the average fill rate and the probability of overreaching the target fill rate when a supplier has multiple customers. Under the multiple customer contracts, two service policies for demand fulfilment. In the first policy, First-Come-First-Served (FCFS), demand is filled with no prioritization (e.g., in the case of two customers, there is a 50% chance that the first customer is served first). In the second policy, Prioritized Lowest Fill Rate (PLFR), customers are prioritized so that the customer with the highest negative deviation from its target fill rate in the current performance review period is served first. The results and findings in Chapter 3 provide insights that can assist suppliers in the design and negotiation of SLAs. The second research problem is addressed in Chapter 4. Previous studies on the finite horizon fill rate are limited and assume a zero lead time for the supplier. We create a model to examine the impact of different supplier lead times on the finite horizon fill rate, considering either single customer or multiple customers. As lead time exists in reallife supply chains, we explore the effect of various lead times on the fill rate distribution and required base stock over finite horizons with a variety of review period lengths. The results revealed that to fix the long-run fill rate, as the lead time increases, more stock is required; however, the probability of exceeding the target fill rate (the probability of success) increases as the lead time increases. The results indicate that the increase in the probability of success as the lead time increases is higher when the review period is shorter. For the third research problem Chapter 5 presents further results related to the fill rate, an important measure of supply chain performance, specifically ensuring that a customer’s service need is met with maximum reliability. These results mainly concentrate on variability, an aspect that is largely ignored in the literature on fill rate. Related results concerning consistency and asymptotic normality extend the range of application of the fill rate in evaluating reliability and determining the optimal stock level of a supply chain. Chapter 6 explores the fourth research problem which considers the ready rate, a widely used performance measure in SLAs. The ready rate considered in this study is defined as the long-run fraction of periods in which all customer demand is filled immediately from on-hand stock. Previous studies of SLAs have been solely concerned with one supplier serving one customer, whereas in practice, a supplier usually deals with more than one customer. In multiple customer cases, the supplier has an SLA with each customer, and a penalty is incurred whenever the agreement is violated. In this chapter, we create a model to examine the impacts of various factors such as the base-stock level, the type of penalty (lump-sum and linear penalty), and the review period duration on the supplier’s cost function when the supplier deals with multiple customers. The results show that dealing with more customers is preferable for a supplier (assuming the overall demand is the same) and that under a lump-sum penalty contract, a longer performance review is beneficial. Finally, Chapter 7 closes with a brief review, discussion on the models constructed and suggests areas for future studies

Integrated optimization of safety stock and transportation capacity

In this paper we consider a segment of a supply chain comprising an inventory and a transportation system that cooperate in the fulfillment of stochastic customer orders. The inventory is operated under a discrete time (r, s, q) policy with backorders. The transportation system consists of an in-house transportation capacity which can be extended by costly external transportation capacity (such as a third-party logistics provider). We show that in a system of this kind stock-outs and the resulting accumulation of inventory backorders introduces volatility in the workload of the transportation process. Geunes and Zeng (2001) have shown for a base-stock system, that backordering decreases the variability of transportation orders. Our findings show that in inventory systems with order cycles longer than one period the opposite is true. In both cases, however, inventory decisions and transportation decision must be taken simultaneously. We present a procedure to compute the probability distribution of the number of transportation orders and the resulting excess transportation requirements or rather transportation costs. We show that the increase of transportation costs resulting from a safety stock reduction may offset the change of the inventory costs. This effect may have a significant impact on general optimality statements for multi-echelon inventory systems. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved