BUS606: Operations and Supply Chain Management

With the wide diffusion of e-commerce and the increasingly fierce competition all over the world, online retail channels have been developing rapidly. In China, as of December 2015, the number of netizens reached 688 million, including 413 million online shopping users, whose ratio had increased to 60%. A number of online retail oligarchs have emerged with the rapid development of the internet sales platform and network direct sales. There are both distributors and retailers buying products directly from the manufacturer, and selling to consumers through the network platform. For example, many products are sold through WalMart and Jingdong Mall at the same time, where the former is a traditional super retail firm and the last is new online super retail platform. The prices at WalMart may be properly higher than the prices on Jingdong Mall, but most of the time they offer relatively stable prices, and both retailers take sales as the goal of the competition through service and reputation. Considering the supply chain system is a complex network system, these sales games between retailers often bring demand variability which leads to a common phenomenon called the bullwhip effect.

Many scholars have devoted time to the study of the bullwhip effect, including demand processes and forecasting techniques. In the research on the bullwhip effect in the supply chain, the actual demand model is very important. Lee et al. assumed that the actual demand is subject to a first-order autoregressive AR(1) time series, and established the direction for the quantitative of the bullwhip effect. Luong and Phien were the first to deal with the second-order autoregressive AR(2) and the $p$th-order autoregressive AR($p$) demand process and give the corresponding expression of the bullwhip effect. Gilbert presented a multistage supply chain model based on Autoregressive Integrated Moving Average (ARIMA) time-series models. Duc et al. investigated the effects of the autoregressive coefficient, the moving average parameter, and the lead time on the bullwhip effect, under the Autoregressive Moving Average model (ARMA(1,1)). Gaalman and Disney investigated the behavior of the proportional order up to policy for ARMA(2,2) demand with arbitrary lead-times. Buchmeister et al. experimented (by simulating) with a special case of a simple three-stage supply chain using seasonal and deseasonalized time series of the market demand data in order to identify, illustrate and discuss the impacts of different level constraints on bullwhip effect. Nepal et al. presented an analysis of the bullwhip effect and net-stock amplification in a three-stage supply chain considering step-changes in the production rates during a product's life-cycle demand. The simulation results showed that performance of a system as a whole deteriorates when there was a step-change in the life-cycle demand. Nagaraja et al. measured the bullwhip measure for a two-stage supply chain with an order-up-to inventory policy and derived for a general, stationary SARMA demand process. Wang and Disney investigated the amplification of order and inventory fluctuations in a supply chain model with stochastic lead-time, general auto-correlated demand and a proportional order-up-to replenishment policy. They gave conditions for the ability of proportional control mechanism to simultaneously reduce inventory and order variances. For AR(2) and ARMA(1,1) demand, both variances can be lowered under the proportional order-up-to policy.

Because demand forecasting is one of the key causes of the bullwhip effect, many have scholars sought to develop many forecasting methods and inventory control systems to fulfill the demand within the lead time. Chen et al. quantified the bullwhip effect in a simple, two-stage supply chain consisting of a single retailer and a single manufacturer by using a moving average (MA) method and an exponential smoothing (ES) method. Luong proposed the minimum expected mean squares of error forecast method (MMSE) for lead-time demand to measure the bullwhip effect in supply chains with AR(1) processes. Wang et al. gave a comparison of the bullwhip effect in a single-stage supply chain for series demand function modela (ARiMA(1,0,0), ARiMA(0,0,1), ARiMA(1,0,1)) by using the Correct, MA, and EWMA (Exponentially Weighted Moving Average) methods. Ma et al. found and compared the analytic expressions of the bullwhip effect on product orders and inventory using minimum mean-squared error, moving average and exponential smoothing forecasting techniques. Bray and Mendelson analyzed the bullwhip by information transmission lead time based on public companies' data from years 1974–2008. Shorter reaction times cause significantly more trouble regarding bullwhip. Csik and Foldesi tested the problem of bullwhip effect by adoption of an inventory replenishment policy involving a variable target level. Safety stock was proportional to the actual demand. They proposed a new production plan, which guarantees the stability of the entire supply chain. Costantino et al. proposed a SPC (Statistical Process Control) forecasting system based on a statistical control chart approach to handle the trade-off between order variability amplification and inventory stability and compared with MA and ES methods in a four-echelon supply chain. Simulation comparisons showed that their system outperformed both the smoothing order-up-to policy and the Min-Max inventory policy in terms of bullwhip effect and inventory performances.

A few scholars have applied the theory of entropy to the supply chain management. An entropy-based formulation was proposed by Martínez-Olvera, as the basis of a methodology for comparing different information sharing approaches in a supply chain environment. He also presented a step-by-step comparison of two different information sharing approaches. Durowoju et al. proposed an approach to assess the impact of information disruption using entropy theory coupled with simulation methodology.
Most of the above researches considered only one retailer. Therefore, their demand models can't include the impact of competition between retailers (Duc et al.). Retailers in the supply chain system, in order to gain a greater market share, often adopt a strategy of increasing sales, i.e., they take the sales as the decision-making variable of the competition game. For the interaction behavior between customers and suppliers, the supply chain must exhibit deterministic chaos, and there will be attractors of the model moving with the environment and the initial states. The investigation of the supply chain dynamics from chaos perspective and quasi-chaos perspective is meaningful. Especially, when two supply chains take the Cournot competition affected by supply uncertainty, retailers should adopt corresponding order and inventory strategies.

To the authors' knowledge, there is lack of an investigation about how the bullwhip effect and entropy are affected by retailers' sales game based on the bounded rationality from a complex perspective. In particular, for online retailers there is a statutory policy called 7 days no reason return, which is not applicable to traditional retailers. The sales game of retail oligarchs and online retailers' returned products will result in fluctuations of demand, orders, and inventory, therefore, it is necessary to study their profits and bullwhip effect under sales competition. In particular, when the retailers forecast the expected sales volume and the returns volume for the next period, they often consider whether they can achieve more profits, and don't just consider the past demand information. Therefore, the objective of this paper is to investigate the case of sales competition and return rate with bounded rationality between retailers.

This paper contributes to the existing literature regarding bullwhip effect in several ways. Firstly, this paper gives a framework for investigating the bullwhip effect on the basis of the sales game with weak noise between traditional retailers and online retailers. Secondly, this paper attempts to study the impacts of the sales adjustment speed on the bullwhip effect using the theory of complexity and entropy. Thirdly, this paper gives a new forecasting method (bounded rational expectation) for the bullwhip effect research. At the end, the impact of 7 days no reason for return policy statutory for online retailers is investigated regarding the profits of the both retailers.

This paper is organized as follows: in Section 2 we describe the problem and construct the model of the supply chain system. Section 3 analyses the complexity of the system, then, in Section 4, we design experiments and compare the bullwhip effect under three states through numerical simulations. Section 5 proposes a time-delay feedback method to control the system and mitigate the bullwhip effect. Finally, Section 6 presents the conclusions and insights of this study. Appendix A, Appendix B and Appendix C which present the proofs of propositions are given after the conclusions.