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We study how a monopolist seller should price an indivisible product iteratively to the consumers who are connected by a known link-weighted directed social network. For two consumers $u$ and $v$, there is an arc directed from $u$ to $v$ if and only if $v$ is a fashion leader of $u$. Assuming complete information about the network, the seller offers consumers a sequence of prices over time and the goal is to obtain the maximum revenue. We assume that the consumers buy the product as soon as the seller posts a price not greater than their valuations of the product. The product’s value for a consumer is determined by three factors: a fixed consumer specified intrinsic value and a variable positive (resp. negative) externality that is exerted from the consumer’s out(resp. in)-neighbours. The setting of positive externality is that the influence of fashion leaders on a consumer is the total weight of links from herself to her fashion leaders who have owned the product, and more fashion leaders of a consumer owning the product will increase the influence (external value) on the consumer. And the setting of negative externalities is that the product’s value of showing off for a consumer is the total weight of links from her followers who do not own the product to herself, and more followers of a consumer owning the product will decrease this external value for the consumer. We confirm that finding an optimal iterative pricing is NP-hard even for acyclic networks with maximum total degree $3$ and with all intrinsic values zero. We design a greedy algorithm which achieves $(n-1)$-approximation for networks with all intrinsic values zero and show that the approximation ratio $n-1$ is tight. Complementary to the hardness result, we design a $(1.8+𝜖)$-approximation algorithm for Barabási–Albert networks.

Manufacturers and suppliers offer temporary reductions (or permanent increases) in the price charged to the resellers for a variety of reasons. The trade promotion may be offered to the reseller at a single point in time or over a finite time-span. In addition, in reselling situations, the end demand tends to be sensitive to selling price. It is commonly found that under such trade promotion (or in stockpiling to an announced price increase), not all the quantity purchased by the reseller at discount may be passed on to the final consumer at a reduced selling price. In fact, previous studies have shown that it is optimal for the reseller to carry forward some of the quantity purchased at discount and sell it later at the regular price. It has been suggested in the literature that by placing a restriction on the reseller's purchase quantity, the supplier can restrict the reseller's forward buy quantity. In this paper, we evaluate this approach. In the rest of the paper, we present alternate schemes which are easy to administer and which insure that the supplier avoids the spike in demand that occurs in the unconstrained problem.

In this paper, we consider a seller–buyer channel in which marketing expenditure is an endogenous decision for the buyer. We assume that both the unit marketing expenditure and the unit price charged by the buyer influence the end demand for the product. We model the seller–buyer relationship as a non-cooperative as well as a cooperative game. We investigate the non-cooperative game from two perspectives: the Seller–Stackelberg model and the Buyer–Stackelberg model. In the cooperative game, we provide a procedure for outlining Pareto efficient solutions. For each model, we present a numerical example as well as sensitivity analysis with respect to the two key parameters in the model.

In this paper, an inventory model for deteriorating items with ramp-type time and price dependent consumption rate over a finite planning horizon is considered. In contrast to the traditional deterministic inventory model with static price over the entire planning horizon or fixed number of price changes over the finite time horizon, an alternative model is derived in which prices and the number of price change are to be decision variables. We show that the total profit function is concave. With the concavity, a solution procedure is presented to determine optimal prices, optimal number of pricing cycles and optimal lot size and optimal profit. We illustrate the model with numerical examples. Sensitivity analysis of the model is also carried out.

This paper studies a competitive Hotelling-style market with two symmetric banks that decide the pricing and location of their automated teller machines (ATMs). Two different systems are considered: An unregulated model wherein banks are allowed to set surcharges, and a regulated model in which surcharges are banned. We derive equilibrium outcomes and compare them in the two systems, and find that banks always maintain a certain distance between ATMs. That distance is larger, indeed maximized, under the regulatory scheme. We also show that, surprisingly, banks always perform better in the regulated model, while consumers may be worse off.

