Wansheng Tang

Joint dynamic pricing and investment strategy for perishable foods with price-quality dependent demand

The food quality has always played an important role in the retail process since it has been considered as a direct factor to influence a consumer’s purchase decision. In this paper, we formulate an inventory model for perishable foods, in which the demand depends on the price and quality that decays continuously. The objective is to determine a joint dynamic pricing and preservation technology investment strategy while maximizing the total profit from selling a given initial inventory of foods. We first prove the existence of an optimal solution based on Filippov–Cesari theorem. Then, we obtain all the candidates and provide the conditions that make a certain candidate be an optimal solution according to Pontryagin’s maximum principle. Next, we present an effective algorithm to search for the optimal strategy. Finally, two numerical examples are employed to illustrate the solution procedure and the results, followed by sensitivity analysis and managerial insights.

Optimal dynamic pricing and replenishment policy for perishable items with inventory-level-dependent demand

An inventory system for perishable items with limited replenishment capacity is introduced in this paper. The demand rate depends on the stock quantity displayed in the store as well as the sales price. With the goal to realise profit maximisation, an optimisation problem is addressed to seek for the optimal joint dynamic pricing and replenishment policy which is obtained by solving the optimisation problem with Pontryagin’s maximum principle. A joint mixed policy, in which the sales price is a static decision variable and the replenishment rate remains to be a dynamic decision variable, is presented to compare with the joint dynamic policy. Numerical results demonstrate the advantages of the joint dynamic one, and further show the effects of different system parameters on the optimal joint dynamic policy and the maximal total profit.

Pricing, service and preservation technology investments policy for deteriorating items under common resource constraints

Inventory control for deteriorating items under resource constraints is studied.Optimal pricing, service and preservation technology investments policy is obtained.The effect of resource constraints on the optimal policy is discussed.The firm prefers to invest in service for a relatively low resource capacity. This paper addresses a joint pricing, preservation technology investment, replenishment cycle and dynamic service investment problem for deteriorating items under a common resource constraint with respect to preservation technology and service investments. The evolution of service level is considered to characterize the indirect positive effect of service investment on demand. The analytical solution for dynamic service investment is first obtained under the given sales price, preservation technology and replenishment cycle by solving an optimal control problem. An algorithm is then designed to generate the optimal joint pricing, preservation technology investment, service investment and replenishment policy to maximize the total profit per unit time. Further, a numerical example is presented to illustrate the main theoretical results and the effectiveness of the algorithm, and sensitivity analysis about key parameters is conducted to obtain managerial insights. The impact of common resource constraint on the optimal investment policy is investigated, implying that for a relatively low common resource capacity, the firm prefers to invest in service improvement rather than preservation technology.

A dynamic advertising model with reference price effect

This paper develops an advertising model in which goodwill affected by advertising effort has a positive effect on reference price and market demand. In a finite planning horizon, the optimal advertising strategy is provided by solving the optimization problem on the basis of Pontryagin’s maximum principle, then the optimal sales price is obtained through one time pricing strategy. Furthermore, we extend this problem to an infinite planning horizon and present the corresponding optimal strategies. In addition, the relationships between system parameters and optimal solutions are analyzed. Numerical examples are employed to illustrate the effectiveness of the theoretical results, and to assess the sensitivity analysis of system parameters on the optimal strategies.

Joint pricing and advertising strategy with reference price effect

Consumers are susceptible to reference price effects when they make purchase decisions for a certain product. Meanwhile, the sales price and advertisement are the determinable factors that have impact on consumers’ reference price which are also fundamental marketing strategies. Therefore, how to determine an appropriate sales price and advertising effort level to maximise firms’ profits is an essential task. A joint pricing and advertising problem for a monopolistic firm with consideration of reference price effect is investigated, where consumer demand rate is price-sensitivity and depends on the gap between the sales price and the reference price in consumers’ mind. An optimisation model is established to maximise the firm’s total profit by making a joint pricing and advertising strategy. The static and dynamic joint strategies are obtained by applying Pontryagin’s maximum principle. Results show that the dynamic strategies dominate the static ones. Furthermore, the dynamic pricing and dynamic advertising strategies are strategic complements. Additionally, the length of the sales period plays a key role in determining the superiority of the two dynamic strategies. Specifically, a relatively short sales period highlights the value of the dynamic advertising while a long sales period strengthens the function of the dynamic pricing.

