An EOQ model for a deteriorating item with non-linear demand under inflation and a trade credit policy

This paper develops an infinite time-horizon deterministic economic order quantity (EOQ) inventory model with deterioration based on discounted cash flows (DCF) approach where demand rate is assumed to be non-linear over time. The effects of inflation and time-value of money are also taken into account under a trade-credit policy of type "α/T1 net T". The results are illustrated with a numerical example. Sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out

Modelos de Inventarios con Productos Perecederos: Revisión de la Literatura

This paper presents a review of the main characteristics of the mathematical modelsdeveloped by the scientific community in order to determine an optimal inventory policyfor deteriorating items. Thus, a classified bibliography of 390 articles published from2001 to 2014 in high-impact journals is submitted while considering the type of demandand deterioration, the integration of inventory and pricing decisions, the inclusionof shortage and/or the time value of money, the consideration of multiple items and/ormulti-echelon systems, and the incorporation of uncertain parameters other than demand.Finally, research questions not yet addressed by the research community in the field ofinventory control for deteriorating items are pointed out.En el presente artículo se lleva a cabo una revisión de las principales características estudiadas por la comunidad científica en el desarrollo de modelos matemáticos que buscan definir una política de inventario óptima para productos que se deterioran. De este modo, se referencian 390 artículos publicados a partir del año 2001 en revistas de gran impacto, teniendo en cuenta: el tipo de demanda y deterioro representado en los modelos matemáticos, el estudio de una política de precio óptima, la inclusión de faltantes y/o valor del dinero en el tiempo, el estudio de múltiples productos y/o dos o más eslabones de la cadena de suministro, y la utilización de parámetros o variables difusas. Finalmente, se identifican oportunidades de investigación que a la fecha no han sido abordadas por la comunidad científica en este campo del conocimiento

Responsible Inventory Models for Operation and Logistics Management

The industrialization and the subsequent economic development occurred in the last century have led industrialized societies to pursue increasingly higher economic and financial goals, laying temporarily aside the safeguard of the environment and the defense of human health. However, over the last decade, modern societies have begun to reconsider the importance of social and environmental issues nearby the economic and financial goals. In the real industrial environment as well as in today research activities, new concepts have been introduced, such as sustainable development (SD), green supply chain and ergonomics of the workplace. The notion of “triple bottom line” (3BL) accounting has become increasingly important in industrial management over the last few years (Norman and MacDonald, 2004). The main idea behind the 3BL paradigm is that companies’ ultimate success should not be measured only by the traditional financial results, but also by their ethical and environmental performances. Social and environmental responsibility is essential because a healthy society cannot be achieved and maintained if the population is in poor health. The increasing interest in sustainable development spurs companies and researchers to treat operations management and logistics decisions as a whole by integrating economic, environmental, and social goals (Bouchery et al., 2012). Because of the wideness of the field under consideration, this Ph.D. thesis focuses on a restricted selection of topics, that is Inventory Management and in particular the Lot Sizing problem. The lot sizing problem is undoubtedly one of the most traditional operations management interests, so much so that the first research about lot sizing has been faced more than one century ago (Harris, 1913). The main objectives of this thesis are listed below: 1) The study and the detailed analysis of the existing literature concerning Inventory Management and Lot Sizing, supporting the management of production and logistics activities. In particular, this thesis aims to highlight the different factors and decision-making approaches behind the existing models in the literature. Moreover, it develops a conceptual framework identifying the associated sub-problems, the decision variables and the sources of sustainable achievement in the logistics decisions. The last part of the literature analysis outlines the requirements for future researches. 2) The development of new computational models supporting the Inventory Management and Sustainable Lot Sizing. As a result, an integrated methodological procedure has been developed by making a complete mathematical modeling of the Sustainable Lot Sizing problem. Such a method has been properly validated with data derived from real cases. 3) Understanding and applying the multi-objective optimization techniques, in order to analyze the economic, environmental and social impacts derived from choices concerning the supply, transport and management of incoming materials to a production system. 4) The analysis of the feasibility and convenience of governmental systems of incentives to promote the reduction of emissions owing to the procurement and storage of purchasing materials. A new method based on the multi-objective theory is presented by applying the models developed and by conducting a sensitivity analysis. This method is able to quantify the effectiveness of carbon reduction incentives on varying the input parameters of the problem. 5) Extending the method developed in the first part of the research for the “Single-buyer” case in a "multi-buyer" optics, by introducing the possibility of Horizontal Cooperation. A kind of cooperation among companies in different stages of the purchasing and transportation of raw materials and components on a global scale is the Haulage Sharing approach which is here taken into consideration in depth. This research was supported by a fruitful collaboration with Prof. Robert W. Grubbström (University of Linkoping, Sweden) and its aim has been from the beginning to make a breakthrough both in the theoretical basis concerning sustainable Lot Sizing, and in the subsequent practical application in today industrial contexts

