A joint dynamic pricing and advertising model of perishable products

Advertising and dynamic pricing play key roles in maximizing profit of a firm. In this paper a joint dynamic pricing and advertising problem for perishable products is investigated, where the time-varying demand rate is decreasing in sales price and increasing in goodwill. A dynamic optimization model is proposed to maximize total profit by setting a joint pricing and advertising policy under the constraint of a limited advertising capacity. By solving the dynamic optimization problem on the basis of Pontryagin’s maximum principle, the analytical solutions of the optimal joint dynamic pricing and advertising policy are obtained. Additionally, to highlight the advantage of the joint dynamic strategy, the case of the optimal advertising with static pricing policy is considered. Numerical examples are presented to illustrate the validness of the theoretical results, and some managerial implications for the pricing and advertising of the perishable products are provided.     

A simulation of the impacts of dynamic price management for perishable foods on retailer performance in the presence of need-driven purchasing consumers

Numerous studies have investigated dynamic pricing for perishable products. The models have been designed to determine an optimal pricing structure and improve retailer performance. Previous studies on pricing models for perishable products have considered various assumptions of consumer demand and purchasing behaviour from deterministic and stochastic price-dependent demands to myopic and strategic consumer purchasing behaviour. They have not, however, considered consumer demand in reaction to a situation where the display stock of a particular product has different qualities (such as shelf-life) and prices available at the same time. This is particularly applicable in the analysis of dynamic pricing models for perishable foods. In this paper, we investigate the impact of frequency of discount during a product’s selling period on retailer performance, by considering changes in consumer purchasing behaviour in response to the display stock of a particular food product having different remaining shelf-life and prices. On the basis of a literature review and data obtained from interviews with food retailers, a simulation study is performed to compare the performance of different pricing policies. The results demonstrate the benefits gained by adopting more dynamic price policies.     

A multi-period ordering and clearance pricing model considering the competition between new and out-of-season products

The joint management of pricing and inventory for perishable products has become an important problem for retailers. This paper investigates a multi-period ordering and clearance pricing model under consideration of the competition between new and out-of-season products. In each period, the ordering quantity of the new product and the clearance price of the out-of-season product are determined as decision variables before the demand is realized, and the unsold new product becomes the out-of-season one of the next period. We establish a finite-horizon Markov decision process model to formulate this problem and analyze its properties. A traditional dynamic program (DP) approach with two-dimensional search is provided. In addition, a myopic policy is derived in which only the profit of the current period is considered. Finally, we apply genetic algorithm (GA) to this problem and design a GA-based heuristic approach, showing by comparison among different algorithms that the GA-based heuristic approach is more performance sound than the myopic policy and much less time consuming than the DP approach.     

Integration of pricing and capacity allocation for perishable products

For years pricing and capacity allocation decisions in most revenue management models have been carried out independently. This article presents a comprehensive model to integrate these two decisions for perishable products. We assume that the supplier sells the same products to different micro-markets at distinct prices. Throughout the sales season, the supplier faces decisions as to which micro-markets or customer classes should be served and at what prices. We show that (i) at any time, a customer class is active (being served) if and only if the price offered is over a threshold level, but the optimal price may not be the highest one of the supplier’s choice; (ii) when the price decision is made in conjunction with inventory, it is similar to the procedure shown in pure pricing models, i.e., the optimal price comes from a subset of prices that forms a maximum increasing concave envelope; (iii) because of dynamic changes in the optimal prices, the nested-price structure does not necessarily hold in general and needs to be redefined; and (iv) the optimal pricing and capacity control policy is based on a sequence of threshold points that incorporate inventory, price and demand intensity. Numerical examples are provided.     

