Jianxiong Zhang

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.

Joint dynamic pricing and inventory control policy for a stochastic inventory system with perishable products

This paper considers the joint dynamic pricing and inventory control policy for a stochastic inventory system with perishable products. The inventory system, with random disturbance, is modelled as a continuous-time stochastic differential equation. Combined dynamic pricing and production control, a stochastic dynamic optimisation problem that maximises the total discounted profit is developed. By applying the stochastic optimal control method, we formulate the problem of finding the optimal joint dynamic pricing and production schedule as the problem of solving a Hamilton–Jacobi–Bellman (HJB) equation. It is shown that the optimal dynamic pricing and production rate take the linear feedback form of the inventory level, which allows the decision-maker to effectively adjust the strategies as time evolves. In addition, to highlight the advantage of the joint dynamic pricing and production strategy, the case of the optimal production with static price is considered. Numerical examples are given to illustrate the validness of the theoretical results.

Letters: Some novel double-scroll chaotic attractors in Hopfield networks

In this paper, a 3-neuron chaotic Hopfield network is presented. Numerical simulations show that the network displays rich dynamics by changing the self-connection weight. The dynamic of the network is studied by using the Lyapunov exponents spectrum, bifurcation diagram, power spectrum and topological horseshoe theory. It is shown that the proposed network exhibits some novel double-scroll chaotic attractors.

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.

Optimal control of production and remanufacturing for a recovery system with perishable items

In this paper, a recovery system for perishable items is introduced and developed considering production and remanufacturing capacity constraints. The system consists of two inventories, one for serviceable items and the other for returned and recoverable items. Taking the production cost, remanufacturing cost, disposal cost, and the loss caused by deterioration into account, the optimal control model is established to minimise the total cost. The continuous-time dynamic optimal production, remanufacturing and disposal rates that minimise the total cost are obtained using Pontryagin’s maximum principle. Additionally, to highlight the advantage of the dynamic optimal policy, the case of the static optimal policy that does not vary with time is investigated and compared with the dynamic policy. It is shown that the dynamic optimal policy is significantly better than the static optimal policy. A numerical example is provided to illustrate the proposed methods.

Robust H∞ output feedback control for uncertain complex delayed dynamical networks

Abstract In this paper, the robust H ∞ control problem of uncertain complex delayed dynamical networks with non-identical nodes is investigated. The dynamic output feedback controllers are designed to ensure robustly global stability and a smaller prescribed H ∞ disturbance attenuation level for the resulting closed-loop systems. The controller design problem can be solved by a cone complementary linearization algorithm involving linear matrix inequality (LMI) conditions. A numerical example is given to illustrate the effectiveness of the proposed method.

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 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.

Dynamic pricing for non-instantaneous deteriorating items

An optimal dynamic pricing strategy for non-instantaneous deteriorating items exhausted in a sales period without replenishment is explicitly characterized. Originally, the inventory level of the items reduces simply as a result of customer demand, and subsequently decreases owing to both demand and deterioration. This paper formulates a dynamic pricing model to maximize the enterprise’s profit. The optimal dynamic pricing strategy is obtained by solving the optimization problem based on Pontryagin’s maximum principle. Two static pricing models, including a uniform pricing model and a two-stage pricing model, are carried out to compare with the dynamic pricing model to show the significant advantage of the dynamic strategy. Furthermore, numerical examples, together with sensitivity analysis of the optimal solution with respect to major parameters, are provided to illustrate the effectiveness of the proposed method.

Guaranteed cost control of synchronisation for uncertain complex delayed networks

In this article, the synchronisation for a class of complex delayed dynamical networks with uncertain inner coupling configuration is investigated under the quadratic guaranteed cost control. The coupling delay and nodes delay are considered in the networks. Based on Lyapunov–Krasovskii stability theory, sufficient conditions for the existence of the optimal guaranteed cost control laws are given in terms of linear matrix inequalities. Under these sufficient conditions, the networks are globally asymptotically synchronous, and the optimal upper bound is also guaranteed. Numerical examples are given to illustrate the effectiveness of the proposed methods.