Time-varying Deterioration Rate Research Articles

Impact of green technology on production inventory model with time-varying deterioration rate

Industries are under increasing pressure to implement eco-friendly practices as the world struggles with the growing issues of environmental sustainability and resource conservation. This study considers a dynamic and time-varying deterioration rate as it investigates the incorporation of green technology into the production inventory model. With an emphasis on implications for cost savings, sustainability, and overall system performance, the study examines the interaction between environmentally friendly production methods and inventory management techniques. Numerical illustration is carried out by using the software MATHEMATICA 12.0. Sensitivity analysis is carried out to show the effect of different parameters on optimal solution.

Optimal ordering policy and preservation technology for deteriorating items with maximum lifetime under a resilient hybrid payment decision

<p style='text-indent:20px;'>This study demonstrates an inventory system with items changing value over time under various realistic environments. It is assumed that the time-varying deterioration rate depending on the maximum lifetime of items and the items exceeding the maximum lifetime are regarded as scarp and no longer serviceable. As a result, the retailer will invest in preservation technology to reduce the reckless deterioration. On the other hand, the retailer receives an upstream advance-cash-credit payment plan from the supplier while offering a downstream cash-credit payment plan to customers to stimulate sales. As above description, we incorporate the relevant phenomena into the proposed inventory model, then the primary objective is to determine the replenishment cycle time and the preservation technology which maximizes the retailer's total profit. Consequently, the contributions of this study have three parts as follows: (1) Addressing the economic (total profit) and technology (preservation technology) impacts simultaneously; (2) The propositions and theorems are derived along with a solution procedure; (3) It is proved that the optimal solution not only exists but also is unique under some conditions. Next, an algorithm is developed which simplifies the search for the sustainable optimal ordering strategies. Numerical examples and a sensitivity analysis are elaborated to validate the mathematical formulation. Findings are summarized and managerial implications are also discussed.</p>

Optimal replenishment, pricing and preservation technology investment policies for non-instantaneous deteriorating items under two-level trade credit policy

<p style='text-indent:20px;'>In the business world, both the supplier and the retailer accept the credit to make their business position strong, because the credit not only strengthens their business relationships but also increases the scale of their profits. In this paper, we consider an inventory model for non-instantaneous deteriorating items with price sensitive demand, time varying deterioration rate under two-level trade credit policy. Besides, to reduce deterioration rate, retailers invest some cost to prevent product degradation/decay, known as preservation technology, is also inserted. Consumption of such items within shelf life prevents to deterioration, which can be achieved by bulk sale. In order to stimulate the selling, trade-credit policy is also considered here. In the sequel, not only the supplier would offer fixed credit period to the retailer, but retailer also adopt the trade credit policy to the customers in order to promote the market competition. The retailer can accumulate revenue and interest after the customer pays for the amount of purchasing cost to the retailer until the end of the trade credit period offered by the supplier. The main objective is to determine the optimal replenishment, pricing and preservation technology investment strategies including whether or not invest in preservation technology and how much to invest in order to maximize the average profit of the system. It is proved that the optimal replenishment policy not only exists but is unique for any given selling price and preservation technology cost. An algorithm is presented to derive the optimal solutions of the model. Numerous theorems and lemmas have been inserted to obtain the optimal solution. Finally, numerical examples and managerial implications are incorporated to validate the proposed model.</p>

Erratum to “An Inventory Model for Deteriorating Items with Generalised Exponential Decreasing Demand, Constant Holding Cost and Time-Varying Deterioration Rate” [American Journal of Operations Research 8 (2018) 1-16

The original online version of this article (Isiyaku Aliyu, Babangida Sani (2018) [18] An Inventory Model for Deteriorating Items with Generalised Exponential Decreasing Demand, Constant Holding Cost and Time-Varying Deterioration Rate. AJOR, 8, 1-16. doi: 10.4236/ajor.2018.81001.) was published as some results data reported mistakenly. The author wishes to correct the errors to:

Optimal replenishment decision for retailers with variable demand for deteriorating products under a trade-credit policy

In this study one obtained the optimal decision of a retailer for the replenishment rate with selling-price and credit-period dependent demand to maximize the profit. A time-varying deterioration rate was considered for those products. A credit-period was offered by the retailer to the end customer to settle the whole payments. The aim of the model was to obtain the maximum profit for the retailer based model. A solution methodology with an algorithm was used to obtain the global optimum profit. An illustrative numerical example was given to test the practical applicability of the model. Numerical study indicated that the profit was at a maximum when the permissible delay-period for payment offered by the suppliers was lies between the permissible delay-time, and the cycle time, offered by the retailer.

