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• deposit-refund system for the circulation of RTIs (Returnable transport Items) to maximize supply chain profitability. • effects of RTI-related parameters to determine optimal policies under different retail price structures are investigated. • results lead to important implications for the design of deposit-refund systems for RTIs. While the use of Returnable Transport Items (RTI) is a common practice in supply chains committed to sustainability. An efficient RTI circulation mechanism must be implemented to ensure the profitability of the approach. Within this context, this paper presents a deposit-refund system (DRS) designed for RTI circulation to maximize supply chain profitability. The profit optimization analysis considered three scenarios: the vendor's profit, there tailer's profit, and the overall system profit. Tailored solution strategies are developed for each case, considering retail price components, and leading to the identification of the optimal deposit amount required to maximize RTI circulation. We further examinehow the retail price affects the profits of supply chain actors relative to the RTI return rate and studystudy how changes in return rates influence the profit patterns of supply chain actors. The results are scrutinized via several sensitivity analyses, leading to important implications for the design of deposit-refund systems for RTI. We for example find that the vendor's wholesale price has a significant effect in establishing the decision-maker's optimal policy in designing a DRS for RTI circulation. In other words, the wholesale price is a key component in assessing the economic viability and determining the deposit amount for RTI. Moreover, through a couple of hypothetical, butrealistic cases of RTI applications considering specific parameter settings, we shown that the vendor's position can be either significant or insignificant dependong on the difference between the value of the RTI and that of the goods it holds. [ABSTRACT FROM AUTHOR]

Generally, the transportation of cargo plays a vital role in effective supply chain management. For the safe transportation of the goods, the Returnable Containers (RCs) are provided by the container management organization to the consignee as rental basis. Unfortunately, some of the RCs are returned as delay in time for some situations. This study explores a situation of container management organization that unexpected delay of empty containers and then suggests a restoring strategy for shortfall units. As a strategy of restoring the shortfall units, this research considers the leasing option instead of buying the new RCs. This paper examines the container inventory model with the consideration of the delayed return of containers under the fuzzy arena. Because the container's return rate is unpredictable and uncertain, the container inventory model is formulating under fuzzy environment. This research describes a container inventory model with price-sensitive demand. In this model, the container return rate as well as the proportion of repairable from received RCs as Triangular Fuzzy Numbers (TFNs). The optimal duration of inspection of the container and the optimal duration of the lease of an RC are obtained. The expected total cost using the fuzzy return rate and the fuzzy proportion of repairable RCs is computed. The container inventory model under fuzzy arena is proposed to attain the approximate outcome for the unpredictable and uncertain parameters. The impact of the fuzzy proportion of retuned RCs, fuzzy reparable from received RCs, and the changes in some parameters on optimal solutions are performed in the sensitivity analysis. [ABSTRACT FROM AUTHOR]

Estimating market demand for a product is essential to business growth; yet, it is exceedingly difficult. This article considers various demand patterns for a single product in a three-echelon supply chain where a single supplier, a single manufacturer and a single retailer are involved. A robust inspection process is considered at the manufacturer's end to deliver a high-quality product to the retailer. The backorder strategy is incorporated to enhance the company's trust and reputation among consumers. The major idea of this research is to analyze the nature of the product's demand in three distinct situations, as well as the benefits of implementing the backorder technique. Three cases are analyzed on the basis of different demand patterns, in which the demand rate is assumed to be constant (i.e., deterministic), price-dependent and fuzzy in the first, second and third cases, respectively. To verify this model, numerical examples are tested independently with identical information for each case and owing to the complexity of the objective function; a genetic algorithm is employed to obtain the best solution. Finally, sensitivity analysis, managerial insights and conclusions, including the future directions, are provided. [ABSTRACT FROM AUTHOR]

