Inventory routing problem with stochastic demand and lead time

In the supply chain, the integration of the different processes is critical to obtain high levels of coordination. Inventory control and its distribution are two of these processes whose coordination have been demonstrated by researchers as key in order to gain efficiency and effectiveness. They affect the synchronization of the supply chain management. With the intention to contribute to the integration of these processes and improve the problems of demand variability, we propose an integration of operations research area and the help of metaheuristics in a multi-objective approach. The expected results are to reduce the costs associated with inventory and its distribution, as well as to reduce the uncertainty in making decisions based on demand. This thesis presents methods for obtaining and analyzing near optimally solutions for dynamic and stochastic inventory-routing problems. The methods include retailers selection and clustering methods, algorithms and experiments on benchmark instances. We focus on problems with one and several suppliers that serve several dispersal geographically retailers. The thesis contains four parts. In Part I, we focus on the literature review. We first provide an overview of the literature on problems related to the coordination of the inventory and its distribution. Then we make a point in four elements: information management, inventory policies, stochastic demand and optimization methods. Also, we provide a scientometric analysis of the documentation collected in the last ten years. We provide a thorough review of papers working with dynamic and stochastic demand. The contributions of this part are i) the review of papers working with stochastic demand and stochastic lead times focusing on its stochastic and multi-depot aspects, ii) identify critical factors for the performance of many logistics activities and industries, iii) have shown that studying the behavior of the demand and the lead time are essential in order to achieve a useful representation of the system to take proper decisions and iv) provide the trends and patterns in the research in IRP problems. In Part II, we focus on the methodology of the research and of development. We first introduce the problem, state of the science, the gaps in the literature, variables under study, the instruments applied and assumptions. The development methodology is presented by a general model to address this type of research proposed in this thesis. Here, the general development process, decomposition of the problem and how the possible solutions are explained.. The importance of the this chapter is provided an effective way to face IRP problems. In Part III, the foundations in formulations for IRP problems are proposed. We begin with the formulation of the TSP problems with variants for one and many suppliers, likewise for VRP and IRP problems. The contributions of the model presented here aim identifying the variables and mathematical models frequently used to deal with these problems. In Part IV, we perform a single criteria objective and multi-criteria analysis of the solutions for one and many suppliers instances. Our methods yield significant improvements over a competing algorithm. Our contributions are i) propose three new customer selection methods for a dynamic and stochastic inventory-routing vii problem, ii) perform a multi-criteria analysis of the solutions, comparing distribution versus inventory management, iii) perform a single criteria objective experiment on benchmark instances from the literature.En la cadena de suministro, la integración de los diferentes procesos que la conforman, es fundamental para obtener altos niveles de coordinación. El control del inventario y su distribución son dos de estos procesos, cuya coordinación ha sido demostrada por los investigadores como clave para lograr mejoras en eficiencia y efectividad. Estos a su vez, afectan la sincronización y la administración de la cadena de suministro. Con el propósito de contribuir en la integración de éstos procesos y mejorar los problemas derivados de la variabilidad de la demanda, se propone usar los fundamentos del área de investigación de operaciones y la ayuda de metaheurísticas en un enfoque multi-obejtivo. Los resultados esperados son reducir los costos asociados a los procesos de inventario y distribución, así como también reducir la incertidumbre en la toma de decisiones a partir de la demanda. Ésta tesis presenta métodos para el análisis y obtención de soluciones cercanas a las óptimas para problemas de inventario y routeo, dinámico y estocástico. Los métodos incluyen selección de retailers y métodos de clustering, algoritmos y experimentos en instancias de prueba disponibles en la literatura. Se hace énfasis en instancias de un solo proveedor y varios proveedores que sirven varios retailers distribuidos geográficamente. La tesis está organizada en cuatro partes. En la Parte I, se revisa la literatura, para ello, primero se presentan los problemas relacionados con la coordinación del inventario y su distribución. Ésta revisión resalta cuatro elementos que han sido identificados como claves en la literatura como son: la administración de la información, políticas de inventario, demanda estocástica y métodos de optimización. Luego, se presenta un análisis cienciometrico de la literatura encontrada en los últimos 10 años. La revisión de la documentación se realiza de manera exhaustiva trabajando con demanda dinámica y estocástica. Las contribuciones de esta parte son: i) proporcionar una revisión pertinente y actualizada de artículos que emplean demanda estocástica, enfatizando en sus elementos dinámicos y estocásticos, así como también en aspectos que permitan abordar problemas con múltiples depósitos, ii) identificar factores críticos para el desempeño de actividades logísticas, iii) Demostrar que el estudio de la demanda es esencial para lograr una representación útil del sistema, la cual influye en la toma de decisiones y iv) proporcionar tendencias y patrones en la investigación de problemas de IRP. En la Parte II se aborda la metodología de la investigación y de desarrollo. Primero, se presenta el problema, el estado de la ciencia y los gaps encontrados en la literatura. Luego se identifican las variables de estudio, los instrumentos aplicados y los supuestos utilizados. La metodología de desarrollo es presentada por medio de un modelo general para abordar éste tipo de investigaciones que nosotros proponemos en ésta tesis. Esta metodología aborda aspectos como: el procedimiento general de desarrollo, la descomposición del problema y la forma en que se prueban las posibles soluciones. En la Parte III, se presentan los fundamentos en la formulación de IRP. Primero se formulan los problemas TSP con variantes para un solo depósito y también paramúltiples depósitos, igualmente se hace para VRP e IRP. La contribución de los modelos presentados son la identificación de las variables y los modelos matemáticos que frecuentemente son usados para tratar con éste tipo de problemas. En la Parte IV se presentan dos experimentos. El primero para el análisis de instancias con uno sólo depósito y en el segundo para analizar instancias con múltiples depósitos. Los métodos usados producen mejoras sobre resultados obtanidos con algoritmos similares. Las contribuciones de ésta parte son: i) proponer tres nuevos métodos para la selección de retailers para IRP dinámicos y estocásticos, ii) realizar análisis multi-criterio de las soluciones, comparando la distribución con la administración del inventario y iii) realizar análisis de un solo objetivo sobre instancias de pruebas proporcionada por la literatura existente

