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In this present study, a single-manufacturer and single-retailer supply chain management model are formulated for a single product. This study specifically looks at a supply chain with variable production rate, stochastic lead time demand, and price- and advertisement-dependent demand. By incorporating these complex aspects into a model, which enables to examine their combined effects on supply chain performance, this study adds to the body of knowledge. The study reveals unique insights into the complex interplay between pricing tactics, advertising efforts, production dynamics, and the variability brought on by stochastic lead times through meticulous study and modelling. Finally, the total system profit is calculated and optimized with all the decision variables. A classical approach is performed to obtain the optimized solution of the joint profit function along with the decision variables. Two models are discussed in the study: (1) the model with normally distributed lead time demand and (2) the model with distribution-free lead time demand. The joint profit of the supply chain is found to be lesser by 1% for the normally distributed lead time demand than the distribution free pattern. The comparison of the shipment policies and the safety factors for the different distribution patterns of the lead time demand are shown. Though the huge increment in the safety factor for unknown leadtime demand distribution may help in reducing the uncertainity factor and disruptions in the supply chain, but also it may unnecessarily tie up more capital which can be invested in other sectors of the supply chain. [ABSTRACT FROM AUTHOR]

• 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]

Time, price, and servicing are three important factors which affect the demand for any product. In a multi-period inventory model, different pricing in different periods may have a positive impact on demand. Offering discounts to customers during a shortage period is an efficient way to reduce lost sales. To address all these issues, a multi-period inventory model is developed and analyzed in this paper to obtain optimal pricing and replenishment periods where the market demand depends on price, time and service level provided by the retailer. The time horizon is fixed; the replenishment cycles are of equal length, but the shortage period may vary in different cycles. The retailer is allowed to charge different prices in different periods and provide discounts if someone places demand during a shortage period. Learning effects in holding and ordering costs are considered. Under a dynamic pricing framework, this study examines service improvement through learning and price discounts during shortages as an incentive for customers. It demonstrates that discounting indeed helps to produce more revenue when the back-order rate is low, and the service level is critical in generating demand when the stock-out period is lengthy, revealing a critical relationship between shortage periods and service level. A numerical experiment is performed to investigate the optimal policy in different situations and obtain some managerial insights. [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]

Perishable products in Europe, the United States, and Canada typically have expiration dates or maximum lifetimes assigned to them. As these products approach their predetermined lifetimes , there is a gradual increase in the rate of decay, leading to a reduction in their freshness. To examine the impact of these two distinct attributes on a perishable product with a predetermined expiration date, we introduce two inventory models that utilize a demand function incorporating a linearly decreasing price dependence and a nonlinear increase that is influenced by advertising. These models consist of: (i) a zero-ending stock scenario and (ii) a partially backlogged shortage situation. Under certain conditions, the optimal cycle length for the stock zero-ending model and the optimal period with positive inventory for the model with shortages are obtained. The frequency of advertisement is a discrete and integer decision variable, we devise two algorithms for both models to determine the optimal frequency of advertisement that maximizes the profit. Finally, we suggest some strategies in order to increase the profit by studying marginal insights from a sensitivity analysis. It is recommended that the manager focuses on creating more impactful advertisements that are affordable to promote the product’s information through popular media channels.

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]

Perishable products in Europe, the United States, and Canada typically have expiration dates or maximum lifetimes assigned to them. As these products approach their predetermined lifetimes , there is a gradual increase in the rate of decay, leading to a reduction in their freshness. To examine the impact of these two distinct attributes on a perishable product with a predetermined expiration date, we introduce two inventory models that utilize a demand function incorporating a linearly decreasing price dependence and a nonlinear increase that is influenced by advertising. These models consist of: (i) a zero-ending stock scenario and (ii) a partially backlogged shortage situation. Under certain conditions, the optimal cycle length for the stock zero-ending model and the optimal period with positive inventory for the model with shortages are obtained. The frequency of advertisement is a discrete and integer decision variable, we devise two algorithms for both models to determine the optimal frequency of advertisement that maximizes the profit. Finally, we suggest some strategies in order to increase the profit by studying marginal insights from a sensitivity analysis. It is recommended that the manager focuses on creating more impactful advertisements that are affordable to promote the product's information through popular media channels. [ABSTRACT FROM AUTHOR]

