Single Retailer Research Articles

A closed-loop supply chain inventory model with stochastic demand, exchange rate, green investment, and carbon tax

In this paper, a mathematical inventory model for a closed-loop supply chain consisting of a single manufacturer and a single retailer is investigated under a stochastic environment and imperfect production. The manufacturer adopts a remanufacturing policy to recover returned products from the market. The model takes into account exchange rate disparities because the supply chain’s participants are in separate countries. The model also considers carbon emissions, which are expected to be produced from storage, transportation, and production. A carbon policy, namely carbon tax, is implemented to manage the overall emissions resulting from the supply chain. To cope with carbon restrictions, the manufacturer has an opportunity to invest in green technologies. The objective of the study is to find optimal shipment quantity, number of deliveries, safety factor, and green investment such that the joint total cost is minimized. An iterative procedure is suggested to solve the proposed problem, and a numerical example is presented for model validation. The findings imply that variations in the production rate and carbon tax have a significant influence on the model’s performance. Aside from that, the results reveal that uncertainty in the exchange rate and production flaws are important factors that must be considered by managers in making inventory decisions, especially those related to the number of deliveries, frequency of deliveries, and the amount of money invested in green technology. Finally, a sensitivity analysis is provided to explain the behavior of the model.

Pricing policies for a competitive dual-channel supply chain with green investment and sales effort under revenue-sharing contract

In view of the mushroom development of web-based business and green production, a few organizations have moved to produce ecological friendly items and utilized the online channel to build up the competition. This paper deals with a two-echelon sustainable dual-channel supply chain containing two manufacturers and a single retailer. One manufacturer of the investigated supply chain produces a traditional non-green item, and another one releases a substitutable green item. The demand of both the item at the online and offline channel is a function of the sales price, greenness level, sales effort of the retailer. Furthermore, we have discussed the criteria for optimal pricing and greening strategy of supply chain members and the sales effort level of the retailer under a centralized and decentralized model. To enhance the supply chain performance, a revenue-sharing contract has been proposed, subject to the pareto improvement of each channel member. The numerical result demonstrates that the proposed revenue-sharing contract can enhance the manufacturer’s profit as well as system profit compared to the centralized and decentralized model and ensure higher profit for all the members than the decentralized model. Moreover, the item in the centralized model enjoys the highest green level than all other scenarios. Sensitivity analysis exhibits that a higher value of greening cost reduces the manufacturer’s green level, decreasing the sales price.

Existence of equilibrium in a dynamic supply chain game with vertical coordination, horizontal competition, and complementary goods

We consider supply chain competition and vertical coordination in a linear–quadratic differential game setting. In this setting, supply chains produce complementary goods and each of them includes a single manufacturer and a single retailer who coordinate their decisions through a revenue-sharing contract with a wholesale price and a fixed sales revenue share. We study a multiple leader-follower Stackelberg game where the manufacturers are the leaders and the retailers are the followers. Competition occurs at both levels of the supply chains. Retailers play Nash and compete in price; manufacturers also play Nash but they compete in choosing their production capacities by exploiting the equilibrium price decisions made by the retailers. We show that open-loop Nash equilibria exist when the manufacturers only receive a wholesale price (there are no longer exploiting the equilibrium price decision made by the retailers, however). When the manufacturers receive both a wholesale-price and a share of the retailers’ sales revenues, equilibria generally no longer exist. The non-existence of an equilibrium stems from the fact that the manufacturers’ instant profits are discontinuous functions of their production capacities. This discontinuity leads to a major technical difficulty in that one cannot apply standard optimal control approaches to study the equilibria of the dynamic game. Our results illustrate the possibility that competition between supply chains might not be sustainable when they sell complementary products and rely on a revenue-sharing agreement.

