Understanding complex dynamics in inventory management with endogenous demand under social interactions: a chaos perspective

Abstract

This paper investigates the system dynamics and performances of a deterministic inventory model with endogenous demand transitions determined by consumers' purchase behaviours and managers' order decisions under social interactions. With known demand transitions, the manager makes order decisions to maximise the single-period profit by the optimal order policy or commits to a fixed quantity by the constant order policy. With unknown demand transitions, the demand-chasing order policy is adopted. The impacts of various endogenous factors on the system dynamics and performances are examined. It is found that the equilibrium demand can exhibit stability, periodic cycles, and chaos in the long-run dynamics. Strong social interactions can lead to instabilities in demand processes and impair the profitability of the inventory system. The value of information on endogenous demand transitions increases if social interaction intensities and/or sizes of loyal customers become larger. The results suggest that endogenous factors stemming from managers' decision-making, consumers' purchase behaviours, and their interplay can cause persistent and unpredictable demand fluctuations leading to instability and profit losses. Managers should understand the underlying causes of demand variations and the impacts of endogenous factors to improve operational effectiveness in inventory management.

Keywords:

• System dynamics
• inventory management
• social interactions
• simulation
• chaos

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Due to the nature of the research, supporting data is not available.

Notes

1 Getlen, L. (February 22, 2015). How the Beanie Baby craze was concocted -- then crashed. New York Post. https://nypost.com/2015/02/22/how-the-beanie-baby-craze-was-concocted-then-crashed/.

2 In practices, the retailer may have limited inventory storage capacity, and the storage costs can be substantial when the order quantity is beyond the storage capacity. It is reported that retailers even allow customers to keep the returned items for free and refund their money due to huge inventory-related costs under supply chain disruptions in the recent COVID-19 pandemic (https://edition.cnn.com/2022/06/26/business/retail-returns/index.html).

3 There could be many reasons consumers have good purchase experiences when the inventory level is higher. For example, consumers may experience short waiting times or avoid being turned down due to insufficient stocks. Consumers may have more items to choose from, even if products are homogenous.

4 If $\alpha =1$, the term $\frac{1}{1+\beta \exp (d-q)}$ can be interpreted as the repurchase probability of existing consumers.

5 The retailer may make the order decisions to maximise the long-run discounted or average profit if endogenous demand transitions are known. As there are no closed-form solutions to this policy or steady states in the demand dynamics, we will not consider this order policy.

6 To generate the bifurcation plot, for a given α, starting from a randomly generated initial demand, the dynamical system is run 10,000-time units, and the last 100 data points are plotted, considered as in the equilibrium stage. Then, we increase α by 0.001, repeat the simulation 10,000-time units, and plot the last 100 demand values.

7 The Lyapunov exponent is calculated based on the algorithm proposed by Eckmann and Ruelle (1985).

8 For other constant order quantities such that $\tilde{q}>10$, the results are similar.

9 Lau and Bearden (2013) compare several metrics to measure the performance of the demand-chasing order policies in newsvendor models under various scenarios by simulation. It is found that the correlation of orders with lagged demand can be used to measure the newsvendor's demand-chasing behaviour. Kirshner and Moritz (2021) find that regression models can better capture the observed costs associated with demand-chasing in inventory order decisions.

Additional information

Notes on contributors

Xuchuan Yuan

Xuchuan Yuan Dr. is a Senior Lecturer at the School of Business, Singapore University of Social Sciences. His research interests include service operations management, supply chain management, system dynamics and simulation, and applications of complex systems in management.