This paper aims to design an inventory model for a retail enterprise with a profit maximization objective using the opportunity for a price discount facility given by a supplier. In the profit maximization objective, the demand should be increased. The demand can be boosted by lowering the selling price. However, lowering the selling price may not always give the best profit. Impreciseness plays a vital role during such decision-making. The decision-making and managerial activities may be imprecise due to some decision variables. For instance, the selling price may not be deterministic. A vague selling price will make the retail decision imprecise. To achieve this goal, the retailer must minimize impreciseness as much as possible. Learning through repetition may be a practical approach in this regard. This paper investigates the impact of fuzzy impreciseness and triangular dense fuzzy setting, which dilutes the impreciseness involved with managerial decisions. Based on the mentioned objectives, this article considers an inventory model with price-dependent demand and time and a purchasing cost-dependent holding cost in an uncertain phenomenon. This paper incorporates the all-units discount policy into the unit purchase cost according to the order quantity. In this paper, the sense of learning is accounted for using a dense fuzzy set by considering the unit selling price as a triangular dense fuzzy number to lessen the impreciseness in the model. Four fuzzy optimization methods are used to obtain the usual extreme profit when searching for the optimal purchasing cost and sale price. It is perceived from the numerical outcomes that a dense fuzzy environment contributes the best results compared to a crisp and general fuzzy environment. Managerial insights from this paper are that learning from repeated dealing activities contributes to enhancing profitability by diluting impreciseness about the selling price and demand rate and taking the best opportunity from the discount facility while purchasing. [ABSTRACT FROM AUTHOR]

This paper aims to design an inventory model for a retail enterprise with a profit maximization objective using the opportunity for a price discount facility given by a supplier. In the profit maximization objective, the demand should be increased. The demand can be boosted by lowering the selling price. However, lowering the selling price may not always give the best profit. Impreciseness plays a vital role during such decision-making. The decision-making and managerial activities may be imprecise due to some decision variables. For instance, the selling price may not be deterministic. A vague selling price will make the retail decision imprecise. To achieve this goal, the retailer must minimize impreciseness as much as possible. Learning through repetition may be a practical approach in this regard. This paper investigates the impact of fuzzy impreciseness and triangular dense fuzzy setting, which dilutes the impreciseness involved with managerial decisions. Based on the mentioned objectives, this article considers an inventory model with price-dependent demand and time and a purchasing cost-dependent holding cost in an uncertain phenomenon. This paper incorporates the all-units discount policy into the unit purchase cost according to the order quantity. In this paper, the sense of learning is accounted for using a dense fuzzy set by considering the unit selling price as a triangular dense fuzzy number to lessen the impreciseness in the model. Four fuzzy optimization methods are used to obtain the usual extreme profit when searching for the optimal purchasing cost and sale price. It is perceived from the numerical outcomes that a dense fuzzy environment contributes the best results compared to a crisp and general fuzzy environment. Managerial insights from this paper are that learning from repeated dealing activities contributes to enhancing profitability by diluting impreciseness about the selling price and demand rate and taking the best opportunity from the discount facility while purchasing.

Firms proactively search for low‐cost production locations to enjoy cost‐based advantages. In this article, we develop a two‐stage stochastic program to study a firm's capacity investment and production decisions about the exploration of new production locations. In the first stage, the firm determines how much capacity to build at the new location, and in the second stage, after the product demand and the production cost at the new location have been observed, the firm determines the optimal production quantities. We first characterize the firm's optimal decisions and then examine how the optimal capacity level and firm profit are affected by the key parameters. We find that the firm may be better off when either the production cost or the demand is more variable. Using numerical analyses, we also investigate the value of retaining the existing location, and our results demonstrate that retaining the existing location obtains the highest value when the market size is large, the consumers are insensitive to price, the market demand is highly uncertain, or the variability of the production cost at the new location is either sufficiently high or sufficiently low. Finally, we extend our baseline setting in two directions: one in which the firm makes the production decision prior to demand realization, and the other in which there is a finite capacity at the existing location. For both extensions, we demonstrate the robustness of the results obtained for the baseline setting. [ABSTRACT FROM AUTHOR]