Information Design and Sharing in Supply Chains

We study the interplay between inventory replenishment policies and information sharing in the context of a two-tier supply chain with a single supplier and a single retailer serving an independent and identically distributed Gaussian market demand. We investigate how the retailer’s inventory policy impacts the supply chain’s cumulative expected long-term average inventory costs [Formula: see text] in two extreme information-sharing cases: (a) full information sharing and (b) no information sharing. To find the retailer’s inventory policy that minimizes [Formula: see text], we formulate an infinite-dimensional optimization problem whose decision variables are the MA([Formula: see text]) coefficients that characterize a stationary ordering policy. Under full information sharing, the optimization problem admits a simple solution and the optimal policy is given by an MA(1) process. On the other hand, to solve the optimization problem under no information sharing, we reformulate the optimization from its time domain formulation to an equivalent z-transform formulation in which the decision variables correspond to elements of the Hardy space H2. This alternative representation allows us to use a number of results from H2 theory to compute the optimal value of [Formula: see text] and characterize a sequence of ϵ-optimal inventory policies under some mild technical conditions. By comparing the optimal solution under full information sharing and no information sharing, we derive a number of important practical takeaways. For instance, we show that there is value in information sharing if and only if the retailer’s optimal policy under full information sharing is not invertible with respect to the sequence of demand shocks. Furthermore, we derive a fundamental mathematical identity that reveals the value of information sharing by exploiting the canonical Smirnov–Beurling inner–outer factorization of the retailer’s orders when viewed as an element of H2. We also show that the value of information sharing can grow unboundedly when the cumulative supply chain costs are dominated by the supplier’s inventory costs. Funding: R. Caldentey acknowledges the University of Chicago Booth School of Business for financial support. Supplemental Material: The online appendix is available at https://doi.org/10.1287/moor.2023.008 .

Obtaining Conservative Estimates of Integrated Profitability for a Single-Period Product in an Own-Branding-and-Manufacturing Enterprise with Multiple Owned Channels

The achievable capacity index (ACI) is a simple and efficient approach for estimating the profitability of newsboy-type products, wherein profitability is defined as the probability of achieving the target profit by optimizing the order quantity. At present, the ACI is applicable to single retail stores (i.e., single demand) but not to multiple sales channels (i.e., multiple demand). This paper presents an integrated achievable capacity index (IACI) by which to measure the aggregate profitability of multiple mutually independent channels under normally distributed demand. An unbiased IACI estimator is also developed, to which is applied the Taylor expansion to approximate its sampling distribution, wherein the sizes, means, and variances of demand differ in each channel. Furthermore, overestimates due to sampling error are avoided by deriving the lower confidence bound for the IACI. This paper also provides generic tables to aid managers seeking conservative estimates of profitability. The applicability of the proposed scheme is demonstrated numerically using a real-world example involving an own-branding-and-manufacturing (OBM) enterprise with multiple owned channels.

Supply chain model having stochastic lead time demand with variable production rate and demand dependent on price and advertisement

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.

Optimal investment and coordination strategies for digital technology adoption in a dual-channel supply chain

Digitization has become a necessity. How upstream and downstream companies in the supply chain coordinate digital transformation is a challenge. To this end, this paper develops a dynamic differential game model that includes a single manufacturer and a single retailer, both of which can decide whether or not to invest in digital applications and thus classify them into Scenarios M and R. The result shows that, compared to the R model, in the M model, the manufacturer sets a higher wholesale price that will suppress the sales volume in the online channel, but its overall profit increase; adopting the M model may be more favorable to both parties, but for the retailer, there is a risk that the manufacturer may charge high wholesale prices. In contrast, for the manufacturer, the retailer has a free-riding behavior. Based on this, this paper proposes an improved model F, where the retailer shares a certain percentage of the investment cost of digital technology to incentivize the manufacturer to invest in digital technology and share information with the retailer. It shows that in this scenario, the supply chain participants realize a win–win situation and make the level of digital technology higher than in the previous two scenarios.

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.

