Time Dependent Deterioration Rate Research Articles

Inventory Optimization Model with Quadratic Demand Pattern and Non-instantaneous Deterioration Rate with Mixed Cash and Advance Payment Scheme

Objectives: To develop a mathematical model for cost minimization by examining a scenario involving a seasonal product retail market, evaluating the outcome, and providing solutions to unanswered queries of existing models are the highlights of this present work. Methods: 1. Using dynamic differential equations with initial and boundary conditions, we mathematically model a retail market scenario for perishable commodities and determine the retailer's total cost. 2. We consider a quadratic function of time to precisely describe the maintenance cost and demand function. Also, a combination of cash and advance payment schemes is implemented in our model. 3. Our model was numerically formulated using a dataset deduced from earlier research. We have included a sensitivity analysis and a numerical example with a graphical depiction of the total cost function that highlights the most and least influential factors. 4. Based on the Hessian matrix condition and the calculus derivative approach, we developed an algorithm to calculate the optimal cost. Findings: This model provides retailers with insights for effective stock management while optimizing the cost of retailing perishable commodities with non-linear demand patterns. Sensitivity analysis showed that the two factors that have the biggest impact on retailers' overall costs are non-linear demand and holding cost parameters. The smaller optimal inventory cycle time and the large value of time at which a shortage happens raise the overall cost. Additionally, because of higher demand, the time-dependent deterioration rate has the least impact on overall cost. Additionally, a three-dimensional graph of cost minimization is offered to illustrate the convexity of total cost. Novelty: Implementation of Quadratic time-dependent demand and non-linear holding costs under a mixed cash advance payment structure, along with time-dependent deterioration and partial backlog shortages. Keywords: Quadratic Demand pattern, Non­instantaneous decay rate, Cash and Advance Payment scheme, Partial Backlog Shortages

Statistical Data Analysis for Trackway Asset Management Using Low-Level Nonconformance Rates

Well-documented conditions of the country’s subway systems suggest that the development of a management strategy for aging infrastructure is an important asset management challenge. The purpose of this work is to address this challenge by developing a statistical data analysis approach for forecasting the aging effect on the time-dependent deterioration rate of an identified trackway cluster. The infrastructure database is the New York City subway system and the trackway that supports the delivery of service. While much focus has been given to the steel rail subcomponent of the trackway, little has been done in the way of statistical analysis on the low-level nonconformances in the support structure of those rails—namely, the invert, ties, fasteners, and plates. Though detectable, these conditions pose no risk to either safety or the serviceability of that asset, yet they do provide a certain degree of awareness that an entirely intuitive lifecycle deterioration process is underway. This paper illustrates the development of a statistical data analysis methodology using available trackway data sets for forecasting the aging effect on the system performance.

Inventory Model for Non-instantaneous Deteriorating Items with Time-dependent Deterioration Rate and Price Discounts

In this article, we study a periodic review inventory model for non-instantaneous deteriorating items when the length of a reorder cycle is known and the rate of deterioration is time dependent. In order to stimulate demand within the customers, the inventory manager offers a temporary discount on the selling price in three different stages—(a) before the items start to decay, (b) after deterioration sets in and (c) during shortage. The optimum ordering policy and the discounts to be given are determined so as to maximize the total expected profit over a reorder interval. Numerical examples are cited to illustrate the model. Sensitivity analysis is also carried out to study the effect of change in the model parameters on the optimal policy. AMS subject classification: 90

Procurement and Pricing Decision for Trapezoidal Demand Rate and Time Dependent Deterioration

Deterioration rate may be constant or varies with time. In real life time dependent deterioration is observed in many products like fruits, bakery products, milk products etc. Generally deterioration rate increases as the time passes. In this paper we present an inventory model for the trapezoidal type demand function and time dependent deterioration rate. Demand rate depends on time as well as price. Shortages are allowed with partial backlogging. In order to illustrate solution procedure numerical examples and sensitivity analysis have been demonstrated.

Fuzzy inventory model for deteriorating items in a green supply chain with carbon concerned demand

With the environment deterioration becoming a serious concern, numerous industries have realized that it’s critical to focus on manufacturing with reduced waste and low carbon emission. Studies show that consumers are getting cognizant of environment preservation and prefer low-carbon developed products. It is seen that in some cases, customers are willing to pay even more for products developed using low carbon emission technologies. Furthermore, government initiatives towards going green has resulted in industries focusing on reducing their carbon footprints throughout the supply chain by employing green supply chain methodologies. In this study, we will develop an inventory model for deteriorating items in green supply chain considering recycling, reverse logistics and remanufacturing. Demand is assumed to be carbon dependent. Products are considered to be deteriorating in nature with time dependent deterioration rate. A crisp model is developed to minimize total average cost. In the crisp model, it is assumed that demand, deterioration and returned rate are precisely known. However, in reality these parameters are imprecise in nature. To model this impreciseness, a fuzzy model is developing considering these parameters as triangular fuzzy numbers. Total cost function is defuzzified using signed distance method and is shown to be convex and a unique solution exists. Numerical analysis is carried out for both crisp and fuzzy cases.

