Non-instantaneous Deterioration 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

A two-phase production inventory model for imperfect quality items with multivariate demand, upstream and downstream credit period offers under a carbon tax, and green subsidy

Generating customer-friendly products is a big task nowadays. Green products are famous all over the world now. In quite few manufacturing processes, carbon emissions become an unavoidable fact. To reduce emissions, the government enacted enormous rules and regulations. This developed model consists of a supply chain with two phase production containing defective products and rework through the same manufacturing system, where the product deterioration is considered after production and rework (i.e. where the deterioration starts when the product is out for sale), as three cases: (1) no deterioration, (2) instantaneous deterioration and (3) non-instantaneous deterioration. Demand function is selling price, green product price, advertisement and credit period dependent for first two cases and for case 3, the market scale of the demand is exponentially increasing considering uncertainty. Supplier offers a full credit period offer to the retailer and the retailer gives a partial credit period offer to his customer. Various methods are implemented to reduce carbon emissions during various production processes, and we have implemented preservation technology to reduce emissions even with a carbon tax policy involved. With government subsidies, the greenness of the product is considered to make it more environmental friendly. Numerical examples and sensitivity analysis are carried out to verify the results of the developed model.

Optimal strategy on inventory model under permissible delay in payments and return policy for deteriorating items with shortages

In this model, the manufacturer offers a trade credit policy to the retailer. Demand depends upon selling price and time for non-instantaneous deterioration items. The retailer offers the customer a returns policy. Customers can return the product to the retailer if the product is unsatisfactory for the customer. The retailer does not ultimately return the amount to its customer for the returned product. The manufacturer offers the retailer a trade credit policy. The retailer resale the returned products at the same selling price. A partially backlogged shortage is permitted and its rate is thought to depend on how long it takes for the following lot to arrive after a lot has been replenished. The main objective is to increase the retailers' overall profit by determining the optimal order quantity, optimal selling price, and optimal replenishment cycle. An EOQ is framed for analyzing the sample, which can obtain the optimal solution.

Impact of waste management and regulatory mechanism on sustainable EOQ model with controllable non-instantaneous deterioration and trade credit-and carbon-sensitive demand

Impact of waste management and regulatory mechanism on sustainable EOQ model with controllable non-instantaneous deterioration and trade credit-and carbon-sensitive demand

A sustainable inventory model for deteriorating items with power demand and full backlogging under a carbon emission tax

Environmental degradation due to carbon emissions occurring in the production, storage and marketing of products has increased notably in recent years. To maintain a sustainable development, it is necessary to penalize commercial activities that generate high carbon emissions. This paper develops and analyzes a sustainable inventory system for a product whose demand follows a power pattern with respect to time. It is considered that the stock items have an estimated life period, after which a percentage of these items begins to deteriorate over time. The inventory system allows shortages which are fully backordered. Several sources of carbon emissions are considered in this article: transportation, stock holding and deterioration. The main objective is to determine the sustainable inventory policy that maximizes the benefit per unit of time, which is given by the difference between the income obtained from sales and the costs associated with inventory management and carbon emissions. Two scenarios are analyzed. In the first, the optimal inventory policy for a system without deterioration is derived. In the second, an algorithm to determine the optimal policy for an inventory system with non-instantaneous deterioration is proposed. Thus, our findings serve to determine the best inventory policy that helps decision-makers to obtain the lot size and the reorder point that maximize the profit per unit time under carbon emission taxes in transporting, storage and deteriorating of items. Some numerical examples are solved in order to illustrate the theoretical results previously obtained. Finally, a sensitive analysis of the optimal inventory policy with respect to some input parameters of the system is presented and interesting managerial insights from the numerical examples are proposed.

Optimal inventory policies for finite horizon deterministic inventory models for non-instantaneous deteriorating items and permissible-delay in payment

This paper is concerned with the search for the optimal inventory policy for a finite horizon inventory model with time-varying demand, non-instantaneous deteriorating items, and permissible delay in payment. The optimal inventory policy consists of the determination of the number and timing of replenishment schedules that minimise some total inventory costs. The search for such policy is formulated as a mixed integer nonlinear programming problem (MINLP). It turns out that the non-instantaneous deterioration phenomenon coupled with permissible delay in payment introduce non-smoothness in the objective function of the MINLP. This leads to failure of direct applications of known solution methods to the MINLP. To circumvent this problem, a methodology is proposed for solving fully the MINLP problem. It is shown, through careful mathematical analysis, that earlier results on similar problems can be adapted to solve this problem. Conditions under which the solution of the MINLP is unique are identified. Moreover, convexity with respect to the number of replenishment orders is established. This makes the search for the optimal inventory policy handy. Numerical experiments are also conducted to test the applicability, to identify the key elements and to provide managerial insights to the model.

