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Carbon emission is a significant issue for the current business market and global warming. Nowadays, most countries have focused to reduce the environmental impact of business with durable financial benefits. The purpose of this study is to optimize the entire cost functions with carbon emission and to find the sustainable optimal ordering quantity for retailers.

This paper illustrates a sustainable inventory model having a set of two non-instantaneous substitutable deteriorating items under joint replenishment with carbon emission. In this model demand and deterioration rate are considered as deterministic, constant and triangular fuzzy numbers. The objective is to find the optimal ordering quantity for retailers and to minimize the total cost function per unit time with carbon emission. The model is then solved with the help of Maple software.

This paper presents a solution method and also develop an algorithm to determine the order quantities which optimize the total cost function. A numerical experiment illustrates the improvement in optimal total cost of the inventory model with substitution over without substitution. The graphical results show the convexity of the cost function. Finally, sensitivity analysis is given to get the impact of parameters and validity of the model.

This study considers a set of two non-instantaneous substitutable deteriorating items under joint replenishment with carbon emission. From the literature review, in the authors’ knowledge no researcher has undergone this kind of study.

The purpose of this paper is to review and analyze the perishable inventory models along various dimensions such as its evolution, scope, demand, shelf life, replenishment policy, modeling techniques and research gaps.

In total, 418 relevant and scholarly articles of various researchers and practitioners during 1990-2016 were reviewed. They were critically analyzed along author profile, nature of perishability, research contributions of different countries, publication along time, research methodologies adopted, etc. to draw fruitful conclusions. The future research for perishable inventory modeling was also discussed and suggested.

There are plethora of perishable inventory studies with divergent objectives and scope. Besides demand and perishable rate in perishable inventory models, other factors such as price discount, allow shortage or not, inflation, time value of money and so on were found to be combined to make it more realistic. The modeling of inventory systems with two or more perishable items is limited. The multi-echelon inventory with centralized decision and information sharing is acquiring lot of importance because of supply chain integration in the competitive market.

Only peer-reviewed journals and conference papers were analyzed, whereas the manuals, reports, white papers and blood-related articles were excluded. Clustering of literature revealed that future studies should focus on stochastic modeling.

Stress had been laid to identify future research gaps that will help in developing realistic models. The present work will form a guideline to choose the appropriate methodology(s) and mathematical technique(s) in different situations with perishable inventory.

The current review analyzed 419 research papers available in the literature on perishable inventory modeling to summarize its current status and identify its potential future directions. Also the future research gaps were uncovered. This systemic review is strongly felt to fill the gap in the perishable inventory literature and help in formulating effective strategies to design of an effective and efficient inventory management system for perishable items.

With the pressing need for environmental conservation, regulatory authorities are actively looking for measures to prevent global warming. In the proposed inventory model for deteriorating items, demand is dependent on the selling price and green technology investment (or carbon reduction investment) for the green product (GP), as well as an investment in price-based preservation technology to slow down the pace of deterioration. Furthermore, emission reduction measures are put in place to reduce carbon emissions (CEs).

The current study executed a thorough literature review to determine how to improve supply chain management performance. Furthermore, assumptions are made to fill research gaps, and a mathematical model is created to address the problem mentioned above. To collect the data, the available inventory literature was reviewed. Additionally, numerical illustrations and sensitivity analyses are presented to emphasize the model's robustness.

The research indicates that it is more prudent to invest in preservation technology based on its selling price in order to control the rate of deterioration. In addition, the proposed model facilitates the management of deteriorated waste through salvage trading and emission reduction investment. The findings validate sustainable practices with a 20.86% increase in profit and a 21.4% decrease in CEs, thereby signifying environmental and economic benefits.

The proposed model enhances understanding of the impact of investments in price-based preservation technology and carbon reduction efforts on consumer perceptions of their intention to purchase GPs. Moreover, the study provides valuable insights by identifying important recommendations for policymakers regarding areas that require further investigation. This guideline can help identify both current and unexplored gaps, enabling researchers to direct future research efforts toward producing new products.

The purpose of this paper is to propose a model for relief inventory ordering considering declining demand and realized shortage (RS) costs. This study is motivated by the overflow of unsolicited items in affected areas, which hinder the urgent relief flow.

This study proposes a dynamic programing model reflecting the change of demand and urgency during relief operations. A solution algorithm for finding a replenishing point of relief is also introduced here.

Relief ordering policy based on the RS cost increases the service level (in terms of time). The service level is dependent on the deterioration rate.

Deterioration is not applicable for all relief items. Therefore, the proposed model is applicable for certain relief items. Additionally, computation of temporal urgency is not included.

The study outcomes can be invaluable for resource planning. The model shows a gradual decrease of ordering quantity and a gradual increase of cycle length. This observation can be utilized for resource (e.g. truck) planning and fewer truck can be used in later stages of relief operations.