An enhanced approximation mathematical model inventorying items in a multi-echelon system under a continuous review policy with probabilistic demand and lead-time

An inventory system attempts to balance between overstock and understock to reduce the total cost and achieve customer demand in a timely manner. The inventory system is like a hidden entity in a supply chain, where a large complete network synchronizes a series of interrelated processes for a manufacturer, in order to transform raw materials into final products and distribute them to customers. The optimality of inventory and allocation policies in a supply chain for a cement industry is still unknown for many types of multi-echelon inventory systems. In multi-echelon networks, complexity exists when the inventory issues appear in multiple tiers and whose performances are significantly affected by the demand and lead-time. Hence, the objective of this research is to develop an enhanced approximation mathematical model in a multi-echelon inventory system under a continuous review policy subject to probabilistic demand and lead-time. The probability distribution function of demand during lead-time is established by developing a new Simulation Model of Demand During Lead-Time (SMDDL) using simulation procedures. The model is able to forecast future demand and demand during lead-time. The obtained demand during lead-time is used to develop a Serial Multi-echelon Inventory (SMEI) model by deriving the inventory cost function to compute performance measures of the cement inventory system. Based on the performance measures, a modified distribution multi-echelon inventory (DMEI) model with the First Come First Serve (FCFS) rule (DMEI-FCFS) is derived to determine the best expected waiting time and expected number of retailers in the system based on a mean arrival rate and a mean service rate. This research established five new distribution functions for the demand during lead-time. The distribution functions improve the performance measures, which contribute in reducing the expected waiting time in the system. Overall, the approximation model provides accurate time span to overcome shortage of cement inventory, which in turn fulfil customer satisfaction

Sourcing and outsourcing of materials and services in chemical supply chains

Ph.DDOCTOR OF PHILOSOPH

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes

Response Time Reduction and Service Level Differentiation in Supply Chain Design: Models and Solution Approaches