Sustainable inventory model with environmental impact for non-instantaneous deteriorating items with composite demand

Global warming and climate change become a sensitive issue worldwide, and many countries try to control the CO2 emissions by investigating in many projects. This study proposes a sustainable inventory model to reduce carbon emission. It is generally assumed that demand is increasing at starting of an inventory level and decreasing at ending for a particular newly launched product. In this situation, demand is usually represented by Normal distribution or imprecise fuzzy demand. However, in reality, those assumptions do not always hold. In most of the inventory models, it is seen that demand is a linearly increasing function of time before starting deterioration; then, the demand decreases inversely proportional to the deterioration rate after starting the deterioration. To describe the possible situations more clearly, we introduce here a new type of demand, called as composite demand. Most of the products have a fixed life span for maintaining the quality in original condition which is known as non-instantaneous deterioration. Therefore, we design an inventory model for non-instantaneous deteriorating items with composite demand function. The deterioration rate is assumed to follow an exponential distribution; the holding cost is considered as time dependent. The model is formulated based on retailer’s perspective and, thereafter, the total cost for the retailer is calculated. Numerical examples are provided for better understanding of this model. The results show that the total profit for non-instantaneous deteriorating items is higher than for instantaneously deteriorating items. A sensitivity analysis is conducted based on the important parameters. Finally, the paper ends with conclusions and an outlook to future research.

Optimal Pricing Policies with an Allowable Discount for Perishable Items under Time-Dependent Sales Price and Trade Credit

Trade credit is generally used by businesses to obtain external funds. This article demonstrates an inventory system from the retailer’s point of view in which (1) the influence of trade credit on expanding small businesses and their consumers is the focus of this research, and (2) the retailer’s on-hand inventory follows the non-instantaneous deterioration. (3) To maximize profit, the demand is disclosed, which is based on not just the sales price, but also on cumulative demand, which indicates saturation and diffusion. (4) The product’s initial price and the permitted discount rate at the time of deterioration are considered to be time-dependent functions of the sales price. In the absence of deterioration, the item is sold at a constant rate, and whenever deterioration occurs, the sales price is assumed to be an exponential function of the discount variable. The main aim is to optimize the total profit of the retailer in terms of cycle time and sales price. The traditional algorithm of optimization is used to address the optimization problem. Finally, the theoretical results are validated by solving three numerical illustrations and conducting a sensitivity analysis of the main factors resulting from the following managerial implications: (1) credit period provides the maximum profit margin of any financing method, and (2) an increase in the initial rate of demand raises sales price while increasing overall profit significantly.

Optimal policies for finite horizon model with time-varying demand rate, non-instantaneous deterioration and backlogging

This paper is concerned with the problem of finding an optimal replenishment policy for a finite planning horizon inventory model with time-varying demand, non-instantaneous deteriorating items and backlogging. This is formulated as a problem of solving some mixed integer non-linear program whose optimal solution delivers the frequency of orders as well as the timing of orders. The phenomena of non-instantaneous deterioration introduce a non-smoothness in the objective function which makes direct application of existing results, in the literature, not possible to the present model. A complete mathematical analysis of the problem is undertaken to overcome the non-smoothness of the objective and derive the optimal inventory policy. Uniqueness of the policy is shown under some technical conditions. Numerical results are presented for illustration.

Inventory management with hybrid cash-advance payment for time-dependent demand, time-varying holding cost and non-instantaneous deterioration under backordering and non-terminating situations

During the current pandemic period, the number of online transactions to purchase products through a mixed cash and prepayment agreement has increased significantly. Under this agreement, the buyer pays off a predefined percentage of the purchase price in advance, and the rest of the percentage is accomplished through the cash-on-delivery method. Adopting a practical scenario where the buyer has a storeroom with limited capacity, two sustainable inventory procedures for perishable items are developed, viz. (i) the inventory scheme with allowable shortages and fractional backlog, and (ii) the inventory scheme without ending. In both the schemes, not only the demand function but also the decay rate reveal an upward trend against storage time. However, the deterioration commencing moment is not instant but after a specific time interval from the products’ storage moment. The cost of storing items is adopted as a linear function of storing time as the decay rate shows an ascending trend against storing time. A salient criterion is developed to examine when the non-ending situation with salvage values is more economical for the industry manager than the zero ending situation with the regular selling price. Finally, several decision-making findings are presented after completing four numerical examples along with a real-life case study for the validation of the inventory schemes.