Since pricing is recognized as one of the most important tools for profit optimization, price competition is one of the major issues facing companies. Determining the appropriate inventory control policy and optimal selling price of various products is a major subject of scientific and industrial research in recent years. On the other hand, today, some of the products on the market have the potential to become obsolete, which means that their demand is reduced at once with the development of new technology. Therefore, determining the optimal price and inventory policies for these types of products is very crucial. In this research, an inventory control model for a retailer is formulated to optimize the inventory and pricing decisions for profit maximization simultaneously. According to the problem assumptions, demand is price-dependent, the time that product becomes obsolete has an exponential distribution, the type of product obsolescence is also sudden, and the retailer determines the optimum price and order quantity of replenishment. The proposed model has a nonlinear profit function, in which the partial derivatives of the objective function are used to reach the optimal value. Finally, the effects of various parameters such as the speed of obsolescence, the holding cost of each item unit, the cost of selling obsolete items, and the purchasing price were studied on the total profit. For this purpose, a numerical example is solved along with a sensitivity analysis to evaluate the validity of the model and investigate the effect of parameters on the optimal solution. The key achievement of this study was the development of a new model and providing a solution to determine the optimal values of product sales price and retailer order quantity with maximum profit. [ABSTRACT FROM AUTHOR]

The process of deterioration may not start immediately after the consignment reaches the go down; there generally occurs a delay. In certain cases, deterioration might begin after a certain period which may further prolong due to the introduction of better methods of inventory management. To take into cognizance of these situations, in contrast to the ordinary assumption in the existing models, we have considered that the decay in owned warehouse begins earlier than that in case of rented warehouse as the latter always provides for better inventory management and facilities. Applying these phenomena, a two-storage inventory model has been formulated with advance payment under three different situations according to different possibilities of starting times of deterioration in both warehouses. In this model, demand depends upon the selling price wherein shortages are considered partially with fixed backlogging rate. Analyzing and investigating the proposed problem, three different optimization problems are formulated and the optimality of these problems is proved theoretically. To solve the model, an algorithm is proposed. Then, to illustrate the model numerically, an example is considered and solved. Finally, post optimality is performed in order to investigate the effects of changes of different system parameters. [ABSTRACT FROM AUTHOR]

This study develops an operational policy for a three-echelon supply chain. A mathematical programming model is proposed to maximize the combined profit of the suppliers, manufacturers, and distributors. The model is developed under the supply chain management paradigm, which highlights the cooperation of all the nodes along the supply chain to improve performance criteria like total profit. We take into account the deteriorating nature of raw materials and final products. The proposed model was then applied to a real-world case of an Iranian supply chain active in the detergent production industry using its historical data for parameters. The model was solved using GAMS. Results indicate that the integrated approach was able to increase the supply chain's total profit by 15%. Sensitivity analysis also showed that variable costs of final products are high, leaving a shallow margin. Other managerial insights are also drawn from results. [ABSTRACT FROM AUTHOR]

• Buyer invests in the vendor's process to improve its competitive market position. • Develops an EOQ model with price dependent demand, analogous to head flow. • A faster learning rate than competitors ensures a prolonged profitability. • Improvements beyond learning-by-doing could be required for firms survivability. The economic order quantity model and its variants are the oldest reported scientific inventory models in the literature. They are mathematically simple to use and understand. This characteristic contributed to their popularity. However, they have limitations that restrict their application in practice. Researchers have extended those models by relaxing some of their restrictive assumptions. One of the main limitations of the EOQ model is the estimation of its cost parameters, such as setup and holding costs, which include some hidden (or difficult to estimate) components. Emerging research proposes using the second law of thermodynamics when to measure the hidden (entropy) costs of inventory systems. Another research stream focuses on learning-by-doing, which reduces the unit cost of a product, thus reducing its price and enhancing a firm's competitiveness. This paper assumes that a buyer receives a shipment from its vendor following the EOQ model. The buyer invests in the vendor's process to accelerate learning (mainly workers training, among other things). The buyer's unit purchase cost reduces because of learning at the vendor's side. The buyer's competitors also learn, increasing competitiveness. For this purpose, we develop an EOQ model where price-dependent demand is analogous to a heat transfer equation, which is used to determine the entropy cost. It accounts for improvement by learning as a result of the buyer's investment to compete in a market. The implementation and management of improvement programs are not usually smooth, resulting in disorder quantified by an entropy cost function. The developed EOQ model is investigated with and without entropy costs. Numerical results representing different scenarios are provided to illustrate the behavior of the models and identify the factors affecting the decision variables and, subsequently, the buyer's profitability. The results showed that in a competitive market, the buyer has to maintain a learning rate faster than those of its competitors to ensure a prolonged, but indefinite, profitability. The results also showed that investment in learning is meaningful when the competition is fierce. [ABSTRACT FROM AUTHOR]