Modelling and Determining Inventory Decisions for Improved Sustainability in Perishable Food Supply Chains

Since the introduction of sustainable development, industries have witnessed significant sustainability challenges. Literature shows that the food industry is concerned about its need for efficient and effective management practices in dealing with perishability and the requirements for conditioned storage and transport of food products that effect the environment. Hence, the environmental part of sustainability demonstrates its significance in this industrial sector. Despite this, there has been little research into environmentally sustainable inventory management of deteriorating items. This thesis presents mathematical modelling based research for production inventory systems in perishable food supply chains. In this study, multi-objective mixed-integer linear programming models are developed to determine economically and environmentally optimal production and inventory decisions for a two-echelon supply chain. The supply chain consists of single sourcing suppliers for raw materials and a producer who operates under a make-to-stock or make-to-order strategy. The demand facing the producer is non-stationary stochastic in nature and has requirements in terms of service level and the remaining shelf life of the marketed products. Using data from the literature, numerical examples are given in order to test and analyse these models. The computational experiments show that operational adjustments in cases where emission and cost parameters were not strongly correlated with supply chain collaboration (where suppliers and a producer operate under centralised control), emissions are effectively reduced without a significant increase in cost. The findings show that assigning a high disposal cost, limit or high weight of importance to perished goods leads to appropriate reduction of expected waste in the supply chain with no major cost increase. The research has made contributions to the literature on sustainable production and inventory management; providing formal models that can be used as an aid to understanding and as a tool for planning and improving sustainable production and inventory control in supply chains involving deteriorating items, in particular with perishable food supply chains.the Ministry of Science and Technology, the Royal Thai Government

A forward with backward inventory policy algorithm for nonlinear increasing demand and shortage backorders

The traditional inventory policies have been developed for constant demand processes. In reality, demand is not always stable; it might have an increasing pattern. In this paper, a forward with backward inventory policy algorithm is developed to determine the operational parameters of an inventory system with a nonlinear increasing demand rate, shortage backorders and a finite planning horizon. Numerical experiments are also conducted to compare the results with the existing techniques and to illustrate the applicability of the proposed technique

Inventory Model with Partial Backordering When Backordered Customers Delay Purchase after Stockout-Restoration

Many inventory models with partial backordering assume that the backordered demand must be filled instantly after stockout restoration. In practice, however, the backordered customers may successively revisit the store because of the purchase delay behavior, producing a limited backorder demand rate and resulting in an extra inventory holding cost. Hence, in this paper we formulate the inventory model with partial backordering considering the purchase delay of the backordered customers and assuming that the backorder demand rate is proportional to the remaining backordered demand. Particularly, we model the problem by introducing a new inventory cost component of holding the backordered items, which has not been considered in the existing models. We propose an algorithm with a two-layer structure based on Lipschitz Optimization (LO) to minimize the total inventory cost. Numerical experiments show that the proposed algorithm outperforms two benchmarks in both optimality and efficiency. We also observe that the earlier the backordered customer revisits the store, the smaller the inventory cost and the fill rate are, but the longer the order cycle is. In addition, if the backordered customers revisit the store without too much delay, the basic EOQ with partial backordering approximates our model very well

Logística y distribución comercial : modelos de gestión de inventarios con patrón de demanda potencial