Retail Category Management with Slotting Fees

Problem definition: Slotting fees are lump-sum payments retailers demand from manufacturers to include manufacturers’ products in their assortments. Although retailers regard slotting fees as part of doing business, some manufacturers claim that slotting fees limit their ability to compete on a level playing field with other manufacturers. Considering these conflicting views, we study the role of manufacturer competition in the emergence of slotting fees and how slotting fees affect retailers’ category management (i.e., assortment and pricing) decisions. Methodology/results: We consider a game-theoretic model with a single retailer and two competing manufacturers, each offering a single product. The retailer makes slotting fee, assortment, and pricing decisions in the presence of an operational cost term that increases in the assortment size. The manufacturers that can afford the slotting fee set the wholesale prices for their products. This study leads to three key findings. First, slotting fees can be suboptimal when their absence would trigger intense wholesale price competition. Second, depending on the retailer’s operational cost and the intensity of manufacturer competition, slotting fees create three distinct effects -category expansion, rent extraction, and competitive exclusion under which product variety (i.e., the retailer’s assortment size) increases, remains unchanged, and decreases, respectively. Third, slotting fees are most (least) beneficial for the retailer when they lead to a decrease (increase) in product variety. Managerial implications: This study not only illustrates that retailers can use slotting fees as a strategic tool to control the intensity of manufacturer competition but also reveals how slotting fees impact retailers’ assortment and pricing decisions, with implications for manufacturers and policy makers. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0143 .

Integrated conservative profitability evaluation for newsboy-type product in an OBM group

ABSTRACT Manufacturers in competitive markets can enhance profit opportunities by transforming their business model to own branding and manufacture (OBM). Note however that in situations involving limited storage and production capacity, OBM groups must determine the optimal preparation quantity and frequently evaluate profitability in all channels. This is particularly important when dealing with newsboy-type (i.e. single-period) products. The achievable capacity index (ACI) can effectively measure and estimate the profitability of a newsboy-type product. However, the ACI is applicable only to measure a single product in a single retail point. In the current study, we developed an integrated achievable capacity index (IACI) to enable OBM groups with owned channels to measure the overall profitability with multiple independent normal demands. To estimate the true IACI, we derived the statistical properties of the IACI estimator based on the historical demand data. The lower confidence bound on IACI (LCBIA) was also presented to prevent overestimation due to sampling error. The LCBIA values for various values of parameters were summarized as the generic tables for the manager’s convenience pertaining to decision-making in conservative profitability evaluation. Finally, the applicability of the proposed scheme was assessed by applying numerical and sensitivity analyses to a real-world OBM example.

Low-Carbon supply chain optimisation with carbon emission reduction level and warranty period: nash bargaining fairness concern

This study incorporates fairness concern in a low-carbon supply chain coordination mechanism where a single manufacturer sells its product to consumers through a single retailer. We develop four different scenarios of the Stackelberg master-slave game utility model—both members are neutral (NN), the manufacturer (FN) or retailer (NF) has fairness concern, and both are not neutral (FF), where the Nash bargaining fairness reference is leveraged to capture the impact of fairness preference on low-carbon supply chain optimisation decision-making profits, level of carbon emission reduction, warranty period, and revenue-sharing. Finally, numerical studies are conducted to quantify the impact of the Nash bargaining fairness concern. Research shows that: (1) fairness concern made it worse for the retailer but beneficial for the manufacturer and the system. (2) fairness concern causes a reduction in the level of carbon emission reduction and warranty period. However, the reduction of carbon emission reduction trading price and a certain range of revenue sharing effectively reduces the impact of fairness concern on members. (3) The revenue-sharing contract effectively reduces the negative impacts of fairness concern on supply chain members. The paper is a guide for enterprises development and cooperation but also provides empirical evidence for the government.

Production-and-order strategy with demand information updating and uncertain spot price

We study production-and-order strategy in a two-echelon supply chain consisting of a single manufacturer and a single retailer in which both market demand and spot price are uncertain. The retailer updates early demand information through observing new market signal during long production season. The retailer may order product before the demand is updated by signing wholesale price contract (called a contract order), or order from the manufacturer in spot market after the demand is updated (called a spot order). In a retailer-led Stackelberg game, we construct a two-stage dynamic decision model to derive the optimal equilibrium solutions for the production and order quantity under both contract order strategy and spot order strategy. We characterize the conditions under which demand information updating benefits or hurts the members and a win-win is achieved. In sharp contrast to the existing findings in that the retailer always prefers to order late until demand information is updated, we discover that the retailer may prefers to order early when the spot price uncertainty is above a certain threshold. Then, we design a single-side payment contract to stimulate the manufacturer to choose order mode satisfying the retailer’s preference.