Inventory management and control are needed, especially for retailers, to make their business run smoothly. Inventory management is related to the purchase, storage, and sale of goods. Therefore, the determination of the right amount of inventory in hands is crucial in this situation. Low inventory levels will cause a higher probability of shortage, but on the other hand, having a lot of inventory in hands will incur higher holding costs, extra storage space, and deterioration of goods in hands. In this paper, we propose an inventory model with the inventory and price-dependent demand. We also consider a deterioration factor in our model. There are two models developed in this paper, namely the linear deterioration rate model with constant holding cost and the model of the deterioration rate with Weibull distribution with linear time-dependent holding cost. The purpose of the model is to find the optimal price and ending inventory level that maximizes the average profit. Sensitivity analysis is also performed to find the effect of parameter changes in our model to the optimum solution. We found that model with Weibull deterioration rate and linear holding costs will give a higher average profit.

When perishable products are priced uniformly, regardless of the amount of time remaining until expiration, consumers may gravitate towards fresher products, leaving some inventory unsold. This research considers dynamic pricing policies as well as replenishment policies in the context of perishable products with a fixed shelf life. Consumers are assumed to be heterogeneous in their sensitivity to freshness, i.e. their willingness to pay more for fresher products. We develop a model for identifying an optimal (profit-maximising) dynamic pricing policy and for evaluating the extent to which both the retailer and the consumer benefit from the implementation of a dynamic pricing policy as opposed to a static policy. The model assumes that the retailer is able to utilise knowledge regarding the heterogeneous characteristics of incoming customers (e.g. the retailer can gather specific information about customers’ historical purchases). Unexpectedly, it is proven that in an optimal pricing policy, the retailer should assign a lower price to fresher products and then raise the price as the products approach expiration. A numerical illustration shows that profits are strongly influenced by the volatility of consumer sensitivity to freshness; specifically, this variable has the potential to reduce optimal profits by up to 8%. [ABSTRACT FROM AUTHOR]

This study renders a location-inventory problem for a closed-loop supply chain network under the circumstance of price-dependent demands, in which there are suppliers/recovering centers, stores and consumer areas. In this respect, the demand is supposed to be correlated, and the inventory of new and returned products are controlled via a continuous review system (Q, r) in the stores. What is more, the shortage is allowed and could be emerged as back-ordered and lost sales. A nonlinear programming model is offered to formulate the problem, which maximizes the total profit of the supply chain. In this regard, miscellaneous decisions are determined, such as location-allocation facilities, inventory levels and prices of products. So as to solve the proposed model, two well-known meta-heuristic algorithms with particular encoding and decoding procedures, including a genetic algorithm (GA) and an imperialist competitive algorithm (ICA), are employed due to the Np-hard nature of the model. Finally, with the intention of illustrating the validation and applicability of the model, a real case study of a wireless network is investigated. [ABSTRACT FROM AUTHOR]

In the business world, it is generally observed that the supplier gives a cash discount due to advance payment. The buyer may either pay off the total purchase cost or a fraction of the total purchase cost before receiving the products. If the buyer makes full payment then he receives a cash discount instantly. If the buyer pays a fraction of the total purchase cost, then (s)he receives the cash discount while paying the remaining amount at the time of receiving the lot. Moreover, in most of the inventory models, it is generally assumed that the delivered lot contains only perfect items. But in reality, the presence of imperfect items in the received lot cannot be overlooked as it will affect the total profit of the system. Thus, the study of inventory models considering the presence of imperfect items in the lot makes the model more realistic and it has received much attention from inventory managers. This paper develops a model that jointly considers imperfect quality items and the concept of an advance payment scheme (full and partial). The objective is to determine optimal ordering quantity to maximise the total profit of the system. The necessary theoretical results showing the existence of global maximum is derived. The model is illustrated with the help of numerical examples, and sensitivity analysis is carried out on some important system parameters to see the effects on the total profit of the system. The study shows that a full advance payment scheme is beneficial for the buyer. [ABSTRACT FROM AUTHOR]

We consider a periodic review stochastic inventory system where the current on-hand inventory exceeds the maximum supply needs in the future. Consequently, one must make an immediate inventory liquidation decision on the liquidation quantity and promotional price with the goal of maximising the overall profit where the demand during the liquidation period (DDLP) is a random variable whose distribution depends on the promotional price. We develop a price-dependent DDLP model and an inventory model for optimising the liquidation quantity and unit promotional price. The model is applicable for general distributions of the DDLP and regular demand (i.e. demand during the future periods following the promotion period). We also investigate four special cases where the DDLP and regular demand are assumed to be either exponential or uniform random variables. The two models that assume the exponential distribution for regular demand can be examined analytically and simplified using the mathematical properties we derive. The additional two models that assume the uniform distribution for regular demand do not have closed-form expressions but can be solved numerically. Some numerical examples are presented for further elaboration of the models and to demonstrate their practical use. [ABSTRACT FROM AUTHOR]

