Complexity

Volume 2018 (2018), Article ID 3495096, 11 pages

https://doi.org/10.1155/2018/3495096

## Discrete Switched Model and Fuzzy Robust Control of Dynamic Supply Chain Network

^{1}School of Logistics, Linyi University, Linyi 276005, China^{2}School of Management, Harbin University of Commerce, Harbin 150028, China^{3}Faculty of Business and Economics, The University of Melbourne, Melbourne, VIC 3010, Australia^{4}Library, Linyi University, Linyi 276005, China

Correspondence should be addressed to Songtao Zhang; moc.361@6260tsz

Received 17 September 2017; Revised 30 November 2017; Accepted 19 December 2017; Published 16 January 2018

Academic Editor: Roberto Dominguez

Copyright © 2018 Songtao Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Supply chain network is more complex and dynamic under the uncertain demand and the lead time. Robustness is a key index of the stable operation for the supply chain network. We investigate a fuzzy robust strategy to realize the robust operation of the supply chain network with the production lead times and the ordering lead times under the uncertain customer demand. A discrete switched model of the dynamic supply chain network with the lead times and the uncertain customer demand is established based on T-S fuzzy systems. Then a fuzzy switched strategy is proposed to control the switching actions among subsystems. Furthermore, by introducing the inhibition rate , a fuzzy control strategy for the dynamic supply chain network is put forward to suppress the impacts of the lead times and the uncertain customer demand on the operation of the dynamic supply chain network. The fuzzy robust strategy composed of the fuzzy switched strategy and the fuzzy control strategy can guarantee the robust operation of the supply chain network at low cost. Finally, the simulation researches show the advantage of the proposed fuzzy robust strategy through the comparisons with the common robust strategy.

#### 1. Introduction

As an important management mode, supply chain management is a key factor to enhance the performance of firms in the global marketplace. With the fast changes of global economy and the increasing pressure of market competition, supply chain system has become a complex dynamic network system. The complexity of the supply chain network includes two aspects: on the one hand, the supply chain network consists of numerous economic subjects (such as manufacturers, distributors, and dealers), and there exists a variety of demand and supply relationships among the economic subjects, which form the structural complexity of the supply chain network; on the other hand, the uncertain demand and the lead time in the supply chain network cause the demand forecast to be more difficult, which forms the operational complexity of the supply chain network. For the structural complexity of the supply chain network, there are many research results about mathematical optimization strategies [1–7] and control strategies [8–10].

However, the uncertain demand and the lead time make the supply chain network more dynamic, which will make it more difficult for the supply chain network to achieve smooth operation. For the robustly stable supply chain network with the uncertain demand and the lead time, the system variables (such as inventory) can return to the normal states within a certain amount of time. Conversely, the unstable system will encounter the inventory backlog or serious out of stock phenomena, which will lead to the high operation cost of the system. For example, the operation cost of the supply chain under chaotic state will be more than 500 times higher than that under stable state [11]. Therefore, how to cope with the impacts of the uncertain demand and the lead time on the supply chain network and realize the robustly stable operation of the supply chain network with low cost has received much attention.

For the supply chain network with the uncertain demand, using a scenario-based approach, Almansoori and Shah [12] presented key strategic and operational decisions on the future hydrogen supply chain network with uncertainty arising from long-term variation in hydrogen demand. Khatami et al. [13] applied Benders’ decomposition to solve the stochastic mixed-integer model to optimize the closed-loop supply chain network with the uncertainties of products demand and returned products. For the stochastic demands of a multistage and multiperiod supply chain network, Govindan and Fattahi [14] applied a Latin hypercube sampling method to obtain risk-averse and robust solutions. Utilizing the combination of sample average approximation and Latin hypercube sampling methods, Hamta et al. [15] addressed the optimization of strategic and tactical decisions in the supply chain network design under demand uncertainty. Using a simulation-optimization approach to capture the randomness of the uncertain parameters, Salem and Haouari [16] investigated a three-echelon stochastic supply chain network design problem under the uncertain supply and the demand to minimize the total expected cost. Hamta et al. [17] proposed a scenario generation algorithm to deal with demand uncertainty for the supply chain network design considering assembly line balancing. Constructing a three-stage hybrid robust/stochastic program model, Haddadisakht and Ryan [18] optimized the design of a closed-loop supply chain network with uncertainty in demands for both new and returned products.

There are few literature sources on the supply chain network with the lead time. Eskigun et al. [19] modeled the relationship between the lead times and the volume of flow through the nodes of an automotive supply chain network. For companies that implement a Make-to-Order production system in a global supply chain network, Xiao [20] proposed a theory named the Key-Part Based Lead Time Management to reduce nonvalue added waste. In order to deal with the approximate optimal inventory control problem of the supply chain networks with lead time, introducing a sensitivity parameter, Han et al. [21] transformed the original optimal problem into a sequence of two-point boundary value problems without time-delay term.

There are fewer literature sources on the supply chain network with the uncertain demand and the lead time. Li and Liu [22] stated a robust control method to minimize the negative effect of uncertainties in demand, production process, supply chain network structure, inventory policy implementation, and vendor order placement lead time delays. Fattahi et al. [23] exploited the mitigation and contingency strategies for a multiperiod supply chain network with stochastic demands and delivery lead times.

Moreover, the management and control of the inventory is one of the most important subjects in the supply chain network. Because the inventory levels of firms often change, firms will carry out different strategies of production or ordering for the different inventory levels to reduce cost [24]. However, all of the literature sources mentioned above did not consider the different production strategies and ordering strategies for the different inventory levels.

In this article, a dynamic fuzzy model of the supply chain network with the uncertain demand and the lead times is constructed, which involves not only manufacturers’ safety inventories and expected inventories, but also distributors’ safety inventories and expected inventories. Then, based on the different production strategies and ordering strategies for the different inventory levels, we present a fuzzy switched strategy to suppress the fluctuations of the system variables in switching processes. What is more, we propose a fuzzy control strategy to make the fuzzy supply chain network robustly asymptotically stable in the presence of the lead times and the uncertain customer demand. Finally, simulation experiments are executed to study the impacts of the lead times, the uncertain customer demand, and the fluctuation of the switching processes among subsystems on the supply chain network under the common robust strategy and the proposed fuzzy robust strategy composed of the fuzzy switched strategy and the fuzzy control strategy, respectively.

The rest of this article is organized as follows: In Section 2, a basic dynamic supply chain network system is constructed and then the constructed system is transformed into a fuzzy supply chain network model with the uncertain customer demand and the lead times. In Section 3, we develop a stability theorem of the supply chain network. In Section 4, a simulation example is provided to show the effectiveness of the proposed fuzzy robust strategy for the supply chain network system. In Section 5, discussions are given. Finally, some conclusions are presented in Section 6.

#### 2. Models of Supply Chain Network

##### 2.1. Basic Model of Supply Chain Network

The basic notations in models of supply chain network are listed in Notations section.

We consider a type of dynamic supply chain network with a dual-echelon network including manufacturers and distributors, and the microstructure of the network in Figure 1 illustrates the structure characteristics of the supply chain network.