An Inventory Model for Non-Instantaneously Deteriorating Items with Nonlinear Stock-Dependent Demand, Hybrid Payment Scheme and Partially Backlogged Shortages

This research work presents an inventory model that involves non-instantaneous deterioration, nonlinear stock-dependent demand, and partially backlogged shortages by considering the length of the waiting time under a hybrid prepayment and cash-on-delivery scheme. The corresponding inventory problem is formulated as a nonlinear constraint optimization problem. The theoretical results for the unique optimal solution are presented, and eight special cases are also identified. Moreover, a salient theoretical result is provided: a certain condition where the optimal inventory policy may or may not involve deterioration. Finally, two numerical examples are provided using a sensitivity analysis to show the validity range of the inventory parameters.

An inventory model displayed stock and price dependent demand under non-instantaneous deterioration with inflation for partially backlogged shortages.

In this paper we have considered stock and price dependent demand and developed a non-instantaneous economic order quantity model for decaying goods under inflation. Shortages are allowed in this model and they are partially backlogged. Stock and price constantly plays an essential part and influence the demand rate. Demand function is depending on price and stock. Deterioration of the growing inventory can be understood as when stock remains for a longer period in a vendor's home following that deterioration will begin with price and stock dependent demand. It is implicit that the deterioration rate arises as soon as items are received into inventory. Aside from deterioration, the effect of inflation is another important factor of inventory. General increase in price of goods is reflected due to decrease in the purchase power of money is inflation. The plan of this representation is to establish the best solution including the estimated Total cost (Holding cost, Shortage cost, Ordering cost, Deterioration cost, Purchase cost, partially backlog cost) diminished. Additional, compulsory and satisfactory circumstances are afforded to illustrate the survival and exclusivity of the best solution. Here we have solved this problem by using Wolfram Mathematica 12.0 software. Lastly, numerical exemplifications, perceptivity study all along graphical demonstrations are revealed to exemplify the realistic purpose of the projected model.

Optimal pricing model for non-instantaneous deterioration items with price and freshness sensitive demand under the e-commerce environment in China

PurposeThe purpose of this paper is to focus on determining the optimal sales price for non-instantaneous deterioration items according to consideration of freshness and demand.Design/methodology/approachIn this model, the authors have described the demand function which is dependent on price as well time. The products that the deterioration is considered as non-instantaneous have a determinate shelf life, and their demand rate will decrease over time after the beginning of the selling period. This paper depicts that the total profit of non-instantaneous deterioration items using the dynamic pricing strategy is higher than that using fixed pricing strategy.FindingsFinally, to illustrate and validate the model, the authors have used some numerical examples. A new freshness function and the model to study pricing policy are developed as well applied to solve managerial decision problems.Originality/valueThis paper complements the lack of the existing theoretical research of pricing for non-instantaneous deterioration items under an e-commerce environment. A new freshness function and the model to study pricing policy are developed as well applied to solve managerial decision problems.

An EOQ Model of Selling-Price-Dependent Demand for Non-Instantaneous Deteriorating Items during the Pandemic COVID-19

A pricing factor plays a dominant role in consumer behavior in most countries affected by the COVID19 pandemic. People have lost their job while others renegotiated for low-paying jobs during this pandemic. Thus, this article aims to develop a viable model to consider various aspects of the COVID19 pandemic. Here, we develop an optimal ordering quantity inventory model of deteriorating items, which are still in demand depending upon the selling price of the product. The items are assumed to be non-instantaneous deteriorating. The shortage is allowed in lead time and is partially backlogged. A solution procedure is presented to determine an optimal cycle, order quantity, and total average cost. A realistic numerical example is given to validate the proposed model by changing different systems of parameters, where sensitivity analysis has been carried out. The effectiveness of the system has been observed through graphical representation. HIGHLIGHTS The study considers the inventory model for non-instantaneous deteriorating items. Selling price dependent demand is incorporated. The shortage is allowed in lead time and is partially backlogged. Theoretical results have been formed to characterize the optimal solutions. The effect of key parameters is studies rigorously. GRAPHICAL ABSTRACT

A sustainable inventory model with controllable carbon emissions in green-warehouse farms

Global warming has become a sensitive issue, and many countries are trying to control CO2 emissions by investing in many projects and promoting green industrial practices. This study proposes a sustainable price-reliant demand inventory model with controllable carbon emissions to reduce the CO2 emissions from farm warehousing activity. This study extends previous research that has proposed a sustainable inventory system with greenhouse facilities by controlling carbon emissions through green investment. This study involves an investment in energy-efficient green technology in a two-warehouse inventory system to curb carbon emissions during the transportation of products from the owned to the rented warehouse and also to the final customers. Two warehouses are frequently used in practice to avoid stock-out situations and make the business more profitable. Case 1 represents the model with allowable shortages, and Case 2 represents the model without shortages. Pricing strategies and a hybrid payment scheme are applied throughout this study to make the business more profitable as well as to entice new customers. The retailer has to prepay some portion of the purchasing cost, with the payment scheme requiring multiple installments. Non-instantaneous deterioration is considered in this study to show the lifetime of product freshness in the presence of a constant backorder. A nonlinear model is proposed, and a solution algorithm is suggested. A real case study is introduced, which provides an illustration of the proposed model. The examples are solved and are followed by a sensitivity analysis that reveals the validity of the model, and conclusions are presented.