An Optimal Energy Efficiency Investment and Product Pricing Strategy in a Two-Market Framework

Energy efficiency (EE) level has become an essential environmental index of products and can be improved by EE innovation. With consideration of EE level evolution and market differentiation, an optimal control model under a two-market framework is proposed to investigate EE innovation and two-stage pricing strategies. Impacts of consumer environmental awareness (CEA) and EE standard on optimal investment and pricing strategies are discussed. Results indicate that environmental awareness and standard result in strategy shift. As environmental awareness increases, the EE level driven by investment strategy may switch from staying in traditional market, to expanding markets by entering the green market and remaining at the standard, till capturing the green market and keeping above that standard. Impacts of standard on strategy shift exhibit a tricky trend. For loose and appropriate standards, the producer prefers to invest more to expand market by entering the green market with the increase of standard. However, a stringent standard may prevent the producer from entering the green market. In addition, optimal prices in both stages are positively impacted by the CEA and the standard.

Who should determine energy efficiency level in a green cost-sharing supply chain with learning effect?

Abstract The increasing environmental awareness and green demands drive channel members to jointly take efforts to improve energy efficiency level of products. Considering the cost learning effect, this work develops a differential game model where the retailer (leader) sets retail margin, the manufacturer (follower) determines wholesale price and they jointly invest in energy efficiency level. Two scenarios are considered, where the decision right of energy efficiency level is respectively held by manufacturer (ME) and retailer (RE). Main results indicate that the energy efficiency level is usually governed by the manufacturer rather than the retailer, unless the retailer has a large bargaining power. Besides, the retailer’s preference on the decision right is weakened by a larger cost learning effect or energy efficiency effectiveness, but improved by a greater investment cost. This work contributes to researches of the channel members’ preference on holding the decision right of energy efficiency level in the presence of cost learning effect, and provides important managerial insights on firms’ investment and pricing strategies.

A Supplier Switching Model With the Competitive Reactions and Economies of Scale Effects

To minimize costs, a buying firm would seek sources which offer a more affordable price for the required products. On the basis of a principal-agent framework, this paper presents a buyer’s supplier switching model under asymmetric information to minimize the buying cost considering the volume-dependent switching cost, the competitive reactions and economies of scale effects of the incumbent supplier. The proposed model is first converted into an optimal control problem. Then the optimal supplier switching strategy and the corresponding transfer payment are obtained by virtue of Pontryagin’s maximum principle. It is shown that the switching cost components and competitive reactions have significant impacts on the switching decision. Only if the maximum price discount is greater than the fixed component of the switching cost, there may exist a partial switching strategy for the buyer to benefit from the competitive effects. Otherwise, the buyer should take an all-or-nothing switching strategy or no switching strategy. Some managerial implications for sourcing strategies with respect to the competitive reactions and economies of scale effects are provided. Furthermore, we propose a revenue sharing contract to highlight the advantage of the contract designed based on the principle-agent theory. Finally, we employ numerical examples to account for the proposed methods.

Coordinating a supply chain with negative effect of retailer’s local promotion on goodwill and reference price

This paper investigates a distribution channel consisting of a manufacturer and a retailer under a cooperative program, where the manufacturer determines the national advertising and quality improving effort, while the retailer decides the local promotion effort and may undertake parts of the costs of national advertising and quality improving of the manufacturer. It is assumed that the manufacturer’s national advertising and quality improving efforts positively affect the brand goodwill and reference price, whereas the retailer’s local promotion effort damages them. Three scenarios of the non-cooperative and cooperative scenarios in the decentralized supply chain, and the centralized supply chain scenario, are analyzed. The corresponding equilibrium strategies and profits are obtained and compared, which shows that the cooperative program can achieve payoff-Pareto-improving, but cannot coordinate completely the supply chain. Furthermore, a revenue sharing contract combined with two-subsidy policy is designed to coordinate the decentralized supply chain. Numerical simulation and sensitivity analysis of the coordinating results on the key system parameters are provided to verify the effectiveness of the contract, and some managerial insights are provided.

Strategic technology licensing in a supply chain

This paper deals with R&D investment and technology licensing in a supply chain formed of an original equipment manufacturer (OEM) and a contract manufacturer (CM). The R&D is conducted by the CM and the OEM agrees to pay a share of the cost. At the R&D stage, we assume that there are some uncertainties both in terms of performance of the developed technology and market uncertainties. These uncertainties are resolved in the sales stage, as technology matures and information about consumers’ preferences become available. Further, the OEM can license the technology to a third party and share the revenues with the CM. We characterize equilibrium pricing and licensing strategies in two scenarios, namely, the licensing decision is made before or after the uncertainties are resolved. A comparison of the two equilibria indicates that the OEM is indifferent between making the licensing decision in the first or the second stage in most cases. But when the market potential, competition intensity, royalty rate and revenue sharing rate are moderate, there exists a small region in the parameter space where the OEM prefers to make the licensing decision in Stage 2. Interestingly, we obtain that for a large region of the parameter space, the two partners have the same preferences in terms of licensing. It is also found that different probability distribution of stochastic technology efficiency results in different licensing strategies.