The paper aims to develop and introduce a price-dependent management model of electricity demand schedules at industrial enterprises. The research methodology comprises Smart Grid Concept and Demand-side management, in particular. The authors analyse demand-side management tools applied in Russia and abroad and substantiate the urgency of introduction of demand management tools at Russian industrial enterprises. We also develop a classification of factors hindering the process of introducing an electricity demand management model at manufacturing plants. The authors propose a model for price-dependent management of industrial demand for energy resources which allows for identified factors and the structural interconnections between enterprises’ production divisions. With a view to accelerating the introduction and increasing the efficiency of the model, the paper provides an algorithm for its consistent implementation. The algorithm consists of five stages following the principles of a gradual increase in the number of industrial units covered, growing complexity of the management model and a step-by-step increase in the economic effect. The article gives an in-depth description of the stages of implementation of the price-dependent management model with the development of the parameters of the introduced changes in all areas of an industrial enterprise’s activity.

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 demand for perishable food products is often influenced by the selling price and the age of the items. This is because perishable food products have become commodities from consumers’ point of view, hence, there are very little differences between competing brands. Consequently, factors like price and freshness (or age) become important determinants of consumer demand. This fact has been used to develop several models for managing perishable inventory. However, most of these models were developed from the perspective of a retailer. Today’s increasingly competitive business environment has forced companies to collaborate with fellow supply chain members in an effort to improve profitability and operational efficiency. With this in mind, this article presents a model for managing inventory in a perishable food products supply chain that begins with farming operations where live inventory items are reared and ends with the consumption of processed inventory. The farming and consumption (retail) stages are connected by a processing stage during which live inventory is processed into a consumable form. Consumer demand at the retail stage is a function of the selling price and the freshness of the processed inventory. The farming, processing and retail stages are the three-echelons of the proposed supply chain aimed at maximising the joint supply chain profit. Through a numerical example, the benefits of jointly optimising the inventory replenishment policy (among all three echelons) are quantified by comparing the network performance of a joint optimisation approach (i.e. centralised) to that of an equivalent independent (i.e. decentralised) optimisation policy.

The concept of supply chain equilibrium has been widely employed to solve real-life cases. Under this concept, decisions makers move simultaneously and compete in a noncooperative manner to achieve a supply chain network equilibrium. This paper proposes a supply chain network equilibrium model consisting of multiple raw material suppliers, manufacturers and retailers. Unlike previous studies, we assume that the demand for the product at each retail outlet is modeled as general stochastic functions of price that encompass additive-multiplicative demand models used in previous studies. Under general price-dependent demand functions, we derive the optimality conditions of suppliers, manufacturers and retailers, and establish that the governing equilibrium conditions can be formulated as a finite-dimensional variational inequality problem. The existence and uniqueness of the solution to the variational inequality are examined. A sensitivity analysis and a series of numerical tests are conducted to illustrate the analytical effects of demand distribution, model parameters, demand level and variability on quantity shipments, prices, and expected profits. Managerial insights are reported to show the impact of different types of demand functions and model parameters on the equilibrium solutions.

In the world of limited resources, recovery of used products for reselling or recycling is a critical issue from the economic and environmental point of view. In this paper, we have assumed that a retailer sells the new product to customers as well as collects and sells the used products. We adopt a price dependent quadratic demand function, and the return of used product as a price and time-dependent linear function. The proposed problem is formulated as a profit maximization problem for the retailer. The objective is to find the optimal selling price, the optimal ordering quantity for the new product, and the optimal quantity of used product simultaneously such that the retailers total profit is maximized. The model is validated by a numerical example and sensitivity analysis is performed for the key parameters.

