Price-dependent Stochastic Demand Research Articles

How power structure and markup schemes impact supply chain channel efficiency under price-dependent stochastic demand

Although considerable attention has been separately given to factors such as power structures, price-dependent demand, and markup pricing schemes, there has been limited exploration of the combined effects of these factors on supply chain efficiency and the leader’s advantage. We propose a game theoretic model in which a manufacturer sells a single product to a newsvendor retailer who sets both optimal order quantity and selling price under uncertain price-dependent demand. Furthermore, we examine a supply network wherein a single retailer fulfills orders using a global manufacturer for regular orders and a local manufacturer to clear any shortages. Through numerical analysis, we show that the retailer always prefers to charge a percentage markup. In a two-player game, channel efficiency is higher when the retailer is the leader under linear demand; however, under iso-elastic demand, the manufacturer being a leader brings a higher channel efficiency. When a local manufacturer is involved as a second manufacturer, channel efficiency is higher when the retailer remains a follower, as this induces more fierce wholesale price competition between the two manufacturers. Additionally, when demand uncertainty is high in the two-player game with linear demand, the retailer as a follower can achieve higher profits, whilst high uncertainty under iso-elastic demand decreases both players’ profits. Moreover, it becomes advantageous for the retailer to have a local manufacturer as demand uncertainty increases, even when the local manufacturer announces the wholesale price first.

An integrated inventory model for non-instantaneous deteriorating item under credit policy and partial backlogging with advertising and price dependent stochastic demand

In today’s business world, advertising is one of the most important policies to attract more customers. This policy increases the retailer’s sales and makes the retailer’s business position strong. In this paper, we have considered an integrated inventory model for non-instantaneous deteriorating items with a single supplier and single retailer, where a supplier sells his/her products in the market through a retailer who faces a stochastic demand depending on both retail price and advertisement. Here, to increase the retailer’s demand, the supplier wholesales his/her products to the retailer with a credit period. Since the long credit period increases the demand rate but at the same time, it increases the supplier’s opportunity loss. In this paper, we have discussed about the credit policy and find out, how this policy effective on profit of the supplier, the retailer as well as the whole system. After purchasing, the retailer sells his/her products to his customers with a markup. This markup is based on the supplier’s wholesale price and also on advertising costs. Finally, an integrated profit function has been developed and we have illustrated numerical examples to justify the feasibility of the proposed model. The result indicates that not only the credit period but also an appropriate number of advertisements is more important for maintaining the profit of the supplier, the retailer as well as the integrated profit of the system. We have analyzed the effect of markup on the profit function. We have also analyzed how the profit structure of the suppliers and retailers changes along with the changes in the length of the credit period. An effective algorithm has been presented in the solution procedure to find the optimal solutions of the proposed model. Also, the numerical example with uniform distribution has been carried out. Finally, sensitivity analysis of major parameters has been illustrated to provide managerial insights

Price timing and financing strategies for a capital-constrained supply chain with price-dependent stochastic demand

We investigate the pricing timing strategy in the context of trade credit (TC), under which the capital-constrained retailer applies for deferred payments from its supplier. Based on the wholesale price offered by the supplier, the retailer determines the order volume before observing the random demand and the selling price after observing it (a.k.a., price postponement). We formulate the Stackelberg game to show how their equilibrium decisions and profits are affected by: the pricing timing, financing mode, the demand structure. In a multiplicative demand framework, the analytical and numerical results indicate that TC alleviates double marginalization problem, depending on price timing and demand structure. With the traditional bank finance (BF) as a benchmark, the supplier is reluctant to provide TC to the retailer without postponement when the market is extremely sensitive to price. Postponement not only benefits both members, but also enhances retailer’s repayment ability and thus participants’ preference for TC. They can reach an agreement on utilizing price postponement and trade credit as long as the supplier choose a suboptimal wholesale decision for deferred payment that is slightly lower the optimal one. We further extend our results to consider the additive demand structure.

Price Timing and Financing Strategies for a Capital-Constrained Supply Chain with Price-Dependent Stochastic Demand

Price Timing and Financing Strategies for a Capital-Constrained Supply Chain with Price-Dependent Stochastic Demand

A distribution-free newsvendor model considering environmental impact and shortages with price-dependent stochastic demand.