This study introduces temporal urgency for disaster logistics (DL) and proposes a relief inventory policy by incorporating temporal urgency. This model highlights the importance of considering declining demand for DL.

The 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.

In 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.

Finally, 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.

This 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.

This paper aims to simultaneously consider an inventory model with price and advertisement dependent demand, non-instantaneous deterioration rate with preservation technology investment, partially backlogged shortages and trade credit.

This model considered a non-instantaneous deterioration, which starts after a certain storage period with a constant rate. The proposed model focused on two things. The first one is to reduce the deterioration rate by preservation technology investment, and the second one is using an appropriate trade credit period to maximize the total profit. The classical optimization technique is used to solve the problem.

The authors found that trade credit, advertising cost, preservation technology affect the total cost and selling price is one of the most important decision variables affecting the model.

This study provides a reference for a manufacturer and a retailer on making inventory decisions under different pricing, advertisement expense, preservation technology investment and credit strategies. Four cases are presented to illustrate the inventory model. Sensitivity analyses are performed to gain managerial insights for decision-making.

The study simultaneously considers a non-instantaneous deterioration inventory model, trade-credit, and preservation technology and advertisement policy. From our literature search, no researcher has undergone this type of study.

This paper deals with finding economic order quantity, number of orders to be placed and/or the time to place each order for four different special types of problems that may be encountered in practice. The first problem (Problem 1a) assumes a fixed planning horizon and a perishable product such as Christmas trees or fashion merchandise whose value deteriorates as the item gets aged. Under constant demand assumption, solution for this type of problem is worked out by capturing the deterioration in value by increasing holding cost. The second problem (Problem 2) has the same assumption as the first, except that the demand is assumed to increase as we move forward in time. The third problem (Problem 2a) is a restricted version of the second, which allows a specific number of integer orders during the planning horizon. The fourth problem (Problem 3) allows the ordering cost to increase as time progresses. All formulae derived can be easily applied to find numerical answers. The answers may have to be adjusted to reflect container size, minimum order quantity and any other restriction not modeled, or to take into account any violation of the model assumptions.

This paper aims to consider a sustainable inventory model with price dependent demand, non-instantaneous deterioration rate, discount facility, partially backlogged shortages and advance and delay in payments for a two-warehouse system.

This model considered a non-instantaneous deterioration, which starts after a certain period with a constant rate. The deterioration rate in the rented warehouse is more compared to own warehouse. The proposed model focused on two things. The first one is to the benefits of the advance payments strategy and delayed payment for the retailer and supplier, where the two-warehouse system is available and the second one is using an appropriate discount facility on no of the installment to maximize the total profit. The classical optimization technique is used to solve the problem.

The combination of trade-credits and advance payments is initiated to provide more benefits to the retailer. The findings prove that advance payments, which are received from the retailer to the supplier are beneficial for the supplier, who can influence the demand increase because of higher lower selling prices. Decreasing the selling price is used as a catalyst to increase demand. It also extends the discount concept of Khan et al. (2019, 2019b).

This model is limited by the fact that it does not consider variable deterioration. Therefore, the proposed inventory model could be extended by considering variable deterioration, as well as fully backlogged shortages and time-dependent demand function.

The study simultaneously considers a non-instantaneous deterioration inventory model, advance-payment, trade-credit for a sustainable two-warehouse inventory system. From the literature search to the best of knowledge no researcher has undergone this sort of study.

Integrated decision of pricing and inventory control for a deteriorating product is known as a good practice in revenue management discipline. The purpose of this paper is to formulate the problem of joint pricing and inventory decision in a manufacturer–retailer supply chain with deteriorating items and backlogging. Furthermore, the other purpose is to develop an efficient algorithm to obtain the equilibrium solution.

In this study, a manufacturer–retailer supply chain of a deteriorating product is considered. The retailer aims to maximize his profit, for which he jointly determines the retail price and replenishment cycle. In addition, the manufacturer should decide on the wholesale price to maximize her profit. Considering the problem as a manufacturer-Stackelberg game, the equilibrium solution is formulated and analyzed for both the manufacturer and the retailer. Moreover, two different procedures are developed to obtain the equilibrium solution. The first procedure is an exact procedure for the Taylor-approximated model and the second is a simulated annealing (SA)-embedded algorithm for the actual model.

It is found that Taylor-approximated procedure is more accurate than SA-embedded procedure. However, the latter is more time-efficient. Moreover, it is observed that the obtained solution is highly sensitive to demand parameters, while it is not the case for the cost parameters.

The paper models a real industrial problem, and its results could be used in analyzing any manufacturer–retailer supply chain with deteriorating items. Among others, the fruit and vegetable supply chains are more likely to have a similar setting, and this study’s results are applicable for such chains in food industry.

External 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.

In 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.

An 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.

This 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.