An EOQ Model for a Deteriorating Item with Time Dependent Quadratic Demand and Variable Deterioration under Permissible Delay in Payment

Abstract In a recent paper, Khanra, Ghosh and Chaudhuri's (2011) presented an EOQ model for a deteriorating item with time dependent quadratic demand under permissible delay in payment. Deterioration considered in most of the EOQ models is constant, while in most of the practical cases the deterioration rate increases with time. This work is motivated by Khanra, Ghosh and Chaudhuri's (2011) paper extending their model to allow for a variable rate of deterioration when delay in payment is permissible. The time varying demand rate is taken to be a quadratic function of time. For settling the account, the model is developed under two circumstances: case-1: The credit period is less than or equal to the cycle time and case-2: the credit period is greater than the cycle time. A numerical example is provided to illustrate the model. Sensitivity analysis has also been conducted to study the effect of the parameters

An optimization of an inventory model of decaying-lot depleted by declining market demand and extended with discretely variable holding costs

Inventory management is considered as major concerns of every organization. In inventory holding, many steps are taken by managers that result a cost involved in this row. This cost may not be constant in nature during time horizon in which perishable stock is held. To investigate on such a case, this study proposes an optimization of inventory model where items deteriorate in stock conditions. To generalize the decaying conditions based on location of warehouse and conditions of storing, the rate of deterioration follows the Weibull distribution function. The demand of fresh item is declining with time exponentially (because no item can always sustain top place in the list of consumers’ choice practically e.g. FMCG). Shortages are allowed and backlogged, partially. Conditions for global optimality and uniqueness of the solutions are derived, separately. The results of some numerical instances are analyzed under various conditions

Inventory model with different demand rate and different holding cost

This paper deals with the development of an inventory model for time varying demand and constant demand; and time dependent holding cost and constant holding cost for case 1 and case 2 respectively. Previous models incorporating that the holding cost is constant for the entire inventory cycle. Mathematical model has been developed for determining the optimal order quantity, the optimal cycle time and optimal total inventory cost for both cases. Differential calculus is used for finding optimal solution. Numerical examples are given for both cases to validate the proposed model. Sensitivity analysis is carried out to analyze the effect of changes in the optimal solution with respect to change in various parameters

The New Mathematical Models for Inventory Management under Uncertain Market

Abstract: This paper presents the new mathematical model for determining the optimal ordering policy for industrial and commercial companies. In the previous research, the numerous inventory models under inflationary conditions have been developed. In these models, the demand rate, usually, has been considered constant and well known, time-varying, stock dependent or price-dependent. But, the demand rate, usually, is uncertain in the real world. Therefore, in this study, the new inflationary inventory models under stochastic demand conditions have been developed. The inventory system is in the state of multi-items with budget constraint. The numerical examples have also been given to illustrate and validate the theoretical results

Replenishment Policy for Pareto Type Deteriorating Items With Quadratic Demand under Partial Backlogging And Delay in Payments

The present model develops a replenishment policy in which the demand rate is quadratic polynomial-time function. Deterioration rate is a Pareto type function. Shortages are partial backlogging and delay in payments are allowed. Holding cost is a linear function of time. The backlogging rate varies with the waiting duration for the next replenishment. The present paper determines the optimal policy for the individual by minimizing the total cost. The optimization procedure has been explained by a numerical example and a detailed sensitivity analysis of the optimal solution has been carried out to display the effect of various parameters

OR in Spare Parts Management:A Review

Abstract Spare parts are held to reduce the consequences of equipment downtime, playing an important role in achieving the desired equipment availability at a minimum economic cost. In this paper, a framework for OR in spare parts management is presented, based on the product lifecycle process and including the objectives, main tasks, and OR disciplines for supporting spare parts management. Based on the framework, a systematic literature review of OR in spare parts management is undertaken, and then a comprehensive investigation of each OR discipline's contribution is given. The gap between theory and practice of spare parts management is investigated from the perspective of software integration, maintenance management information systems and adoption of new OR methods in software. Finally, as the result of this review, an extended version of the framework is proposed and a set of future research directions is discussed

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

Inventory Management and Supply Chain Coordination Mechanisms

This dissertation is on inventory management and supply chain coordination mechanisms within an economic order quantity framework. Specifically, this research focuses on modeling optimal order policies and coordination mechanisms for a supply chain involving items which experience probabilistic failure during storage. These items are common types of manufactured items which, nonetheless, require specialized order policy considerations due to their unique characteristics. We first develop the solution for the buyer’s problem through the use of an economic order quantity (EOQ) model incorporating item failure. We then proceed to model the manufacturer’s problem through the use of an economic production quantity (EPQ) model. Finally, we consider mechanisms to promote mutually-beneficial cooperation between the supplier and n buyers in service of coordinating the entire supply chain. While prior research has focused on items which can be repaired or sold at a discount upon failure, such models are inappropriate for systems where repair costs exceed or are equivalent to item costs and imperfect items are unacceptable. Examples of industries featuring these inventory conditions include the medical, defense, and electronics industries where defective items are largely useless. First, our EOQ model considers a buyer-supplier relationship featuring delivery and stocking of items which experience probabilistic failure in storage. Thereafter, our EPQ model considers in-house production of such items. Collectively, our EOQ and EPQ models provide methods for developing optimal order policies necessary to achieve practicable supply chain coordination. In order to validate the necessity of the developed models, we include an empirical analysis of item reliability for some common mechanical components used in the defense industry, thereby identifying items which fail in the manner modeled in this dissertation. Having considered optimal order policies for both buyers and suppliers, we next develop an optimal solution for a coordinated supply chain. The proposed solution allows the manufacturer to coordinate a supply chain consisting of n buyers in order to achieve a common replenishment time. Through this optimization framework, we minimize total system-wide costs and derive the cost savings associated with our coordinated solution. Numerical examples are then used to demonstrate the magnitude of cost savings achievable through our coordination framework. We conclude by proposing several mechanisms for leveraging the resulting cost savings to induce mutually-beneficial cooperation between the supplier and multiple buyers. Given the lack of buyer-supplier cooperation noted in empirical research related to supply chain coordination, our identification of specific mechanisms useful for inducing mutually-beneficial cooperation between buyers and suppliers represents an important practical contribution to the supply chain coordination literature. These models are accompanied by a thorough overview and discussion of economic order quantity theory, optimal order policies, and supply chain coordination mechanisms.Ph.D., Business Administration -- Drexel University, 201