In today's competitive and volatile market, demand prediction for seasonal items is a challenging task. The variation in demand is so quick that the retailer cannot face the risk of understocking or overstocking. Unsold items need to discarded, which has environmental implications. It is often difficult to calculate the effects of lost sales on a firm's monetary values, and environmental impact is not a concern to most businesses. These issues concerned with the environmental impact and the shortages are considered in this paper. A single-period inventory mathematical model is formulated to maximize expected profit in a stochastic scenario while calculating the optimal price and order quantity. The demand considered in this model is price-dependent, with several emergency backordering options to overcome the shortages. The demand probability distribution is unknown to the newsvendor problem. The only available demand data are the mean and standard deviation. In this model, the distribution-free method is applied. A numerical example is provided to demonstrate the model's applicability. To prove that this model is robust, sensitivity analysis is performed.

Optimal Procurement Management by Reverse Auctions for a Price-Setting Newsvendor

In this paper, we study the optimal procurement management by reverse auctions for a price-setting newsvendor (retailer) in a single period setting. The retailer facing price-dependent stochastic demand first designs a procurement contract and then invites the suppliers to bid for this contract in the reverse auction. The winning supplier produces and delivers the demanded quantity. The retailer obtains the procurement quantity and simultaneously determines the retail price. By using the price elasticity of the lost-sales rate, we show that the retailer’s expected profit (excluding the procurement cost) is a concave function of the purchased quantity, which can be used to obtain the optimal procurement and retail pricing decisions for the retailer. Further, when the underlying random term of demand function is normally distributed under left-truncation (at 0), we get the analytical expressions of the purchased quantity and expected profit function for the retailer. Moreover, some numerical examples are given.

Coordinating a three-level supply chain with effort and price dependent stochastic demand under random yield

Coordinating a three-level supply chain with effort and price dependent stochastic demand under random yield

Bartering: Price-Setting Newsvendor Problem with Barter Exchange

Barter exchange is a system of swapping goods or services for other goods or services in a moneyless and direct manner. Barter has become an effective model of a circular economy because it reduces the consumption impact. Bartering maximizes the utility of assets and existing resources, and can unleash the unspent social, economic, and environmental value of underutilized assets. The present article analyzes the price-setting newsvendor problem with a barter exchange option. The retailer facing a stochastic price-dependent demand sells a product on the market and, additionally, needs another product for its own purposes. Therefore, first, the retailer trades the unsold product for the product it needs by means of barter, and next disposes of the unsold product at a discounted price at the end of the selling season. The retailer’s optimal order quantity and optimal price are derived assuming additive uncertainty in demand. This type of demand function has special characteristics, for example, the actual demand may attain negative values in times of economic uncertainty. The possibility of negative demand realizations is taken into consideration in the study. It proves that, in certain cases, the optimal solution belongs to the set of high barter prices which implies that the actual demand may be negative.

Coordinating a Socially Responsible Supply Chain with Random Yield under CSR and Price Dependent Stochastic Demand

Coordinating a Socially Responsible Supply Chain with Random Yield under CSR and Price Dependent Stochastic Demand

Transfer of Risk in Supply Chain Management with Joint Pricing and Inventory Decision Considering Shortages

This study is the first to consider a distribution-free approach in a newsvendor model with a transfer of risk and back-ordering. Previously, in many articles, discrete demand is considered. In this model, we consider a newsvendor selling a single seasonal item with price-dependent stochastic demand. Competition in markets has forced the retailer and manufacturer to coordinate in decentralized supply chain management. A coordination contract is made between a retailer and manufacturer to overcome the randomness of demand for a short-life-cycle product. The retailer pays an additional amount per product to transfer the risk of unsold items. The manufacturer bears the cost of unsold products from the retailer. Shortages are allowed with back-ordering costs during the season. The distribution-free model is developed and solved with only available demand data of mean and standard deviation. Stackelberg’s game approach is used to calculate the optimal ordering quality and price. This model aims to maximize expected profit by optimizing unit selling price and ordered quantity through coordination. To illustrate that the model is robust, numerical experiment and sensitivity analyses are conducted for both decentralized and centralized supply chain management. For applicability of the model in the real-world business scenario, managerial insights are provided with sensitivity analysis.

The Coordinator Role of Trade Credit Contract for Coordinating Integrated Pricing and Periodic Review Inventory Decisions With Stochastic Demand

The purpose of this study is to analytically coordinate joint pricing and periodic review ordering choices for a supply chain (SC) facing stochastic price-dependent demand. In this paper, first, the optimal inventory and pricing strategies made by SC members are obtained under decentralized and centralized models. Thereafter, employing a trade credit contract, it proposes to provide a win–win coordination for the investigated SC. Sensitivity analyses are provided both analytically and numerically which indicate the significance of trade credit contracts in improving both customer service level and customer satisfaction. The results indicate that using trade credit contracts, the coordination of joint pricing and periodic review ordering choices is achievable. Moreover, the proposed trade credit contract has a unique feature in achieving more economic benefit compared to the centralized model under some circumstances. In addition, sensitivity analyses reveal that the coordination of integrated periodic review ordering and pricing choices is beneficial, especially for items with high price sensitivity and high demand uncertainty. Our findings also show the applicability of the trade credit contract for an SC facing highly uncertain demand.