The Internet is becoming increasingly important as a sales channel. Thus, most large retail firms have adopted a multi-channel strategy that includes both web-based channels and pre-existing offline channels. In this paper, we consider joint pricing and inventory/production decision problems for members in a monopoly two-stage dual-channel retailer supply chain. For a dual-channel retailer, pricing in one channel will affect the demand in the other channel. This subsequently affects the retailer's replenishment (ordering) decisions, which have an impact on the producer's inventory/production plans and wholesale price decisions. It is clear then that pricing decisions and inventory/production decisions are interacting in each member of the supply chain and among the members in the chain as well. In this paper, we analyze joint pricing and inventory/production problems under three scenarios by incorporating intra-product line price interaction in the EOQ model. We show that a unique equilibrium exists under certain realistic conditions. We also provide numerical results that offer insights for pricing strategies for the dual-channel retailer supply chain and for product design for different channels.

Operational decisions of a monopolist firm affect expected social welfare, a fact typically ignored by OM models. Specifically, the price selected directly affects the consumer surplus, which has to be added to firm's profit to find the social welfare. We assume an uncertain, price-sensitive, demand. Production capacity is selected at the outset, but the price is chosen after demand uncertainty realized itself. This model was proposed by Van Mieghem and Dada (1999), but we extend it to other demand functions. We then compute the resulting consumer surplus. Finally, we consider such issues in a decentralized supply chain with revenue sharing.

In this paper, we investigate joint optimal capacity investment, pricing and production decisions for a multinational manufacturer who faces exchange rate uncertainties. We consider a manufacturer who sells its product in both domestic and foreign markets over a multiperiod season. Because of long-lead times, the capacity investment must be committed before the selling season begins. The exchange rate between the two countries fluctuates across periods and the demand in both markets are price dependent. Our model considers three scenarios: (1) early commitment to price and quantity with central sourcing, (2) postponement of prices and quantities with central sourcing, and (3) local sourcing. We derive the optimal capacity and the optimal prices for each scenario, and investigate the impact of the exchange rate parameters and the length of the selling season. We observe that while the price and production decisions in the domestic market are independent of the exchange rate under early commitment and local sourcing scenarios, the exchange rate between two countries directly impacts these decisions under the postponement setting. We identify thresholds and gain insights on capacity and production costs, exchange rate movement, and selling season length for the choice of entering a foreign market under all scenarios.

Firms often utilize promotion (such as coupons, advertisements, recruitment of excellent salespeople, and leafleting etc.) and dynamic adjustment of price to manage customers as well as proper production/inventory plan to satisfy the customers to get maximal profit in a firm. The decision on promotion and pricing and the decision on production/inventory must support each other. This paper addresses coordinated decision on pricing, promotion(non-price promotion) and inventory management. Specifically, we study a single item, periodic review model. The demand function is a linear demand function in which the market scale can be affected by the promotion conducted in that period. Unsatisfied demands are fully backlogged. We characterize the structure of the optimal policy that simultaneously determines the price, the promotion and the ordering quantity to maximize the total discounted profit with finite and infinite period problems. We show that the optimal replenishment policy is the quasi base stock list price target promotion policy, i.e., there exist a critical inventory level, a list price and a target promotion such that it is optimal to order up to the critical level, charge the list price and conduct the target promotion when the initial inventory is below the critical level and order nothing, conduct a higher promotion and charge a proper price to increase the demand otherwise. We also prove that the expected demand and the optimal promotion are increasing in the inventory, and price and promotion are complementary. Then we extend the problem to the case with capacity constraint. We show that the modified quasi base stock list price target promotion policy is optimal. For the joint decision problem on pricing, promotion and inventory control with positive fixed setup cost, we show that the optimal policy is (s, S, p, e) policy. That is, there exist two critical inventory levels s_t and S_t(s_t ≤ S_t), a list price p_t and a target promotion e_t in period t such that order up to S_t, charge price p_t and conduct promotion e_t when the initial inventory is less than s_t and order nothing, charge a proper price and conduct a proper promotion otherwise.

We consider a retailer, facing uncertain supply and price-sensitive stochastic demand, who has to make stocking and pricing decisions for a given selling period. We also consider the case when the demand is price-sensitive deterministic and provide a unified framework for the model with additive errors. For both scenarios, we look at the case when the price is set before receiving the supply, called simultaneous pricing and the case when the price is set after receiving it, which is called postponed pricing. We develop a procedure for finding the optimal policy for the retailer with general distributions for the supply and the demand. To study the effect of supply uncertainty on expected profit, we conduct sensitivity analysis and develop results for both pricing scenarios and give insights. The results have important implications for a retailer in the supply chain, where a portion of the inventory may be lost due to variety of factors including mishandling and failure to meet quality standards. The findings shed light on the nature and role of prices and their relationship to supply and demand.