Revenue management for a supply chain with two streams of customers

In this paper, we consider revenue management for a service supply chain with one supplier and one retailer. The supplier has a limited capacity of a perishable product and both the supplier and the retailer face customers. Each customer may choose to buy a product from either the supplier or the retailer by considering prices and the cost associated with switching. For the centralized model, the supplier determines the selling prices for both herself and the retailer, and the retailer simply collects a commission fee for each product sold. We derive monotone properties for the revenue functions and pricing strategies. Further, we show that the commission fee increases the retailer’s price while decreasing the supplier’s and leads to efficiency loss of the chain. For the decentralized decision-making model, the supplier and the retailer compete in price over time. Two models are considered. In the first, the retailer buys products from the supplier before the selling season and in the second the retailer shares products with the supplier in retailing. For both models, we discuss the existence of the equilibrium and characterize the optimal decisions. Numerical results are presented to illustrate properties of the models and to compare the supply chain performance between the centralized and the decentralized models.     

考虑网络外部性的生鲜企业渠道选择策略研究

考虑到生鲜产品容易变质而且线上配送时间较长,并且线上销售可为消费者带来额外网络外部性,传统生鲜企业在电商冲击的背景下需要考虑是否入驻电商平台开拓线上业务。为解决此类企业所面临渠道选择问题,本文考虑一个传统生鲜企业和一个主导电商市场的电商平台,并通过构建理论模型研究企业最优生鲜产品定价和渠道选择策略。研究结果表明,若平台所收取年服务费较低,则企业应入驻平台;反之,企业不应入驻平台。此外,消费者网络外部性敏感程度对企业入驻平台行为具有正影响。在拓展模型,本文考虑分散式供应链情形下企业最优渠道选择,结果表明相较于集中式决策,分散式供应链情形下零售商更不愿意入驻平台。此外,本文通过设计收益共享契约以协调生鲜企业与电商平台,并发现通过契约协调,零售商更愿意入驻电商平台。     

Supply chain network operations management of a blood banking system with cost and risk minimization

Blood service operations are a key component of the healthcare system all over the world and yet the modeling and the analysis of such systems from a complete supply chain network optimization perspective have been lacking due to their associated unique challenges. In this paper, we develop a generalized network optimization model for the complex supply chain of human blood, which is a life-saving, perishable product. In particular, we consider a regionalized blood banking system consisting of collection sites, testing and processing facilities, storage facilities, distribution centers, as well as points of demand, which, typically, include hospitals. Our multicriteria system-optimization approach on generalized networks with arc multipliers captures many of the critical issues associated with blood supply chains such as the determination of the optimal allocations, and the induced supply-side risk, as well as the induced cost of discarding the waste, while satisfying the uncertain demands as closely as possible. The framework that we present is also applicable, with appropriate modifications, to the optimization of other supply chains of perishable products.     

考虑预定时间限制的酒店客房定价决策

假定顾客是价格敏感的、房价的变化会带来需求的变化以及酒店可在预定期初调整价格策略以便影响市场需求将客房充分预售的条件下,给出了考虑预定时间限制的酒店客房定价决策模型,分析了最优房价、期望收益随预定时限的变化情况.     

Competitive Multi-period Pricing for Perishable Products: A Robust Optimization Approach

We study a multi-period oligopolistic market for a single perishable product with fixed inventory. Our goal is to address the competitive aspect of the problem together with demand uncertainty using ideas from robust optimization and variational inequalities. The demand function for each seller has some associated uncertainty and we assume that the sellers would like to adopt a policy that is robust to adverse uncertain circumstances. We believe this is the first paper that uses robust optimization for dynamic pricing under competition. In particular, starting with a given fixed inventory, each seller competes over a multi-period time horizon in the market by setting prices and protection levels for each period at the beginning of the time horizon. Any unsold inventory at the end of the horizon is worthless. The sellers do not have the option of periodically reviewing and replenishing their inventory. We study non-cooperative Nash equilibrium policies for sellers under such a model. This kind of a setup can be used to model pricing of air fares, hotel reservations, bandwidth in communication networks, etc. In this paper we demonstrate our results through some numerical examples.     