Make-to-order (MTO) and assemble-to-order (ATO) systems are emerging business strategies in managing responsive supply chains, characterized by high product variety, highly variable customer demand, and short product life cycle. Motivated by the strategic importance of response time in today’s global business environment, this thesis presents models and solution approaches for response time reduction and service-level differentiation in designing MTO and ATO supply chains. In the first part, we consider the problem of response time reduction in the design of MTO supply chains. More specifically, we consider an MTO supply chain design model that seeks to simultaneously determine the optimal location and the capacity of distribution centers (DCs) and allocate stochastic customer demand to DCs, so as to minimize the response time in addition to the fixed cost of opening DCs and equipping them with sufficient assembly capacity and the variable cost of serving customers. The DCs are modelled as M/G/1 queues and response times are computed using steady-state waiting time results from queueing theory. The problem is set up as a network of spatially distributed M/G/1 queues and modelled as a nonlinear mixed-integer program. We linearize the model using a simple transformation and a piece-wise linear and concave approximation. We present two solution procedures: an exact solution approach based on cutting plane method and a Lagrangean heuristic for solving large instances of the problem. While the cutting plane approach provides the optimal solution for moderate instances in few iterations, the Lagrangean heuristic succeeds in finding feasible solutions for large instances that are within 5% from the optimal solution in reasonable computation times. We show that the solution procedure can be extended to systems with multiple customer classes. Using a computational study, we also show that substantial reduction in response times can be achieved with minimal increase in total costs in the design of responsive supply chains. Furthermore, we find the supply chain configuration (DC location, capacity, and demand allocation) that considers congestion and its effect on response time can be very different from the traditional configuration that ignores congestion. The second part considers the problem of response time reduction in the design of a two-echelon ATO supply chain, where a set of plants and DCs are to be established to distribute a set of finished products with non-trivial bill-of-materials to a set of customers with stochastic demand. The model is formulated as a nonlinear mixed integer programming problem. Lagrangean relaxation exploits the echelon structure of the problem to decompose into two subproblems - one for the make-tostock echelon and the other for the MTO echelon. We use the cutting plane based approach proposed above to solve the MTO echelon subproblem. While Lagrangean relaxation provides a lower bound, we present a heuristic that uses the solution of the subproblems to construct an overall feasible solution. Computational results reveal that the heuristic solution is on average within 6% from its optimal. In the final part of the thesis, we consider the problem of demand allocation and capacity selection in the design of MTO supply chains for segmented markets with service-level differentiated customers. Demands from each customer class arrives according to an independent Poisson process and the customers are served from shared DCs with finite capacity and generally distributed service times. Service-levels of various customer classes are expressed as the fraction of their demand served within a specified response (sojourn) time. Our objective is to determine the optimal location and the capacity of DCs and the demand allocation so as to minimize the sum of the fixed cost of opening DCs and equipping them with sufficient capacity and the variable cost of serving customers subject to service-level constraints for multiple customer classes. The problem is set up as a network of spatially distributed M/M/1 priority queues and modelled as a nonlinear mixed integer program. Due to the lack of closed form solution for service-level constraints for multiple classes, we present an iterative simulation-based cutting plane approach that relies on discrete-event simulation for the estimation of the service-level function and its subgradients. The subgradients obtained from the simulation are used to generate cuts that are appended to the mixed integer programming model. We also present a near-exact matrix analytic procedure to validate the estimates of the service-level function and its subgradients from the simulation. Our computational study shows that the method is robust and provides an optimal solution in most of the cases in reasonable computation time. Furthermore, using computational study, we examine the impact of different parameters on the design of supply chains for segmented markets and provide some managerial insights

Electronic supply chain management systems in managing the bullwhip effect on selected fast moving consumer goods.

Ph. D. University of KwaZulu-Natal, Durban 2014.The amplitude in order variability as orders surge upstream a supply chain epitomises a phenomenon commonly called the bullwhip effect. The real consumer demand orders are comparatively and tentatively evinced less variability while trading supply chain members on the midstream and upstream stages experience the amplified order vacillations. The oscillator effect reveals a number of pernicious problems throughout the supply chain networks, as downstream sites include harmful bloated inventory and shortages with poor customer service, and the midstream and upstream sites depict the disharmonic capacity on improper planning and inconsistent scheduling in production. This study investigates the selected fast moving consumer goods (FMCG) industry on the amplified consumer demand order variability as orders cascade from downstream (retailers) to the midstream as well as upstream sites of the supply chain network.The effect of electronically-enabled supply chain management (e-SCM) systems remains the central hypothesis for instant information sharing on inventory positioning, integrated supply chain management processes and improved profitability through positive performance targets and outcomes across supply chain trading partners. The main objective aims to understand the on extent of the relationship to which the phenomenon of bullwhip effect can be explained by e-SCM system diffusion, optimal inventory positioning, strategic information sharing and global optimisation strategies. These seamless linkages between supply chain partners seem to entrench velocity on quasi-real-time information flow in consumer demand and supply sides, inventory status and availability, and capacity availability. This study found empirical research evidence on e-SCM systems that retail supply chain businesses have fastidiously adapted to technology clockspeed for the last five years. The majority of the respondents (92%) for both upstream and downstream echelon categories agreed that e-SCM systems have a significant role to play in mitigating the consumer demand order variability in the supply chain network. This study further discovered that the migration from in-house IT systems to integrated e-SCM systems (65%) would entrench close integration of information exchange and processes across different parts of the organisation and inter-organisational linkages. The e-SCM systems diffusion also depicted a positive linear relationship to the extent to which the organisations efficiently and timeously communicate the future strategic needs and demand order replenishments throughout the entire supply chain network. However, the access to advance economic information negatively related to e-SCM systems with the virtue of legal constraints and template-based information attachments

Operational research:methods and applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order

Time-differentiated distribution of service parts and repair materials: an investigation of service time, area partitions, and cost relations