Supply chain coordination with competing suppliers under price-sensitive stochastic demand

In this paper, we investigate a supply chain where two competing suppliers sell substitutable products through a common retailer who faces price-dependent stochastic demand. The retailer jointly decides the order quantity and the retail price for each product. Unlike most existing research assuming customer homogeneity, we divide the customers into two types: i) the price-sensitive type and ii) the brand-loyalty type, and investigate the issues of supply chain coordination. Our results show that neither buy-back contracts nor the buy-back related hybrid contracts (i.e., the hybrid buy-back and revenue-sharing contract and the hybrid buy-back and sales rebate contract) can achieve the coordination of such a supply chain. Furthermore, under buy-back contracts for the decentralized supply chain, we analyze the retailer's optimal retail price and order quantity when each supplier imposes a minimum order-quantity constraint. Our result shows that there exists a unique optimal decision for the retailer under some mild restrictions.

Optimal decisions on fencing, pricing, and selection of process mean in imperfectly segmented markets

This paper integrates the selection of a process mean, production and marketing decisions at a firm’s level. We discussed a manufacturing firm’s problem that integrates its manufacturing decisions on production quantities and selection of a process mean with marketing decisions. The marketing decisions include setting prices, and the fencing investment to mitigate the effect of demand leakages between market segments. The manufacturing firm yields products of varied quality based on a single quality characteristic (e.g., amount of fill). The firm operates in a monopoly, and manufacturing process is assumed to follow a normal distribution, and therefore, it produces multi-grade (class) products distinct in their single quality characteristic. Depending upon the quality characteristic, a product with quality characteristic equal to greater than the upper specification limit is classified as grade 1 product, and sold in primary market at a full price. When the quality characteristic falls between the lower and the upper specification limits, it is referred to as a grade 2 product, and sold in a secondary market at a discounted price. Any product with a quality characteristic lower than the lower specification limit is reworked at an additional cost. A 100% error-free inspection is conducted to segregate the products at a negligible cost. Unlike many related studies in literature, this research proposes a novel integration of the pricing and production quantity decisions along with the process targeting in the two markets with pricing decision in the presence of demand leakages due to cross-elasticity. Furthermore, it is assumed that the firm can mitigate the demand leakage at an additional investment on improving fencing. Thus, the firm’s optimal decision would also include the pricing in each market segment, and fencing investment along with its decision on the production quantity for each product class. Mathematical models are developed to address this problem assuming the price-dependent stochastic demand. Structural properties of these models are explored and efficient heuristic solution methodologies are developed. Later, we also developed models when the stochastic demand information is only partially known, and proposed Harmony Search algorithm on the problem. Numerical experimentation is reported to highlight the importance of the proposed integrated framework and the impact of the problem related parameters on a firm’s profitability and its integrated optimal control decisions on selection of a process mean, pricing, production quantity, and fencing investment.

A solution algorithm for multi-period bi-level channel optimization with dynamic price-dependent stochastic demand

We extend the single-period decentralized channel optimization problem with stochastic demand into a multi-period, non-autonomous one and propose an efficient general solution algorithm for it. A supply channel composed of two price-setting agents in a bi-level (Stackelberg) framework has to address an uncertain dynamic demand for a perishable good at different times. The stochastic demand model is general (additive-multiplicative). A class of price-dependent memory functions is embedded in the proposed representation of uncertain demand such that they carry the effect of demand level at present over to the demand in the future. Due to this dependence of the current demand to the pricing history, the state space of the ensuing games becomes highly nested. The proposed iterative algorithm decouples the nested equilibria into separate yet interdependent sub-problems and provides explicit solutions. All the model variables and parameters are considered explicitly time-dependent enabling the model to cover cases with finite and infinite time-horizons. Flexibility and generality of our solution scheme make it applicable to a wide variety of economic contexts. In a series of examples we demonstrate how, fed by different market specifications and memory functions, the solution algorithm can find equilibrium results for a diverse set of scenarios at different times.