In this paper, we have considered an EOQ inventory model with a price-dependent demand and time varying holding cost in fuzzy environments by employing trapezoidal fuzzy numbers. A fully-fuzzy inventory model is developed where the input parameters and decision variables are fuzzified. For this fuzzy model, an expected value method of defuzzification is employed to find the estimate of the profit function in the fuzzy sense. In addition, a rigorous methodology is constructed to examined for the optimal solution of fully-fuzzy inventory model. The optimal policy for the developed model is determined using the proposed algorithm after defuzzification of the profit function. Finally, a numerical example is provided in order to determine the sensitiveness in the decision variables with respect to fuzziness in the components. [ABSTRACT FROM AUTHOR]

This paper presents a two-period supply chain model which is comprised of one manufacturer and one retailer who are involved in trading a single product. The demand rate in each period is dependent on the selling prices of the current period and the previous period. We assume that the manufacturer acts as the Stackelberg leader and declares wholesale price(s) to the retailer who follows the manufacturer’s decision and sets his selling prices for two consecutive periods. The manufacturer adopts one of the two pricing options: (1) setting the same wholesale price to both the selling periods (2) setting different wholesale prices to two different selling periods. Based on these pricing options, we develop four decision strategies of the manufacturer and the retailer and compare them. For a numerical example, we study the effects of these decision strategies on the optimal results of the supply chain. Further, we graphically analyze under what circumstances a particular decision strategy plays a dominant role. [ABSTRACT FROM AUTHOR]

In this paper, we study a two-echelon supply chain inventory system with a single manufacturer and a single buyer, considering price-dependent demand and variable lead time. Lead time can be reduced by added crashing cost. We first assume that the lead time demand follows a normal probability distribution and then consider the case where it is distribution free. We develop both the centralized and decentralized models and derive the optimal solutions by using profit maximization criterion. Feasibility and efficiency of the proposed models are justified through two numerical examples. We numerically investigate how the optimal decisions are affected by changes in various model-parameters. From numerical study, we observe that even though the lead time reduction diminishes the retailer's selling price, it enhances the system profit significantly. [ABSTRACT FROM AUTHOR]

The paper considers a two-echelon supply chain inventory model with one manufacturer and multiple buyers in which each buyer’s demand is dependent on the selling price of the product. The manufacturer’s lead time is composed of several components and each component can be reduced by an additional crashing cost. We develop the proposed model assuming that the lead time demand follows a normal distribution or it is distribution free. The optimal decisions are obtained by maximizing the total expected profit of the supply chain. It is observed from numerical study that the lead time reduction has minor effect on the selling price of the product, but it enhances the profit of the supply chain system. [ABSTRACT FROM AUTHOR]