La gestión de stocks es una materia transcendental para el correcto funcionamiento de las operaciones empresariales. Una de las actividades de las organizaciones en la que la reducción de gastos puede ser determinante se materializa en la cadena logística y el circuito de la distribución comercial, mediante la gestión y el control de los inventarios. Tras exponer, en la introducción de la tesis, el planteamiento del trabajo con sus correspondientes fases de desarrollo, en el capítulo 1, se ofrece una visión general, de los aspectos esenciales relativos a los sistemas de inventario, en el marco de la Economía de la Empresa y la Investigación Operativa y, todo ello, desde la perspectiva de la logística, el marketing y la distribución comercial. Seguidamente, en el capítulo 2, se refleja la importancia del análisis de los modelos de gestión de stocks, identificando su problemática y definiendo las variables y parámetros más relevantes de los sistemas. En el mismo, se presenta una revisión bibliográfica de modelos deterministas con demanda variable en el tiempo y patrón potencial, asumiendo la existencia o no de roturas y la posibilidad de degradación o deterioro en los artículos, la cual ha servido de base y fundamento teórico para la elaboración del trabajo. Asimismo, se plantean diferentes contextos y situaciones reales, ofreciendo una perspectiva práctica del procedimiento propuesto para la determinación de la política más eficiente. En el capítulo 3, se presenta un análisis detallado de los sistemas de inventario deterministas con patrón de demanda potencial, en los cuales el período de programación no está fijado previamente, con la finalidad de obtener una solución única para el nivel de stock inicial y el ciclo de programación óptimos. En concreto, se estudian tres escenarios diferentes: en primer lugar, se admite la ausencia de roturas en el sistema; posteriormente, se plantea la situación en que se permiten roturas y éstas son recuperables, es decir, los clientes no atendidos estarán dispuestos a esperar a la llegada del siguiente pedido para satisfacer su demanda; por último, se contempla el caso en el que las roturas se traducen en pérdida de ventas. En el capítulo 4, se estudia la política de reposición óptima para un sistema de cantidad económica de pedido, considerando artículos con deterioro y patrón de demanda potencial, donde el ciclo de reposición no es fijo y el costo total promedio depende de esa variable de decisión. También, se aborda el estudio de un sistema de inventario con deterioro cuando se permite roturas de stocks y éstas son recuperables. En el capítulo 5, se realiza un análisis de los sistemas de inventario de tamaño de lote, en los cuáles existe un periodo de reposición del stock y la demanda sigue un patrón potencial. En primer lugar, se estudia la cantidad de producción económica que minimiza el costo total de inventario por unidad de tiempo, admitiendo, en primer lugar, una tasa de reposición uniforme y, posteriormente, permitiendo que esa tasa varíe con el tiempo y sea proporcional a la razón de demanda. Para cada uno de los modelos analizados, se desarrollan diferentes ejemplos numéricos que ilustran la política eficiente y el coste mínimo. Finalmente, se presenta un resumen de los resultados obtenidos aportando las principales conclusiones e implicaciones derivadas del trabajo

Sviluppo di modelli decisionali per la supply chain di prodotti deperibili mediante l’applicazione di tecnologie innovative

The supply chain of perishable products, as fruits and vegetables is affected by environmental abuses from harvest to the final destination which are responsible the uncontrolled deterioration of food. In order to reduce such phenomena the supply chain members should control and monitor the conditions of goods in order to ensure their quality for consumers and to comply with all legal requirements (Garcia Ruiz, 2008). The most important factor influencing the food quality is the temperature able to prolonging the shelf life of the products. Since the temperature can inhibit or promote the maturation and deterioration process, this parameter is involved both in the growing process of fruits and vegetables and in the transport and storage stages. Given this the aim of the present thesis is to show that the monitoring of such parameter during the pre and post harvest stages allows to improve the decision making process. In the context of temperature monitoring the introduction of emerging information technologies such as the Wireless Sensors Networks and the Radio Frequency Identification can now provide real-time status knowing of product managed. The real time monitoring can be of great help in the definition of the actual maturation level of products both in the field and during the cold chain. The suitability of such an approach is evaluated by means of case studies. The first case study concerns the monitoring of grapes growth directly in the vineyard. The suitability of Wireless Sensors Networks in the monitoring of the grapes growth process is evaluated in terms of the possibility to determine the date of starting or ending of phenological phases. This information allows to make faster decisions about the vineyard operations which must be performed during the grape growth and finally allows to predict the maturation date in order to optimize the harvest operations. In the next case study the possibility to apply the Radio Frequency Identification technology to the monitoring of the fresh fruits along the cold chain has been faced and the quality of the products at any stage of the supply chain has been determined through a mathematical model. The knowing of the current quality level allows to make decisions about the destination of products. In this case those products having a shorter shelf life can be distributed to a local market while those with longer shelf life can be distributed to more distant location. In the next case study the information about the current deterioration state of perishable products has been translated into a warehouse management system in order to determine the operational parameters able to optimize the quality of products stored. Even in this case the goal of the study was to provide a decision making tool for the proper management of the perishable products stored. However besides the advantages achievable by the real time evaluation of environmental conditions the costs involved with the implementation of innovative technologies must be determined in order to establish the suitability of the investment in such innovative technologies. The present thesis also faces this question by determining the optimal number of devices to apply to the stock keeping unit in order to minimize the total cost associated to the transferring batch from the producer to the distributor. In this case the methodology employed is that of a mathematical model including all costs associated to the product management. Finally the study conducted through the present thesis shows that in all of the cases treated the use of the innovative technologies allows to support the decision making process in the pre and post harvest phases thus improving the perishables management