Mitigating supply disruption with a backup supplier under uncertain demand: competition vs. cooperation

In case of supply disruption following major disasters, many supply chains tend to break down due to stock-outs and take a long time to recover. However, by keeping emergency sources of supply, some supply chains continue to function smoothly even after a major disaster. In this work, using a game-theoretic-framework, we consider a two-suppliers-one-retailer supply chain with price-dependent stochastic demand in which suppliers are prone to disruption. To investigate the impact of supply disruption we consider two models: SC model, in which the retailer does not maintain any emergency sources of supply against any supply disruption, and SCB model, in which the retailer maintains a backup supplier to mitigate the impact of supply disruption. We mainly focus on the pricing strategies of the suppliers and the mitigating strategies of the retailer under supply and demand uncertainty. We address two coordinating mechanisms to enhance supply chain performance. Our results indicate that in the presence of supply disruption, even with lower probabilities, the retailer would always prefer to take the advantage of a backup supplier and the optimal reserve quantity increases with disruption probabilities. We further investigate the scenario in which the suppliers would always prefer to cooperate with each other.

Dynamic Pricing in a Multi-Period Newsvendor Under Stochastic Price-Dependent Demand

The faster growth of technology stipulates the rapid development of new products; with the spread of new technologies old ones are outdated and their market demand declines sharply. The combined impact of demand uncertainty and short life-cycles complicate ordering and pricing decision of retailers that leads to a decrease in the profit. This study deals with the joint inventory and dynamic pricing policy for such products considering stochastic price-dependent demand. The aim is to develop a discount policy that enables the retailer to order more at the start of the selling season thus increase the profit and market share of the retailer. A multi-period newsvendor model is developed under the distribution-free approach and the optimal stocking quantities, unit selling price, and the discount percentage are obtained. The results show that the proposed discount policy increases the expected profit of the system. Additionally, the stocking quantity and the unit selling price also increases in the proposed discount policy. The robustness of the proposed model is illustrated with numerical examples and sensitivity analysis. Managerial insights are given to extract significant insights for the newsvendor model with discount policy.

Credit financing in economic ordering policies for deteriorating items with stochastic demand and promotional efforts in two-warehouse environment

Retailers are nowadays focusing on promotional activities in order to attract customers because of increasing competition. Promotional efforts have significant impact on the replenishment policy and the sale price of goods. In this paper, a two warehouse inventory model is developed for deteriorating items subject to promotional efforts under permissible delay in payments. Here, a price dependent stochastic demand function is considered with partially backlogged shortages. Several realistic cases, sub cases and scenarios have been taken into account and the corresponding problems have been formulated as nonlinear constrained optimisation problems. To illustrate the proposed model two numerical examples have been solved. Further, a numerical example has been extended to perform sensitivity analysis of the model and discuss specific managerial insights.

Credit financing in economic ordering policies for deteriorating items with stochastic demand and promotional efforts in two-warehouse environment

Retailers are nowadays focusing on promotional activities in order to attract customers because of increasing competition. Promotional efforts have significant impact on the replenishment policy and the sale price of goods. In this paper, a two warehouse inventory model is developed for deteriorating items subject to promotional efforts under permissible delay in payments. Here, a price dependent stochastic demand function is considered with partially backlogged shortages. Several realistic cases, sub cases and scenarios have been taken into account and the corresponding problems have been formulated as nonlinear constrained optimisation problems. To illustrate the proposed model two numerical examples have been solved. Further, a numerical example has been extended to perform sensitivity analysis of the model and discuss specific managerial insights.

Multi-objective framework for process mean selection and price differentiation with leakage effects under price-dependent stochastic demand

Abstract This paper investigates the process mean selection problem that simultaneously considers pricing, production and quality decisions in a multi-objective context when the manufacturing firm experiences a demand leakage in simultaneously observed price-dependent stochastic demand. The output of the manufacturing process is segregated into two grades sold in primary and secondary markets using a differentiation price as the market segmentation tool. Nonconforming items are reworked at an additional cost and only price-dependent stochastic demand with leakage effects is assumed. Three objectives, expected gross income from sales, expected profit and expected product uniformity are considered in the proposed multi-objective optimization model. Two solution algorithms are proposed, a goal programming approach combined with a simulation based optimization and a multi-objective genetic algorithm. A detailed numerical experimentation is employed to compare the two algorithms.

Joint pricing, inventory, and preservation decisions for deteriorating items with stochastic demand and promotional efforts

This study models a joint pricing, inventory, and preservation decision-making problem for deteriorating items subject to stochastic demand and promotional effort. The generalized price-dependent stochastic demand, time proportional deterioration, and partial backlogging rates are used to model the inventory system. The objective is to find the optimal pricing, replenishment, and preservation technology investment strategies while maximizing the total profit per unit time. Based on the partial backlogging and lost sale cases, we first deduce the criterion for optimal replenishment schedules for any given price and technology investment cost. Second, we show that, respectively, total profit per time unit is concave function of price and preservation technology cost. At the end, some numerical examples and the results of a sensitivity analysis are used to illustrate the features of the proposed model.