In the current global market, organizations use many promotional tools in order to increase their sales. One such tool is permissible delay in payments, i.e., the buyer does not have to pay for the goods purchased immediately rather can defer the payment for a prescribed period given by the supplier. This phenomenon motivates the retailer/buyer to order a large inventory lot so as to take full benefit of credit period. But the well decorated showroom (OW) with modern facilities has a limited storage capacity. Thus the retailer has to hire a rented warehouse to store the excess units. In this scenario, retailer usually adopts two types of dispatch policy: FIFO & LIFO, depending upon the situation, e.g., nature of items/deteriorating items, location of warehouse. Further in order to survive in the market, the retailer dynamically adjusts the prices of the goods to boost the demand and enhance the revenues. In the light of these facts, this paper develops an inventory model for deteriorating items with price-sensitive demand under permissible delay in payment in a two warehouse environment. Shortages are allowed and fully backlogged. The objective of this study is to find the optimal inventory and pricing policies so as to maximize the total average profit. Further, the different trade credit scenario has been exhibited with the help of a numerical example. A comprehensive sensitivity analysis has also been carried out to advocate the implication of FIFO and LIFO dispatch policy. [ABSTRACT FROM AUTHOR]

In this paper, an attempt is made to improve profit through a retailer-Stackelberg game in a multi-echelon supply chain involving one supplier, one manufacturer, and one retailer having deterministic price-sensitive demand. Inventory in each echelon is subject to deterioration. We assume that the supplier and the manufacturer follow a multi-shipment policy to deliver to the manufacturer and the retailer, respectively. The proposed model is developed first under centralized decision policy which is the benchmark case. Then the decentralized model is developed and profit improvement is done through a retailer-Stackelberg game. The optimal results are demonstrated and a sensitivity analysis is performed for a numerical data-set. [ABSTRACT FROM AUTHOR]

Abstract: In this study, we determined product prices and designed an integrated supply chain operations plan that maximized a manufacturer’s expected profit. The computational results of this study revealed that as the variance of the demand distribution increases, a manufacturer will increase its inventory to levels that are greater than the anticipated demand to prevent the potential loss of sales and will simultaneously raise product prices to obtain a greater profit. In the cost minimization approach, the manufacturer may earn the highest possible profits, as determined by the profit optimization approach, only if this firm precisely forecasts the mean market demand for its products. Greater inaccuracies in this forecast will produce lower levels of expected profit. [Copyright &y& Elsevier]

Abstract: One of the interesting subjects in supply chain management is supply management, which generally relates to the activities regarding suppliers such as empowerment, evaluation, partnerships and so on. A major objective of supplier evaluation involves buyers determining the optimal quota allocated to each supplier when placing an order. In this paper, we propose a multi-objective model in which purchasing cost, rejected units, and late delivered units are minimized, while the obtained total score from the supplier evaluation process is maximized. We assume that the buyer obtains multiple products from a number of predetermined suppliers. The buyer faces a stochastic demand with a probability distribution of Poisson regarding each product type. A major assumption is that the supplier prices are linearly dependent on the order size of each product. Since demand is stochastic, the buyer may incur holding and stockout costs in addition to the regular purchasing cost. We use the well-known L-1 metric method to solve the supplier evaluation problem by utilizing two meta-heuristic algorithms to solve the corresponding mathematical problems. [Copyright &y& Elsevier]

In this paper, we investigate the simultaneous coordination of price and capacity building decisions in a dyadic supply chain. This problem is a combination of capacity reservation problem and pricing problem. While the coordination of supply chain with stochastic demand and fixed prices has received much attention in the literature, price-dependent and stochastic demand has been less considered. We study the latter case where a price-setting retailer faces a linear decreasing demand with respect to price. To capture the uncertainty of the demand, we add a stochastic variable to the demand function. In addition, we incorporate production rate and inventory cost on the supplier side. We propose Revenue Sharing Reservation Contract with Penalty (RSRP) as a coordination mechanism to align the price and capacity decisions. We then extend the model to include multiple retailers which are geographically dispersed. We next conduct a comprehensive numerical example with an extensive sensitivity analysis to understand the behavior and robustness of the supply chain under a RSRP, and finally, we draw some managerial implications. [ABSTRACT FROM AUTHOR]