This paper investigated a multistage sustainable production–inventory model for deteriorating items (i.e., raw materials and finished goods) with price-dependent demand and collaborative carbon reduction technology investment under carbon tax regulation. The model was developed by first defining the total profit of the supply chain members under carbon tax regulation and, second, considering a manufacturer (leader)–retailer (follower) Stackelberg game. The optimal equilibrium solutions that maximize the manufacturer's and retailer's total profits were determined through the method analysis. An algorithm complemented the model to determine the optimal equilibrium solutions, which were then treated with sensitivity analyses for the major parameters. Based on the numerical analysis, (a) carbon tax policies help reduce carbon emissions for both the manufacturer and retailer; (b) most carbon emissions from supply chain operations negatively impact the total profits of both members; (c) the retailer may increase the optimal equilibrium selling price to respond to an increase in carbon emissions from supply chain operations or carbon tax; and (d) autonomous consumption positively affects both members' optimal equilibrium policies and total profits, whereas induced consumption does the opposite. These findings are very managerial and instructive for companies seeking profits and fulfilling environmental responsibility and governments. [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]

In this article, we establish an inventory model for deteriorating items with a return period and price-dependent demand for the retailer who offers two-phase advance sales to his/her customers. The replenishment cycle is divided into two sales periods: one is the two-phase advance sales period, and the other is the spot sales period. Before customers with reservations receive their orders, they may cancel the order. On the other hand, when the customers receive the order, they can make a request to return products for any reason during the return period. We provide an easy-to-use method to obtain the optimal selling price and the optimal sales period to achieve the retailer's maximum total profit. Finally, we give numerical examples to illustrate the solution procedure. We perform a sensitivity analysis to investigate the effect of changes of some main parameter values on the optimal solution and provide an economic interpretation. [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]

Abstract In this research, an integrated inventory model for non-instantaneous deteriorating items is analyzed when demand is sensitive to changes in price. The price used in this research is a time-dependent function of the initial selling price and the discount rate. To control the deterioration rate of items at the storage facility, investment in preservation technology is incorporated. To provide a general framework to the model, an arbitrary holding cost rate is used. Toward the end of the paper, a numerical case is given to approve the model and the impacts of the key parameters of the model are studied by sensitivity analysis to deduce managerial insights.

The production processes throughout the world aim at improving quality by introducing latest technologies so as to perform well in fierce competition. Despite this due to various unavoidable factors, most of the manufacturing processes end up with certain imperfections. Hence, all the items produced are not of perfect quality. The condition tends to be more susceptible while dealing with items of deteriorating quality; therefore an inspection process is must for screening good quality items from the ordered lot. Demand is assumed to be price dependent and it is represented by a constant price elasticity function. Also to endure with the rapid growth and turbulent markets, the suppliers try to engage and attract retailers through various gimmicks and one such contrivance is offering trade credit, which is proved to be an influential strategy for attracting new customers. In view of this, the present paper develops an inventory model for items of imperfect quality with deterioration under trade-credit policies with price dependent demand. Shortages are allowed and fully backlogged. A mathematical model is developed to depict this scenario. The aim of the study is to optimize the optimal order level, backorder level and selling price so as to maximize the retailer’s total profit. Findings are validated quantitatively by using numerical analysis. Sensitivity analysis is also performed so as to cater some important decision-making insights.

If an exporter or a wholesaler sells goods at a fixed price to be paid in the currency of the seller's country, then the purchase price of the importer depends upon the prevailing exchange rate of their respective currencies. Ideally, in a floating exchange rate system, the purchase price has to change according to shifts in the exchange rate. In such a scenario the entire exchange rate risk is borne by the importer/buyer. However, in international trade, it is customary for the parties to enter into a risk-sharing agreement, under which the buyer does not pay the seller on the basis of the prevailing exchange rate, but pays a mutually agreed upon price that falls within a range of fluctuating exchange rates. In this manner, the profit or loss due to fluctuations in the exchange rate would be shared by both the parties. These stochastic variations in purchase prices are modeled through a Markov chain. In this article, the resulting purchase and inventory problem is analyzed by identifying a regenerative cycle. An optimal selling price that maximizes the expected profit per unit time is also discussed. Further, optimal ordering policies under no stock-out conditions are derived with an optimal uniform demand corresponding to the optimal selling price. Through sensitivity analyses, differences in profit function with respect to carrying cost fraction, setup costs, and purchase prices are also shown. An investigation into the possible loss if this model solution is not implemented is also made through numerical illustrations. A discussion of a special case of two-purchase price scenario gives additional insight into the problem. [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 investigated a multistage sustainable production–inventory model for deteriorating items (i.e., raw materials and finished goods) with price-dependent demand and collaborative carbon reduction technology investment under carbon tax regulation. The model was developed by first defining the total profit of the supply chain members under carbon tax regulation and, second, considering a manufacturer (leader)–retailer (follower) Stackelberg game. The optimal equilibrium solutions that maximize the manufacturer’s and retailer’s total profits were determined through the method analysis. An algorithm complemented the model to determine the optimal equilibrium solutions, which were then treated with sensitivity analyses for the major parameters. Based on the numerical analysis, (a) carbon tax policies help reduce carbon emissions for both the manufacturer and retailer; (b) most carbon emissions from supply chain operations negatively impact the total profits of both members; (c) the retailer may increase the optimal equilibrium selling price to respond to an increase in carbon emissions from supply chain operations or carbon tax; and (d) autonomous consumption positively affects both members’ optimal equilibrium policies and total profits, whereas induced consumption does the opposite. These findings are very managerial and instructive for companies seeking profits and fulfilling environmental responsibility and governments.