An EOQ Model for Deteriorating Items with Selling Price Dependent Exponential Demand for Time Varying Holding and Deterioration Costs

Research investigation of the past few decades shown that the researchers developed economic order quantity (EOQ) model for perishable items under constant deterioration and constant demand. Though, in actual practice it is not true. This paper involved a representation of an inventory control model, in which perishable items has been taken with a price as well as an exponential dependent demand. The measured items in the model are deteriorating in nature based on time dependent deterioration rate. In the earlier studies the holding cost often treated as a constant, which is not suited to the most of the practical life situations. In real practical situation some kind of items treat holding cost is a function of time, which is increase as the time increases. In this paper, a model is developed which included the time dependent linear holding cost. We have achieved the estimated optimal solution under the given assumption according to the situation. A numerical example is presented to demonstrate the model and the sensitivity analysis of various parameters is approved out for the validation of the proposed method. Â

A Deteriorating Inventory Model with Price Dependent Consumption Rate and Exponentially Declining Partial Backlogging

The study of inventory system with deteriorating item has a special significance as it influences the profit and revenue of a retailer. It is generally observed that the demand rate of consumer goods is dependent on the selling price of the product. An inventory model for price dependent demand with partial backlogging and time dependent deterioration rate has been proposed with the objective to determine the maximum average profit, optimal selling price and optimal order quantity of the system. The necessary and sufficient conditions for the existence of the optimal solution are determined. The sensitivity analysis has been carried out and effectiveness of the proposed model has been demonstrated numerically.

A two storage inventory model with variable demand and time dependent deterioration rate and with partial backlogging

A two storage inventory model with variable demand and time dependent deterioration rate and with partial backlogging

Two level production inventory model with exponential demand and time dependent deterioration rate

Two level production inventory model with exponential demand and time dependent deterioration rate

An EOQ inventory model for deteriorating items with time-dependent deterioration rate, ramp-type demand rate and shortages

This paper presents an economic order quantity (EOQ) model for deteriorating items having time proportional deterioration rate, time dependent ramp-type demand rate and shortages. Shortages are allowed to occur in the inventory system and completely backlogged. The ramp-type demand rate is deterministic and varies with time up to a certain point and then becomes constant. The three-parameter Weibull distribution rate indicates the change in deterioration rate with respect to time and takes into account of the items which are already deteriorated while receiving into an inventory system as well as items those might start deteriorating in future. To start with, the model is developed for shortages, but is also valid for the seasonal items and newly launched high tech products like computers, laptops, mobile phones and automobiles, etc. The purpose of this study is to develop an optimal policy, so that the average total cost is minimised by optimising the procurement time point. Furthermore, the solution procedure and the numerical example are provided to illustrate the proposed model. Finally, sensitivity analysis of the various parameters on optimal solution is carried out.

An EOQ inventory model for deteriorating items with time-dependent deterioration rate, ramp type demand rate and shortages

This paper presents an economic order quantity (EOQ) model for deteriorating items having time proportional deterioration rate, time dependent ramp-type demand rate and shortages. Shortages are allowed to occur in the inventory system and completely backlogged. The ramp-type demand rate is deterministic and varies with time up to a certain point and then becomes constant. The three-parameter Weibull distribution rate indicates the change in deterioration rate with respect to time and takes into account of the items which are already deteriorated while receiving into an inventory system as well as items those might start deteriorating in future. To start with, the model is developed for shortages, but is also valid for the seasonal items and newly launched high tech products like computers, laptops, mobile phones and automobiles, etc. The purpose of this study is to develop an optimal policy, so that the average total cost is minimised by optimising the procurement time point. Furthermore, the solution procedure and the numerical example are provided to illustrate the proposed model. Finally, sensitivity analysis of the various parameters on optimal solution is carried out.

An optimal EOQ inventory model for non-instantaneous deteriorating items with ramp type demand rate, time dependent holding cost and shortages

An economic order quantity inventory model for non-instantaneous deteriorating items has been developed with ramp type demand rate, time dependent deterioration rate and time dependent holding cost. Shortages in inventory are allowed in this model, which is partially backlogged. The main objective of this model is to develop an optimal replenishment policy that minimizes the total average inventory cost. Numerical examples are used to illustrate the developed model.

Inflationary Induced EOQ Model for Weibull Distribution Deterioration and Trade Credits

In any business transaction the constant unit price assumption is not true. The tendency in inflationary environment is to buy more in order to reduce the total system cost, which may be true in certain situations but it is not true when consumption rate of items is dependent on initial stock level since buying more quantity under inflationary environment leads to more consumption resulting in higher total system cost. The model developed in this paper helps to determine optimum ordering quantity for stock dependent consumption rate items under inflationary environment with infinite replenishment rate without permitting shortages. The effect of the inflation rate, deterioration rate, Initial-stock-dependent consumption rate and delay in payment are discussed. This study develops an inventory model for constant demand rate and time dependent deterioration rate with delay in payment is discussed. In this study mathematical model are also derived under two different cases. Case-I: The credit period is less then cycle time T; and Case-II: Credit period is greater than cycle time T. This study will proposes an inventory model under a situation in which the supplier provides the purchaser a permissible delay of payments if the purchaser orders a large quantity. Numerical example is given to support the purposed model. Mathematica 7.0 is used for numerical solutions.

