A two-storage model for deteriorating items with holding cost under inflation and Genetic Algorithms

A deterministic inventory model has been developed for deteriorating items and Genetic Algorithms (GA) having a ramp type demands with the effects of inflation with two-storage facilities. The owned warehouse (OW) has a fixed capacity of W units; the rented warehouse (RW) has unlimited capacity. Here, we assumed that the inventory holding cost in RW is higher than those in OW. Shortages in inventory are allowed and partially backlogged and Genetic Algorithms (GA) it is assumed that the inventory deteriorates over time at a variable deterioration rate. The effect of inflation has also been considered for various costs associated with the inventory system and Genetic Algorithms (GA). Numerical example is also used to study the behaviour of the model. Cost minimization technique is used to get the expressions for total cost and other parameters

An EOQ model for time-dependent deteriorating items with alternating demand rates allowing shortages by considering time value of money

The present paper deals with an economic order quantity (EOQ) model of an inventory problem with alternating demand rate: (i) For a certain period, the demand rate is a non linear function of the instantaneous inventory level. (ii) For the rest of the cycle, the demand rate is time dependent. The time at which demand rate changes, may be deterministic or uncertain. The deterioration rate of the item is time dependent. The holding cost and shortage cost are taken as a linear function of time. The total cost function per unit time is obtained. Finally, the model is solved using a gradient based non-linear optimization technique (LINGO) and is illustrated by a numerical example

Inventory models for production systems with constant/linear demand, time value of money, and perishable/non-perishable items

This research considers inventory systems for economic production models where the objective is to find the optimal cycle time, which minimizes the total cost, and optimal amount of shortage if it is allowed. Several aspects such as time value of money, inflation, constant and linear demand rates, shortages, and deterioration are considered in developing different models. Closed formulas are obtained for the optimal policy in one model. For others, more complex models where closed formulas cannot be obtained, search techniques are used to find the optimal solution.;First, a deterministic inventory control problem is considered for determination of optimal production quantities for an item with constant demand rate, while considering the effect of time value of money. Closed formulas are obtained to calculate the optimal cycle time and corresponding production quantity for the model without shortage. However, search procedures are used to find the optimal cycle time and maximum amount of shortage allowed for the models where shortage is allowed.;In the next inventory control problem, a deterministic model for items with linear demand rate over time, for a finite planning horizon, while considering the effect of time value of money, is considered. Search techniques are developed to find the optimal cycle time for the models without shortage, and the optimal cycle time and maximum amount of shortage for the models where shortage is allowed. A proof of the existence of a unique optimal point for the cost function is presented for the model without shortage.;A deterministic inventory control problem is also considered for items with constant rate of demand and exponentially decaying inventory over an infinite planning horizon, while considering the effect of time value of money. Two different search techniques are developed to find the optimal cycle time for the models without shortage, and the optimal cycle time and maximum amount of shortage allowed for the models where shortage is allowed. A proof of the existence of a unique optimal point for the cost function is presented for the model without shortage

Inventory Model for Quadratic Demand and Deteriorating Items Following Weibull Distribution with Trade Credit Policy

In this paper, an inventory model for deteriorating items following two parameter Weibull distribution with trade credit policy is developed, while demand is viewed as quadratic function of time. The supplier gives the retailer a trade credit period. Trade credit is a frequently used method of payment implemented by suppliers, and it generally leads to greater revenue and ultimately, higher income. The suggested inventory model seeks to calculate the ideal replenishment cycle duration in order to maximize the overall profit per unit of time.  Shortages are permitted and partially backlogged. Two categories are applied to the mathematical model. Case I: When the payment to settle the account is made on or before the positive inventory. Case II: When the payment to settle the ac-count is made after the inventory reaches to zero. The model is illustrated through numerical experiments, sensitivity analysis, and graphical depiction

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

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