Does blockchain technology need to be introduced in the closed-loop supply chain based on product lifecycle management?

Resource wastage, prevalent in all industries, hinders sustainable economic and social development. Inspired by the application of blockchain technology in product traceability, we find that government investment in blockchain technology platforms (BTP) can facilitate the recycling of waste products. We develop a closed-loop supply chain (CLSC) model consisting of a single manufacturer and a single retailer, examining the impact of BTP on the CLSC and its potential benefits to the government. The results show that BTP increases retail prices and market demand within the CLSC but has a non-monotonic impact on wholesale prices. Interestingly, we find that even when the BTP unit cost is moderate, BTP can still enhance CLSC profits if the recycling rate falls below a certain threshold. Furthermore, in scenarios with a high service elasticity coefficient, CLSC can leverage BTP to boost profits, even when the unit usage cost is substantial. Under specific conditions, timely investments in BTP can augment social welfare for the government. Notably, government investment in BTP becomes imperative when the recycling rate is relatively low, and the environmental burden is significant. Finally, this paper explores the conditions conducive to collaborative implementation of BTP by the government and CLSC, providing a valuable reference for their effective BTP implementation.

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

Remanufacturing closed-loop supply chain decision comparison under multiple carbon policies

Abstract This article constructs a closed-loop supply chain system including a single manufacturer and a single retailer and studies the optimal decision problem of enterprises under three different carbon reduction policies. Three supply chain game models were constructed to research the impact of different carbon reduction policies on the decisions of supply chain members. The results revealed that:(1) The carbon emission reduction level of the manufacturer is negatively correlated with the recycling price of used products and the abatement cost factor;(2) When the carbon trading price is equal to the tax rate, the carbon cap and trade policy is more conducive to promoting the manufacturer to improve the level of carbon emission reduction;(3) When the carbon trading price is low, mixed carbon policy is more favorable for the manufacturer to increase its carbon emission reduction. The research results of this study can provide certain suggestions for the government to implement a reasonable carbon reduction policy.

Incorporating transportation costs into the single and multiple items newsvendor problems.

The efficiency and responsiveness of supply chains are vitally dependent on inventory replenishment and transportation decisions. In this paper, we study a supply chain consisting of a single retailer ordering seasonal products within the newsvendor framework. The primary objective of the paper is to investigate the retailer's decision-making process, aimed at determining the optimal replenishment quantities and selecting the appropriate mix and size of the truck fleet. Initially, we formulate a mathematical model where the retailer exclusively manages a limited fleet of its own trucks for inbound transportation of a single seasonal product. In this context, we determine a lower breakeven point for the fixed transportation cost than what has been previously proposed in the literature. Subsequently, we examine a commonly encountered transportation scenario where the retailer has the opportunity to expand its fleet size by leasing trucks from the external market. The outcomes of the numerical example indicates that the flexibility resulting from the utilization of different types of trucks can lead to reduced overall costs. We also address the practical transportation problem of efficiently shipping various seasonal products solely with the retailer's own trucks. For this complex problem, we propose an optimal solution procedure based on Lagrangian method. We show that the joint replenishment of multiple products results in cost savings and enhances utilization of the trucks' capacities.

Supply chain contract design considering carbon tax policy under demand information asymmetry

AbstractOur paper constructs a low‐carbon supply chain (LSC) with a single manufacturer producing low‐carbon products and a single retailer. Assume that the retailer possesses private demand information and consider two cases: The manufacturer or the retailer determines the low‐carbon product's retail price. By constructing principal‐agent models, we obtain the optimal menu of contracts in each case. The impacts of the carbon tax rate and information asymmetry on LSC members' equilibrium solutions and expected profits are discussed. The results show that, given certain conditions, both the LSC members may obtain more expected profits under information asymmetry by introducing appropriate contracts.