Two-period dynamic versus fixed-ratio pricing in a capacity constrained duopoly

This paper analyzes the impact of dynamic and fixed-ratio pricing policies on firm profits and equilibrium prices under competition. Firms that have equal inventories of perfectly substitutable and perishable products compete for customer segments that demand the product at different times. In each period, customers first purchase from the low price firm and then from the high price firm up to their inventories, provided the prices are lower than the maximum they are willing to pay. The main conclusions of this paper are as follows: although dynamic pricing is a more sophisticated policy than fixed-ratio pricing, it may lead to decreased equilibrium profits; under both pricing policies, one firm assumes the role of a low-cost high-output firm while the other assumes the role of a high-cost low-output firm; and, the supply demand ratio has more impact on the outcome of the competition than the heterogeneity in consumer reservation prices.     

Dynamic pricing with uncertain production cost: An alternating-move approach

This article studies a two-firm dynamic pricing model with random production costs. The firms produce the same perishable products over an infinite time horizon when production (or operation) costs are random. In each period, each firm determines its price and production levels based on its current production cost and its opponent’s previous price level. We use an alternating-move game to model this problem and show that there exists a unique subgame perfect Nash equilibrium in production and pricing decisions. We provide a closed-form solution for the firm’s pricing policy. Finally, we study the game in the case of incomplete information, when both or one of the firms do not have access to the current prices charged by their opponents.     

Incorporating manufacturing lead times in joint production-marketing models: A review and some future directions

In many industries the pricing of a product over time can be used to manage demand for the product. Lead time, or promised delivery time is often a significant factor in price negotiations. However, the production planning literature has largely treated pricing decisions as exogeneous while focusing on the allocation of production capacity between products over time. On the other hand, the marketing literature has generally ignored the effects of capacity constraints and focused on the effects of pricing. In this paper, we begin by reviewing the existing literature on integrative production-marketing research, focusing on those models that consider lead times and capacity. We suggest a number of directions for future research that take advantage of recent developments in production planning models, as well as explicit modeling of feedback loops governing key parameters, which suggest a broader view of the problem.     

Dynamic channel control and pricing of a single perishable product on multiple distribution channels

This paper studies dynamic channel control and pricing of a single perishable product distributed through multiple channels with the objective of maximizing the total expected profit over a finite horizon. We consider two types of commissions, namely proportional and fixed commissions, on the third-party channels and utilize stylized linear functions to characterize dependent demand flows from different channels. We show that, the magnitude of the opportunity cost of capacity uniquely determines the optimal channel control, at any given inventory level and periods to go. Consequently, we are able to derive the optimal price offered on each channel as a function of the opportunity cost of capacity in closed form. This significantly reduces the computational complexity of the stochastic dynamic program when parameters are constant with time. When channels are independent, we provide a necessary and sufficient condition for the optimality of a nested channel control policy by commission rates. The same condition is also sufficient for the optimality of the nested channel control policy in a distribution system with two dependent channels. We then characterize the structural properties of the optimal pricing and channel control policies. Finally, we explore the impact of the substitution effect on the channel control through numerical studies and gain managerial insights.     

Dynamic pricing for perishable items with costly price adjustments

Dynamic pricing is widely adopted in inventory management for perishable items, and the corresponding price adjustment cost should be taken into account. This work assumes that the price adjustment cost comprises of a fixed component and a variable one, and attempts to search for the optimal dynamic pricing strategy to maximize the firm’s profit. However, considering the fixed price adjustment cost turns this dynamic pricing problem to a non-smooth optimal control problem which cannot be solved directly by Pontryagin’s maximum principle. Hence, we first degenerate the original problem into a standard optimal control problem and calculate the corresponding solution. On the basis of this solution, we further propose a suboptimal pricing strategy which simultaneously combines static pricing and dynamic pricing strategies. The upper bound of profit gap between the suboptimal solution and the optimal one is obtained. Numerical simulation indicates that the suboptimal pricing strategy enjoys an efficient performance.     