A partially backlogged supply chain model for deteriorating items under reverse logistics, imperfect production/remanufacturing and inflation

Reverse logistics increasingly conquered interest in the past decade. It consists of operations related to the reuse of products, such as the collection of products from end users and general processes such as reusing, repairing, and recycling. In this paper, a reverse logistics supply chain inventory model in an inflationary environment is developed. Production and remanufacturing rates are finite and variable. During the production (remanufacturing) process some imperfect quality products are produced (remanufactured), which are reworked after production (remanufacturing) run. Items deteriorate over time with time-varying deterioration rate. Many classical reverse logistics supply chain models are developed with constant demand rate and ignoring the shortages which are not true all the time in practical life. Therefore, in this model, it is assumed that the demand rate of the buyer is a function of on-hand inventory and selling price. Shortages are allowed only for the buyer and partially backordered with a time-dependent backlogging rate. The purpose of this study is to determine the optimal integrated reverse logistics supply chain policy. Finally, numerical examples and sensitivity analysis along with some decision-making implications are provided.

Mathematical modelling for determining the replenishment policy for deteriorating items in an EPQ model with multiple shipments

ABSTRACTThis paper extends an economic production quantity (EPQ) model for deteriorating items when the delivery policy is based on multiple shipments. A continuous inventory policy for satisfying demand has been considered in the classic EPQ model. While in an integrated production–inventory–delivery system, the multi-shipment approach is actually used instead of the continuous issuing policy. On the other hand, the EPQ model has not been developed for deteriorating items with multiple shipments. This paper considers the time-varying deterioration rate and finds optimal replenishment lot size which minimises the long-run average cost function after proving its convexity. Finally, mathematical modelling and analysis are employed for a laboratory kit production system. Then, impact factors which can modify total cost are recognised and optimal replenishment lot size, as well as optimal quantity of each shipment, is found in different situations.

An Inventory Model for Deteriorating Items with Generalised Exponential Decreasing Demand, Constant Holding Cost and Time-Varying Deterioration Rate

In this present paper, an inventory model with a generalised exponential decreasing demand is considered. A numerical example is used to illustrate the application of the model. Sensitivity analysis of the optimal solution with respect to various parameters is carried out to see the effect of parameter changes on the solution.

An EOQ model for deteriorating items with inflation and time value of money considering time-dependent deteriorating rate and delay payments

A finite time horizon inventory problem for a deteriorating item is developed with constant demand and time-varying deterioration rate under inflation and time value of money. Some of the items may deteriorate in the course of time. In this regard, the authors develop an EOQ model for time-varying deterioration rate. Shortages are allowed in each cycle and backlogged them completely. In this model, the fixed credit period is offered by the supplier to the retailer. During the credit period, the retailers are allowed a trade-credit offer by the suppliers to buy more items and earn more by selling their products. The interest on purchasing cost is charged for the delay of payment by the retailers. The objective of the study is to find optimal decision variables and order quantities of the products so that the net present value of total system cost over a finite planning horizon is minimized. Also, the profit function of the model is maximized. Finally, numerical results are presented to analyse the sensitivity of the optimal policies with respect to changes in some parameters of the system.

Optimal inventory model under stock and time dependent demand for time varying deterioration rate with shortages

Effect of deterioration plays a vital role in present environment of market. In this paper, a deterministic inventory model for deteriorating items having stock and time dependent demand under the effect of deterioration has been studied. A two parameter Weibull distribution has been used to represent the deterioration rate. The present model has been solved analytically to minimize the total cost of the system. The necessary and sufficient conditions for the existence and uniqueness of the optimal solutions which could minimize the retailer’s total cost per unit time has been discussed. Some numerical examples have been carried out to illustrate the developed model.

Inventory Models for Fresh Agriculture Products with Time-Varying Deterioration Rate

This paper presents inventory models for fresh agriculture products with time-varying deterioration rate. Due to the particularity of fresh agriculture products, the demand rate is a function that depends on sale price and freshness. The deterioration rate increases with time and is assumed to be a time-varying function. In the models, the inventory cycle may be constant or variable. The optimal solutions of models are discussed for different freshness and the deterioration rate. The results of experiments show that the profit depends on the freshness and deterioration rate of products. With the increasing inventory cycle, the sale price and profit increase at first and then start decreasing. Furthermore, when the inventory cycle is variable, the total profit is a binary function of the sale price and inventory cycle. There exist unique sale price and inventory cycle such that the profit is optimal. The results also show that the optimal sale price and inventory cycle depend on the freshness and the deterioration rate of fresh agriculture products.