Risk management for barter exchange policy under retail industry

Nowadays, barter exchange has become growingly popular in the national and global industries as an alternative to excessive inventory transfers. Many companies exchange their surplus products on barter platforms for products they need without using money. In a traditional supply chain, the retailer holds unsold products that hinder the supply chain's profitability from reaching its maximum level. This paper solves this issue by proposing a stochastic model of two players (single manufacturer, single retailer) with trade-credit (delayed payment) and barter exchange policy under a supply chain management. In this work, to entice the retailer and increase sales, the manufacturer grants a credit payment facility to the retailer on the items ordered for a specified period, and the manufacturer does not charge any interest on the outstanding amount during this credit period. The concept of a credit period raises the possibility of default risk. In this case, some interest is charged. Several investments are made here to diminish setup and ordering costs and improve the product quality of the system. This work focuses on the flexible production to manage the demand uncertainty and the marginal reduction technology to lessen carbon emissions that occur during the production and inventory holding. In contrast, a retailer can exchange unsold items in the barter market for its required products, which is extensively discussed in this study. Finally, the maximum profit is assessed in terms of credit period, investments, quality improvement, and production rate. The result numerically and graphically proves a huge impact of the barter platform for any business industry on overstock transfers, conserving cash, managing unpredictable demand, and reaching the maximum profit. Moreover, the significant finding is observed in the proposed work that the idea of the flexible production, barter exchange policy, and several investments increase the system profit up to 50.55%.

Nash-Bargaining Fairness Concerns under Push and Pull Supply Chains

Unbalanced power structures can lead to an inequitable distribution of the supply chain’s profits, creating unstable supply chain relationships and serious social problems. This paper builds a two-tier newsvendor model composed of a single supplier and a single retailer and introduces Nash bargaining as a reference for fairness. We investigate (1) the impact of fairness concerns on the performance of a retailer-dominated supply chain and a manufacturer-dominated supply chain; (2) how demand uncertainty affects the inequitable state; and (3) how overestimated and underestimated values of fairness concerns affect supply chain performance when fairness concerns are private information. After solving the equilibrium solution of the Stackelberg game and Nash-bargaining games and numerical analyses, it is shown that unilateral fairness concerns by the Stackelberg leader or follower can motivate the leader to sacrifice its profit to reduce their income inequality by offering a coordinating wholesale price. Of course, it is also effective for both participants to be fair-minded as soon as their fairness sensitivity is moderate enough. However, followers’ fairness concerns are more effective at decreasing inequity, while leaders can improve social welfare, i.e., increase the entire supply chain’s efficiency as well as market scale. We also find that in a more uncertain market, fewer fairness-concerned participants are supposed to reach a relatively fair condition. In addition, we conclude that sometimes asymmetric information about fairness concerns can improve the profit share of the disadvantaged and even channel efficiency. This paper extends the study of Nash-bargaining fairness concerns to retailer-dominated newsvendor models and enriches the field, when fairness concerns are asymmetric information.

Research on Supply Chain Pricing Strategies under Carbon Emission Quota Constraints

In order to reduce the carbon emissions of manufacturers and retailers in their business activities, carbon emission limits must be set for manufacturers and retailers respectively, and they must make favorable decisions within the limits. This paper will focus on a two-level supply chain system composed of a single manufacturer and a single retailer, and explore the optimal wholesale price, optimal retail price, and optimal profit under four scenarios: neither is constrained by carbon quotas, only the manufacturer is constrained by carbon quotas, only the retailer is constrained by carbon quotas, and both are constrained by carbon quotas, by constructing Lagrange functions. Comparative analysis will be conducted. Research has shown that only when manufacturers are subject to carbon quotas, the optimal wholesale and retail prices will rise, and the optimal profits of both manufacturers and retailers will decrease; When retailers are constrained by carbon quotas, whether manufacturers are constrained by carbon quotas does not affect the optimal price and profit; When both are subject to carbon emission restrictions and retailers increase their carbon emission quotas, manufacturers will lower wholesale prices and retailers will lower retail prices.