A sustainable inventory model with controllable carbon emissions, deterioration and advance payments

This study involves green technology investment to control the carbon emission from greenhouse operation and to reduce product deteriorations by applying preservation technology due to carbon emission concerns along with the preservation technology strategy is still rare in the literatures. Emissions from different industries and vehicles are the prime reason for ecological imbalance and environmental issues. Firms need to comply with ecological and social obligations to sustain operational activities. Greenhouse product retailers may utilize preservation technology to extend the product lifecycle to reduce environmental impacts. However, other logistics operations may emit CO2 into the air. This study is contributed in twofolds. (1) this study applies preservation technology how to reduce product deteriorations; and (2) this tudy proposes suitable green technology investment and preservation technology to reduce both carbon emission and product deterioration. The proposed model considers non-instantaneous deterioration, advance payments and partial backorder strategies together. The results and sensitivity analysis demonstrate the positive impacts of controllable carbon emission and deterioration on the total inventory model profit. The cases illustrate 12% increased in the total profit from green technology investment and 23% increased from both preservation and green technology investments.

Optimizing multi-supplier multi-item joint replenishment problem for non-instantaneous deteriorating items with quantity discounts

This paper deals with a new joint replenishment problem, in which a number of non-instantaneous deteriorating items are replenished from several suppliers under different quantity discounts schemes. Involving both joint replenishment decisions and supplier selection decisions makes the problem to be NP-hard. In particular, the consideration of non-instantaneous deterioration makes it more challenging to handle. We first construct a mathematical model integrated with a supplier selection system and a joint replenishment program for non-instantaneous deteriorating items to formulate the problem. Then we develop a novel swarm intelligence optimization algorithm, the Improved Moth-flame Optimization (IMFO) algorithm, to solve the proposed model. The results of several numerical experiments analyses reveal that the IMFO algorithm is an effective algorithm for solving the proposed model in terms of solution quality and searching stableness. Finally, we conduct extensive experiments to further investigate the performance of the proposed model.

COMPARISON OF INVENTORY MODELS UNDER NON-INSTANTANEOUS DETERIORATION RATE WITH PROBABILISTIC DEMAND AND SHORTAGES

In this research, present an inventory model with non-instantaneous deterioration rate is consider i.e. depend on time. The purpose of this paper is to deliver a comparative study of diverse probabilistic environment, where demand is considered as a random variable follows probabilistic distributions. Shortages are allowed. The anticipated model is conveyed to highest profit of the formation. Mathematical analysis is carried out at the end to validate models. A parametric analysis is accomplished to explore the impact of key parameters.

Impact of Waste Management and Regulatory Mechanism on Sustainable EOQ Model with Controllable Non-Instantaneous Deterioration and Trade Credit-and Carbon-Sensitive Demand

Impact of Waste Management and Regulatory Mechanism on Sustainable EOQ Model with Controllable Non-Instantaneous Deterioration and Trade Credit-and Carbon-Sensitive Demand

A non-instantaneous inventory model of agricultural products considering deteriorating impacts and pricing policies

PurposeExternal factors such as improper handling, extreme weather and insect attacks affect product quality. It is most obvious in fruit products which have a high deterioration rate. Moreover, decaying fruits will increase the deteriorating of other good ones. The purpose of this study is to derive the optimal pricing and replenishment decisions for agricultural products considering the effect of external factors that induce deterioration.Design/methodology/approachIn this paper, the study investigates ways to reduce the product deterioration rate by separating the near defective items from the other good products and accelerating the quick sales of the near defective items at a discounted price. The objective is to maximize the total profit by optimizing the selling price and the replenishment cycles. Two scenarios are investigated. In the first scenario, the retailer offers a selling price discount for near defective products to stimulate customer demand. In the second scenario, the retailer does not offer such discounts.FindingsAn algorithm to solve the model is derived. Further, numerical examples are developed to compare the total profit for the two scenarios. Theoretical derivations and graphical results show the concavity of the profit function. Finally, the sensitivity analysis shows that the total profit of the discount model is higher.Originality/valueThis study contributes to a new pricing and inventory decision model. The research provides insights to retailers on making optimal pricing and replenishment decisions for non-instantaneous deterioration items, as well as reducing the external factors that influence higher deterioration rate through separating good products from the near defective ones which are sold at a discount to induce the sale.