An inventory planning problem for time-varying linear demand and parabolic holding cost with salvage value

In this manuscript, a model is proposed for the inventory planning problem with items which deteriorate linearly with respect to time. The concept of salvage value for deteriorated items is considered and incorporated in this model. The solution procedure of proposed optimization model is illustrated by a couple of numerical examples. A convexity check of the average total cost function is performed by plotting a two dimensional graph. The sensitivity test of the proposed model is performed to study the effect of changing the least as well as the most sensitive parameters in the proposed optimization model. Some graphical representations are constructed to discuss the outcomes and results so obtained for a choice of various parameters</p

EOQ inventory model for perishable products under uncertainty

Perishable products require accurate inventory control models as their effect on operations management can be critical. This assumption is particularly relevant in highly uncertain and dynamic markets, as for the ones generated by the pandemic era. This paper presents an inventory control model for perishable items with a demand rate variable over time, and dependent on the inventory rate. The model also considers the potential for backlogging and lost sales. Imperfect product quality is included, and deterioration is modelled as a time-dependent variable. The framework envisages the possibility to define variables affected by uncertainty in terms of probability distribution functions, which are then jointly managed via a Monte Carlo simulation. This paper is intended to provide an analytical formulation to deal with uncertainty and time-dependent inventory functions to be used for a variety of perishable products. The formulation is designed to support decision-making for the identification of the optimal order quantity. A numerical example exemplifies the outcomes of the paper and provides a cost-based sensitivity analysis to understand the role of main parameters

EOQ MODEL FOR DETERIORATING AND AMELIORATING ITEMS UNDER CUBIC DEMAND AND PARTIAL BACKLOGGING

The inventory model aims to determine policies in inventory control. Therefore, the availability needs to be managed as well as possible to obtain optimal performance. This study aimed to produce EOQ models for deteriorating and ameliorating products with shortage and partial backlogging policies. The traditional Economic Order Quantity (EOQ) inventory model was used to develop the model. The search algorithm of the model solution was made to get a solution from the model. In the end, a case study of the model implementation at Minimarket SATUMART, Sidoarjo, is give

Deteriorating Inventory Model For Two Parameter Weibull Demand With Shortages

In this paper a deteriorating inventory model have been developed for two parameter Weibull demand rate. Shortages are allowed and are completely backlogged .This inventory system follows an two-parameter exponnential distribution deterioration rate in which the holding cost is constant .The results are described with the numerical example and sensitivity analysis. Keywords: Deterioration, Exponential distribution, holding cost, Inventory, shortages, Weibull demand rate

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

DETERIORATING ITEM INVENTORY MODEL WITH SHORTAGES, VARIABLE HOLDING COST AND TIME DEPENDENT QUADRATIC DEMAND: AN OPTIMIZATION APPROACH USING WITH AND WITHOUT CONTROLLABLE RATE OF DETERIORATION

The purpose of this study is to develop time dependent quadratic demand and variable holding cost, a model of inventory system, for instantaneous deteriorating items with the consideration of the facts that the deteriorating rate can be controlled by using the preservation technology (PT). A solution procedure is presented to find the optimal solution of the cost function. Shortages are allowed and partially backlogged. The backlogging rate is assumed to be dependent on the length of the waiting time for the next replenishment. The longer the waiting time is, the smaller the backlogging rate would be. Results have been validated with relevant examples. Sensitivity analysis is performed to show the effect of changes in the parameters on the optimum solution for both the cases that is with and without using the preservation technology respectively. The analysis of the model shows that the solution of the model is quite stable and can be applied for optimizing the inventory cost of deteriorating items for the business enterprise

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

The Optimal Replenishment Policy under Trade Credit Financing with Ramp Type Demand and Demand Dependent Production Rate

This paper investigates the optimal replenishment policy for the retailer with the ramp type demand and demand dependent production rate involving the trade credit financing, which is not reported in the literatures. First, the two inventory models are developed under the above situation. Second, the algorithms are given to optimize the replenishment cycle time and the order quantity for the retailer. Finally, the numerical examples are carried out to illustrate the optimal solutions and the sensitivity analysis is performed. The results show that if the value of production rate is small, the retailer will lower the frequency of putting the orders to cut down the order cost; if the production rate is high, the demand dependent production rate has no effect on the optimal decisions. When the trade credit is less than the growth stage time, the retailer will shorten the replenishment cycle; when it is larger than the breakpoint of the demand, within the maturity stage of the products, the trade credit has no effect on the optimal order cycle and the optimal order quantity