In this paper, we study a passenger–taxi matching queue system. The system is modeled as a birth-and-death process. Since the system is so complex, we mainly focus on numerical analysis. A centralized system and a decentralized one are considered. In the centralized system, the government sets thresholds for both passengers and taxis to maximize the social welfare. We analyze the performance measures of this model, discuss the range of two thresholds that ensures positive social welfare, and numerically give the upper bound of threshold. In the decentralized system, passengers and taxis determine whether to join the system or balk based on their individual utility functions. Further, we consider the government’s tax and subsidy to the taxi drivers. Numerical results show that the social welfare function in the centralized system is concave with respect to the thresholds and the government central planning benefits the society. In the decentralized system, no matter what the passenger and taxi arrival rates are, the social welfare is concave with respect to the taxi fare. Moreover, we analyze the effect of the arrival rates and the benefits of the tax and subsidy.

In this research, we discuss three different approaches to generate demand forecasting and pricing decision for mix of national brand and store brand products in the era of big data. We derive the equilibrium wholesale price and retail price for the national brand products, and the equilibrium retail price for the store brand products based on demand forecast under three different information scenarios, including Noninformation Sharing ($N$), Information Sharing ($I$), and Retailer Forecasting ($R$). We comprehensively discuss how information collection, information sharing, forecast accuracy under era of big data affect firms’ prices and profits. Our numerical experiments illustrate and verify our analytical findings and provide further managerial insights and interpretations.

This paper investigates the impact of emergency order in a price-dependent newsvendor setting. To this end, we compare two ways handling the excess demand: the excess demand is lost and a penalty cost is incurred, or the excess demand can be satisfied by an emergency order. Which way is better depends on the emergency purchase cost $e$ in emergency-order way and the price $p$ plus penalty cost $g$ in lost-sales way. For a risk-neutral newsvendor, our results indicate that, when $e$ is not larger than $p+g$, the emergency order way can lead to smaller order quantity and higher expected profit. We continue to discuss the impact of newsvendor’s risk aversion and demand uncertainty on the optimal decisions of the two ways. Theoretical analysis and numerical examples indicate that when the emergency purchase cost is not high, the differentials of the optimal order quantities and expected profits will be larger as the degree of risk aversion/demand uncertainty increases. What is more, we prove that there exists a threshold value of the emergency purchase cost so that the two ways handling excess demand can obtain the same expected profit, and this threshold value increases as the degree of risk aversion decreases.

We investigate a setting in which two retailers sell substitutable products to a market. With the rise of group-buying (GB) consumers, each retailer has the option to open a GB channel to cater to their demand and complement its regular sales. We find that the retailers will forfeit this option to only sell in regular channels when they have scarce capacities, but both open GB channels when they have ample capacities. The situation is more intricate when their capacity levels are intermediate, in which case the equilibrium channel structure is influenced by the substitution effect and the consumers’ channel preference. A higher capacity level does not necessarily incentivize a retailer to open group-buying channel. When given the authority, the retailers under strong competition pressure prefer to commit to regular prices over tailoring regular prices to fit the channel structure. Circumstances exist in which both retailers strategically open GB channels but keep them inactive by inducing all consumers to only buy from regular channels. Moreover, the sequence whereby the retailers follow to set regular prices and decide on GB channels is inconsequential on market equilibrium. Our main findings are robust with respect to model assumptions.

Although existing contributions that explore service quality guarantee problem of a logistic service supply chain (LSSC) consider fairness concern behavior of one member, little attention is paid to considering the combination of members’ fairness concern and the joint decision of pricing and service quality guarantee in LSSC. Therefore, it is necessary to research how different fairness concern affects the joint decision of pricing and service quality guarantee in an LSSC. First considering a price and quality-sensitive logistics service market, a basic model without fairness concern of a customized LSSC is established. Then, a new model with fairness concern of a decentralized LSSC is constructed based on the basic model. The optimal decision of the LSSC with fairness concern is investigated in three cases. In each case, we analyze the effect of fairness concern on the optimal decision, and the expected profits and utilities. Finally, some numerical studies are shown to verify our theoretical analyses and some managerial insights are given.