AN INVENTORY MODEL FOR NON-INSTANTANEOUS DETERIORATING ITEMS WITH QUADRATIC DEMAND RATE AND SHORTAGES UNDER TRADE CREDIT POLICY

In this paper, we propose an appropriate inventory model for noninstantaneous deteriorating items over quadratic demand rate with permissible delay in payments and time dependent deterioration rate. In this model, the completely backlogged shortages are allowed. In several existing results, the authors discussed that the deterioration rate is constant in each cycle. However, the deterioration rate of items are not constant in real world applications. Motivated by this fact, we consider that the items are deteriorated with respect to time. To minimize the total relevant inventory cost, we prove some useful theorems to illustrate the optimal solutions by finding an optimal cycle time with the necessary and enough conditions for the existence and uniqueness of the optimal solutions. Finally, we discuss the numerical instance and sensitivity of the proposed model.

Periodic review inventory policy for non-instantaneous deteriorating items with time dependent deterioration rate

The paper studies a periodic review inventory model with no shortages and different demand rates during pre- and post- deterioration periods . Deterioration of units start after a fixed time interval, and the deterioration rate is time dependent. The model determines the optimal reorder interval and the optimal order quantity so as to minimize the total cost per unit length of an inventory cycle. An extension of the model to include price discount has been further considered. Numerical examples are presented to illustrate the model and a sensitivity analysis is also reported.

Mathematical application on inventory cash flow

In this paper, we develop an optimal EOQ inventory model for deteriorating items considering constant demand, inflation factor and time dependent deterioration rate over a finite time horizon. Shortages are allowed and excess demand is backlogged. The aim of this model is to determine the optimal decision variables so that the net present value of total system cost over a finite planning horizon is minimized and the profit function is maximized. For the general model, we give the equations for the optimal policy and cost function. Further, the necessary and sufficient conditions are provided to show the existence and uniqueness of the optimal solution. A numerical example is given to illustrate the solution procedure of the model. Finally, based on this example, we conduct a sensitivity analysis of the model.

Fuzzy EOQ models with ramp type demand rate, partial backlogging and time dependent deterioration rate

In this study, a fuzzy inventory model has been discussed for two cases model start with no shortages model start with shortages. Demand rate is of three folded ramp-type time dependent, deterioration rate of the item is time dependent(Weibull) and shortages are partially backlogged. For real situation, we have assumed the backlogging rate and all the cost coefficients as trapezoidal fuzzy number and defuzzification is made with the help of Function Principle and Graded Mean Integration Representation (GMIR) method. Finally using calculus, we have optimised the total cost function. The solution procedure is illustrated with the help of numerical examples.

Inventory Model: Deteriorating Items with Time-Dependent Deterioration Rate for Quadratic Demand Rate With Unit Production Cost and Shortage

In this paper, an order level inventory unit production system for deteriorating items with a quadratic demand is developed. It is assumed that shortages in inventory are permitted and are completely backlogged. The finite production rate is proportional to the time dependent demand rate and deterioration rate is time proportional. The unit production cost is taken to be inversely related to the demand rate. Sensitivity of the decision variable to changes in the parameter values is examined and numerical example is presented to illustrate the model is developed. Keywords - Deterioration; Inventory model; Quadratic demand rate; Shortage;

Inventory models with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages

Manna and Chaudhuri (Eur. J. Oper. Res. 171(2):557–566, 2006) presented a production-inventory system for deteriorating items with demand rate being a linearly ramp type function of time and production rate being proportional to the demand rate. The two models without shortages and with shortages were discussed. Both models were studied assuming that the time point at which the demand is stabilized occurs before the production stopping time. In this paper, we complete this model by considering that: (a) for the model with no shortages; the demand rate is stabilized after the production stopping time and (b) for the model with shortages; the demand rate is stabilized after the production stopping time or after the time when the inventory level reaches zero or after the production restarting time. In addition, we extend the work of Manna and Chaudhuri (Eur. J. Oper. Res. 171(2):557–566, 2006) assuming a general function of time for the variable part of the demand rate.

An EOQ model with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages

An order level inventory system for deteriorating items has been developed with demand rate as a ramp type function of time. The finite production rate is proportional to the demand rate and deterioration rate is time proportional. The unit production cost is inversely proportional to the demand rate. The model with no shortage case in inventory is first solved. The inventory shortage is discussed next. Results are illustrated with two numerical examples for two models along with its sensitivity.