Variable deterioration and demand—An inventory model

This paper deals with an inventory model for deteriorating items with inventory dependent demand function. Most of the inventory models are considered with constant rate of deterioration. In this article, we consider time varying deterioration rate. Based on the demand and inventory, the model is considered with three possible cases. We establish the necessary and sufficient conditions for each case to show the existence and uniqueness of the optimal solution. Further, a simple solution algorithm has proposed to obtain the optimal replenishment cycle time and ordering quantity such that the total profit per unit time is maximized. Finally, some numerical examples, sensitivity analysis and graphical representations are provided to illustrate the practical usages of the proposed method.

An improved inventory model with partial backlogging, time varying deterioration and stock-dependent demand

This paper expands an inventory model for deteriorating items with stock-dependent demand. This model provides time varying backlogging rate as well as time varying deterioration rate. The aim of this model is to determine the optimal cycle length of each product such that the expected total cost (holding, shortage, ordering, deterioration and opportunity cost) is minimized. Further, the necessary and sufficient conditions are provided to show the existence and uniqueness of the optimal solution. Lastly, some numerical examples, sensitivity analysis along with graphical representations are shown to illustrate the practical application of the proposed model.

An EOQ model with delay in payments and time varying deterioration rate

This article deals with an EOQ ( Economic Order Quantity) model for finite replenishment rate where demand and deterioration rate are both time-dependent. In this model, the retailers are allowed a trade-credit offer by the suppliers to buy more items with different discount rates on the purchasing costs. During the credit period, the retailers can earn more by selling their products. The interest on purchasing cost is charged for the delay of payment by the retailers. Some of the items may deteriorate in the course of time. In this regard, the author develops an EOQ model for time varying deterioration rate. The profit function of the model is maximized. Finally, a numerical example and graphical illustrations are used to illustrate the model.

Modeling Alzheimer's disease progression using the disease system analysis approach

A novel mechanistic model based on a disease system analysis paradigm was developed to explore the role of homeostatic mechanisms involved in Alzheimer's disease (AD) progression. We used longitudinal AD Assessment Scale-cognitive subscale (ADAS-cog) scores from 926 subjects with AD on stable acetylcholinesterase inhibitor therapy randomized to placebo treatment in two 54-week clinical trials. Alternative mechanistic models were evaluated by assuming that the rate of change of ADAS-cog over time was jointly regulated by a process characterizing the deterioration of ADAS-cog and by a process associated with a compensatory regulatory response. The model based on a time-varying deterioration rate of ADAS-cog performed better than the model based on a time-varying homeostatic control. The covariate analysis indicated that baseline Mini-Mental State Examination score, education, age, and apolipoprotein ɛ4 genotype had a significant effect on the level and shape of the trajectories of the mean model predicted ADAS-cog change from baseline.

Optimal selling price and lotsize with time varying deterioration and partial backlogging

The article deals with an EOQ (economic order quantity) model over an infinite time horizon for perishable items where demand is price dependent and partial backorder is permitted. The rate of deterioration is taken to be time proportional and it is assumed that shortage occurs at starting of the inventory cycle. Based on the partial backlogging and lost sale cases, the author develops the criterion for the optimal solution for the replenishment schedule, and proves the optimal ordering policy is unique. Moreover, the article suggests to new functions regarding price-dependent demand and time varying deterioration rate. Finally, numerical examples are illustrated to test the model in various issues.

On reserve money for an EOQ model in an inflationary environment under supplier credits

We propose to derive a deterministic inventory model for a stock with time-varying deterioration rate with a linear trend in demand over a finite planning horizon in this study. We assume that the supplier offers a credit limit to the retailer during which there is no interest charged. However, the retailer has the reserve capital with him to make the payments at the beginning of the transaction, but he decides to take the benefit of the credit limit. Each cycle has shortages, which have been partially backlogged to suit present day competition in the market. Also, the whole study has been done in an inflationary environment using the Discounted Cash Flow (DCF) approach to impart economic feasibility to the model. Numerical examples have been presented to explain the theory, while sensitivity of the optimal solution of the system has been studied with respect to various system parameters.