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.

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 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.

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]

This article is concerned with the problem of single-vendor single-buyer integrated supply chain inventory with price-dependent demand and product recovery. In our model, we assume that the vendor inspects each lot product in one production run in advance before delivering to the buyer, in which if defective items are unrecoverable, then he/she disposes of them; otherwise, which are immediately recovered for reuse. In addition, we consider that the demand rate is a function of unit price charged by the vendor to the buyer to widen applications to the model. The objective of this article is to minimize the joint total cost per unit time by simultaneously optimizing the buyer's order quantity, the size of each shipment of the vendor, and the number of shipments from the vendor to the buyer in one production run. Furthermore, an algorithmic procedure of finding the optimal solution is developed, and finally, some numerical examples are given to illustrate the results. [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]

This paper considers the problem of simultaneously determining the price and inventory control strategies for deteriorating items. It is assumed that the rate of deterioration can be reduced by means of effective preservation technology investment and the demand rate is a function of selling price. The goal of this study is to maximize the total profit per unit time by simultaneously determining the optimal selling price, length of replenishment cycle and preservation technology investment. First, for a given preservation technology investment, we prove that the optimal selling price and the optimal length of replenishment cycle exist and are unique. Next, it is shown that the total profit per unit time is a concave function of the preservation technology investment. Then, an effective algorithm is designed to find the optimal joint policy. Finally, numerical examples to illustrate the solution procedure and some managerial implications are provided. [ABSTRACT FROM AUTHOR]

In last few decades various models developed under inventory control section whether of probabilistic or deterministic nature did not consider the effect of marketing parameters. The marketing parameters especially associated with innovation diffusion theory make the inventory models more realistic. In this paper, an inventory model has been proposed based on the explicit assumptions of interaction of marketing parameters to the optimal inventory replenishment policy. A time-dependent innovation driven demand has been incorporated in the basic economic order quantity (EOQ) model to know the realistic features of the model. This model assumes that potential market size is dynamic over time and is dependent on the price of the product. The model is illustrated with a numerical example and to know the effectiveness of the model a sensitivity analysis of the optimal solution with respect to different parameters has been performed. [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]

Recently, due to rapid economic development in emerging nations, the world's raw material prices have been rising. In today's unrestricted information environment, suppliers typically announce impending supply price increases at specific times. This allows retailers to replenish their stock at the present price, before the price increase takes effect. The supplier, however, will generally offer only limited quantities prior to the price increase, so as to avoid excessive orders. The retail price will usually reflect any supply price increases, as market demand is dependent on retail price. This paper considers deteriorating items and investigates (1) the possible effects of a supply price increase on retail pricing, and (2) ordering policies under the conditions that special order quantities are limited and demand is dependent on retail price. The purpose of this paper is to determine the optimal special order quantity and retail price to maximize profit. Our theoretical analysis examines the necessary and sufficient conditions for an optimal solution, and an algorithm is established to obtain the optimal solution. Furthermore, several numerical examples are given to illustrate the developed model and the solution procedure. Finally, a sensitivity analysis is conducted on the optimal solutions with respect to major parameters. [ABSTRACT FROM AUTHOR]

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]