In this article, an order-level inventory system for deteriorating items has been developed with demand rate as a function of selling price. The demand and the deterioration rate are price dependent and time proportional, respectively. We have considered a perishable item that follows a three-parameter Weibull distribution deterioration. Shortages are not permitted in our model. The optimal solution is illustrated with a numerical example and the sensitivity analysis of parameters is carried out. [ABSTRACT FROM PUBLISHER]

Up to now, many newsboy problems have been considered in the stochastic inventory literature. Some assume that stochastic demand is independent of selling price (p) and others consider the demand as a function of stochastic shock factor and deterministic sales price. This article introduces a price-dependent demand with stochastic selling price into the classical Newsboy problem. The proposed model analyses the expected average profit for a general distribution function of p and obtains an optimal order size. Finally, the model is discussed for various appropriate distribution functions of p and illustrated with numerical examples. [ABSTRACT FROM AUTHOR]

Abstract: The article deals with a stochastic economic order quantity (EOQ) model over a finite time horizon where uniform demand over the replenishment period is price dependent. The selling price is assumed to be a random variable that follows a probability density function. As demand is probabilistic, stock out situation may occur. Based on the partial backlogging and lost sale cases during stock out period, the author develops the criterion for the optimal solution for the replenishment size such that the integrated expected profit is maximized. Moreover, the article suggests a new function regarding price dependent demand. Finally, numerical examples and its sensitivity analysis of key parameters are given to illustrate the proposed model. [Copyright &y& Elsevier]

This paper discusses the optimal pricing and replenishment policies of an economic order quantity model for non-instantaneous deteriorating items with partial backlogging over an infinite time horizon. The model is studied under the replenishment policy starting with no shortages. The backlogging rate is any non-increasing function of the waiting time up to the next replenishment. The objective of this model is to maximize the total profit which includes the sales revenue, purchasing cost, set up cost, holding cost, shortage cost, and opportunity cost due to lost sales. Here, the selling price, replenishment quantity, replenishment cycle length, and the time duration of the positive inventory level are taken as decision variables to maximize the profit of the inventory system. The existence and the uniqueness of the solution of the proposed inventory system are examined. We suggest a solution procedure to find the optimal solution of the described model. Numerical examples are presented to determine the developed model and the solution procedure. Sensitivity analysis of the optimal solution with respect to major parameters is carried out and some useful managerial results are obtained. [ABSTRACT FROM AUTHOR]

Abstract: 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. [ABSTRACT FROM AUTHOR]

This article develops a sustainable electricity supply chain mathematical model that assumes linear price-dependent customer demands where the price is a decision variable under setup cost and carbon emission. The sustainable electrical supply chain system contained: (a) power generation; (b) transmission substations; (c) distribution substations; and (d) customer. The production rates depend on the demand rate, and demand for electricity by the customers is dependent on the price of electricity where the electrical energy was generated and transmitted through multiple substations to customers. Moreover, we considered that the capacities of transmission rates, power generation, and distances in between two stations are associated with the distribution costs and transmission cost. Here, we used the theory of inventory to develop a new model and suggested a procedure to deduce an optimal solution for this model. Finally, a numerical example and sensitivity analysis are employed to illustrate the present study and with managerial insights. [ABSTRACT FROM AUTHOR]

In order to identify the optimal structure of an electricity power network under the main assumption of a price dependent demand of electrical energy, we presented an optimization model that aims at analyzing the effect of price-dependent demand on the sustainable electrical supply chain system (SESCS). The system included a power generation system, transmission and distribution substations, and many customers. The electrical energy was generated and transmitted through multiple substations to our customers, and the demand for electricity by the customers is dependent on the price of electricity. In the study, we considered the transmission and the distribution costs which depend on the capacities of power generation, transmission rates and distances between stations. We utilized the inventory theory to develop our model and proposed a procedure to derive an optimal solution for this problem. Finally, numerical examples and sensitivity analysis are provided to illustrate our study and consolidate managerial insights. [ABSTRACT FROM AUTHOR]