Recent developments of information technology have increased market’s competitive pressure and products’ prices turned to be paramount factor for customers’ choices. These challenges influence traditional revenue management models and force them to shift from quantity-based to price-based techniques and incorporate individuals’ decisions within optimization models during pricing process. Multinomial logit model is the simplest and most popular discrete choice model, which suffers from an independence of irrelevant alternatives limitation. Empirical results demonstrate inadequacy of this model for capturing choice probability in the itinerary share models. The nested logit model, which appeared a few years after the multinomial logit, incorporates more realistic substitution pattern by relaxing this limitation. In this paper, a model of game theory is developed for two firms which customers choose according to the nested logit model. It is assumed that the real-time inventory levels of all firms are public information and the existence of Nash equilibrium is demonstrated. The firms adapt their prices by market conditions in this competition. The numerical experiments indicate decreasing firm’s price level simultaneously with increasing correlation among alternatives’ utilities error terms in the nests.

This study considers a shipping supply chain consisting of an ocean carrier (OC) and two competing feeder carriers (FCs) in which the OC and FCs can canvass for cargos. We propose two contrastive structures: structure O (the OC canvasses for cargos) and structure F (the FCs canvass for cargo) to study the carriers’ cargo canvassing strategies. We employ a mean-risk objective function to reflect the cargo-canvassing carriers’ different risk attitudes. We find that the cargo canvassing carrier’s risk attitude has an opposite influence on the equilibrium freight rate of the OC and FCs, which is referred to as vertical reverse effect. We identify the horizontal consistent effect, which implies that an FC’s equilibrium freight rate increases in its and the rival’s risk sensitivity coefficient. In a market with high demand volatility, the OC and FCs should set high freight rates when they are risk-seeking, while set low freight rates when they are risk-averse. In addition, we highlight that FCs canvass for cargos can lead to an incentive alignment of the OC and FCs on cargo canvassing. Our analytical results provide the operational strategies for risk-sensitive OCs and FCs to canvass for cargos.

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.

Frequent problems of counterfeiting have spawned consumer demands to monitor the entire supply chain. The application of blockchain technology with anti-counterfeiting and traceability can improve the reliability and authenticity of product information and eliminate consumer doubts about product quality. Furthermore, based on the transparency of blockchain technology, brand suppliers can independently obtain the market demand information through information sharing. This paper introduces a consumer suspicion coefficient to illustrate the application of blockchain technology in the supply chain. Considering product authenticity verification and information sharing, we study the optimal pricing and product quality decisions in a two-level supply chain under the following three scenarios: (1) no blockchain technology, a traditional supply chain, and no information sharing (case TN); (2) no blockchain technology but a traditional supply chain with information sharing (case TS); and (3) a supply chain based on blockchain technology (case BT). We find that when the consumer suspicion coefficient increases, consumers will have limited faith in the authenticity of the product, which will affect the retailer’s optimal decision and profit. By comparing the equilibrium results of several cases, we also find that demand information sharing by the retailer may not achieve a win-win outcome in a decentralized channel in the absence of blockchain technology. Under demand information sharing based on blockchain technology, however, if the consumer suspicion coefficient exceeds a certain threshold, the brand supplier and retailer can achieve a win–win outcome. In addition, the extended models reveal that in a centralized supply chain, regardless of the state of market demand, blockchain technology can always improve product quality and retail price and optimize supply chain profit.

Copycat issues and unreliable purchasing agents have challenged cross-border consumption and hurt the brands and online platforms significantly. We explicate a setting in which a platform orders from a brand, then sells and competes with the purchasing agents in an overseas market. Worried about the copycat issues, consumers undertake risk when purchasing from both platforms and agents. The blockchain adoption may help release this uncertainty by purchasing from a platform. We show the values and impacts of this new technology on the platform, brand and consumers. It is interesting to observe that the platform does not always have incentive to adopt blockchain, even if it is costless. In the presence of blockchain, we show that the revenue sharing, two-part tariff and profit sharing contracts can achieve supply chain coordination, but the cost sharing contract fails to do so. In the extended models, we discuss what will happen when the brand decides domestic retail price and the platform links optional information nodes to blockchain.