Pricing longevity risk with the parametric bootstrap: A maximum entropy approach

In recent years, there has been significant development in the securitization of longevity risk. Various methods for pricing longevity risk have been proposed. In this paper we present an alternative pricing method, which is based on the maximization of the Shannon entropy in physics. Specifically, we propose implementing this pricing method with the parametric bootstrap (Brouhns et al., 2005), which is highly flexible and can be performed under different model assumptions. Through this pricing method we also quantify the impact of cohort effects and parameter uncertainty on prices of mortality-linked securities. Numerical illustrations based on longevity bonds with different maturities are provided.     

Inventory and coordination issues with two substitutable products

This study considers a two level supply chain in a newsboy setting with two substitutable products. Demands for the two products are assumed independent as long as both are available. If, however, a product stocks out, some of its demand is transferred to the available one with a known probability which ultimately creates a dependence on the amount of purchased items. The retailer is allowed to return some or all of the unsold products to the manufacturer with some credit. The expected chain profit, the retailer’s and the manufacturer’s profit expressions are derived under general conditions. Special cases are inspected to investigate the conditions under which channel coordination is achieved. It is demonstrated that channel coordination can not be achieved if unlimited returns are allowed with full credit, a result that agrees with the findings of Pasternak [B.A. Pasternack, Optimal pricing and return policies for perishable commodities, Market. Sci. 4 (1985) 166–176] for the single item case. For the cases of unlimited returns with partial credit, the conditions for coordination are derived for one way full substitutions. For exponential demand explicit expressions for the channel and retailer’s expected profit functions are provided.     

Dominance,bargaining power and service platform performance

In this paper we study the relationship between a firm (hotel) and a service platform (Ctrip.com). We start with a newsvendor hotel facing two kinds of customers. D-customers order the room directly from the hotel front desk; C-customers order the room through Ctrip.com. Ctrip.com charges the hotel while introducing its members to the hotel. The hotel decides how many rooms are allotted to Ctrip.com to achieve optimal profit. We consider the situation where one party’s demand cannot be observed by another, and study the commonly used wholesale price contract. Interestingly, the contract can always coordinate the system. We then investigate the influence of bargaining power on the profit division under situations where Ctrip.com and hotel, respectively, dominate the system, and find that increasing (or decreasing) a party’s bargaining power without considering the other does not necessarily benefit (or damage) the first party. Further, we discuss how the parties choose dominance and appropriate bargaining power to make a trade-off for better cooperation. An interesting phenomenon is that bargaining power for each party can be identical when any party dominates the system. We also propose a threshold at which the wholesale price contracts can always be the Pareto optimal for the channel.     

基于需求的实时网络定价策略

价格作为一种网络拥塞控制管理与资源分配的机制不断地表现出较高的效率。基于对网络使用实际流量的信息，本提出了一种实时的网络定价策略——基于需求的实时网络定价策略。该定价策略由三部分构成：固定连接费、资源使用费及网络拥塞费。与传统的定价策略相比，基于需求的实时网络定价策略更能反映实际的需求情况，在网络拥塞控制管理与网络资源分配等方面有更高的效率。     

A survey of deterministic models for the EOQ and EPQ with partial backordering

Models for the basic deterministic EOQ or EPQ problem with partial backordering or backlogging make all the assumptions of the classic EOQ or EPQ model with full backordering except that only a fraction of the demand during the stockout period is backordered. In this survey we review deterministic models that have been developed over the past 40 years that address the basic models and extensions that add other considerations, such as pricing, perishable or deteriorating inventory, time-varying or stock-dependent demand, quantity discounts, or multiple-warehouses.     

基于等量订货的可替代易变质产品库存策略研究

零售商常常根据不同"年龄"的易变质产品质量的差异而制定不同的价格,从而会带来不同的顾客需求.而当某个"年龄"的产品缺货时,顾客可能会购买其他"年龄"的产品作为替代.在上述背景下,本文考虑某个销售季节内多周期等量订货策略,分别在单周期和多周期情况下找到了零售商的最优订货量.