Motivation: Manufacturers in sectors like Information Technology (IT), Automotive and Aerospace have increasingly become focused on providing after sales services. One of the forms of after sales services is to provide service parts (or spare parts) to customers within different contracted time windows. Commonly offered by large scale IT sector companies, such services are facilitated by Service Parts Logistics (SPL) systems through a network of parts stocking facilities. The number of stocking facilities in a distribution network affects the service responsiveness and service costs related to inventory, transportation and facility set-up. Higher responsiveness can be attained through increasing the number of facilities in a distribution network, which, in turn, usually increases inventory cost. Generally, studies assume that shorter service time windows result in higher costs, but there is a lack of exploration regarding how reductions in service time limits and changes in the fractions of demand for different time-based service types impact on various service related costs. Service area partitioning (or zoning) is another related issue which is unexplored in general facility location literature when considering multiple service time (or distance) constraints and both inventory and transportation costs. This study is mainly motivated by SPL systems of IT equipment manufacturers that support the provision of service parts at customer sites under different and short service time commitments in a large geographical area. The study is of a generic nature and generates insights that can be relevant for any case where the service responses are provided within different short time windows and involve the provision (or consumption) of some stocks (e.g. emergency infrastructure repairs). Aim and methodology: The aim of this work is to investigate relationships between time-based service levels, service costs and service zones/areas under a hierarchical organization and a non-hierarchical organization of service facilities. The hierarchical organization has variable capabilities to meet different time-based requirements, while the non-hierarchical organization has a uniform capability to meet the toughest requirement for the entire customer base. The investigation is mainly done through analytical, simulation and optimization modelling with the view of producing answers that provide a general understanding and practical insights rather than producing situation specific optimization models. Empirical case studies are also conducted to complement the quantitative modelling work so that the research is not divorced from the reality. The case studies point towards the motivation for the modelling study and its relevance to some of the real-world systems, and provide a broader understanding of the issues being researched. The case studies involve two multinational ICT equipment manufacturers and service provides, and a government agency responsible for providing highway emergency services in England. Key findings: The results from the modelling experiments show that under the non-hierarchical setup, where all facilities provide the full range of service-times in their respective vicinities, inventory and transportation costs are insensitive to the fractions of demand for different time-based service types. However, with an inventory sharing mechanism under the non-hierarchical setup, the increase in the proportion of demand for the service within the longer time window can increase the service availability level while also increasing the average travelling. On the other hand, under the hierarchical setup, which provides a higher level of centralization when there is demand for the service in the longer time window, inventory and transportation costs react to the proportions of demand for different time-based service types. The hierarchical setup results in higher transportation cost compared to the non-hierarchical setup, and, interestingly, does not necessarily lower the inventory level, especially when the overall demand rate is very low. The simulation of the inventory sharing mechanism under the hierarchical setup shows that, in several cases, inventory sharing can not only increase the service availability level, but can also reduce transportation cost. The analysis based on the optimization models shows that there can be cases where it is more cost effective to serve all demand, regardless of the required service time, in a similar fashion through a non-hierarchical setup. The results also show that the demand fractions for different time-based service types, and inventory and transportation costs can significantly impact on the optimum organization of service zone. There can be distinct optimum patterns of service zones depending on whether the inventory cost or the transportation cost dominates

Price of anarchy in supply chains, congested systems and joint ventures

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 169-174).This thesis studies the price of anarchy in supply chains, congested systems and joint ventures. It consists of three main parts. In the first part, we investigate the impact of imperfect competition with nonlinear demand. We focus on a distribution channel with a single supplier and multiple downstream retailers. To evaluate the performance, we consider several metrics, including market penetration, total profit, social welfare and rent extraction. We quantify the performance with tight upper and lower bounds. We show that with substitutes, while competition improves the efficiency of a decentralized supply chain, the asymmetry among the retailers deteriorates the performance. The reverse happens when retailers carry complements. We also show that efficiency of a supply chain with concave (convex) demand is higher (lower) than that with affine demand. The second part of the thesis studies the impact of congestion in an oligopoly by incorporating convex costs. Costs could be fully self-contained or have a spillover component, which depends on others' output. We show that when costs are fully self-contained, the welfare loss in an oligopoly is at most 25% of the social optimum, even in the presence of highly convex costs. With spillover cost, the performance of an oligopoly depends on the relative magnitude of spillover cost to the marginal benefit to consumers. In particular, when spillover cost outweighs the marginal benefit, the welfare loss could be arbitrarily bad. The third part of the thesis focuses on capacity planning with resource pooling in joint ventures under demand uncertainties. We distinguish heterogeneous and homogeneous resource pooling. When resources are heterogeneous, the effective capacity in a joint venture is constrained by the minimum individual contribution. We show that there exists a unique constant marginal revenue sharing scheme which induces the same outcome in a Nash equilibrium, Nash Bargaining and the system optimum. The optimal scheme rewards every participant proportionally with respect to his marginal cost. When resources are homogeneous, we show that the revenue sharing ratio should be inversely proportional to a participant's marginal cost.by Wei Sun.Ph.D