The value of nonlinear control theory in investigating the underlying dynamics and resilience of a grocery supply chain

Abstract

In an empirical context, a method to use nonlinear control theory in the dynamic analysis of supply chain resilience is developed and tested. The method utilises block diagram development, transfer function formulation, describing function representation of nonlinearities and simulation. Using both 'shock' or step response and 'filter' or frequency response lenses, a system dynamics model is created to analyse the resilience performance of a distribution centre replenishment system at a large grocery retailer. Potential risks for the retailer's resilience performance include the possibility of a mismatch between supply and demand, as well as serving the store ine ciently and causing on-shelf stockouts. Thus, resilience is determined by investigating the dynamic behaviour of stock and shipment responses. The method allows insights into the nonlinear system control structures that would not be evident using simulation alone, including a better understanding of the influence of control parameters on dynamic behaviour, the identification of inventory o↵sets potentially leading to 'drift', the impact of nonlinearities on supply chain performance and the minimisation of simulation experiments.

Investigating sustained oscillations in nonlinear production and inventory control models

“…Uninformed replenishment policies and some aperiodic configurations combined with changes in the lead-time can cause the system to have an oscillatory behaviour, which can in turn drive costs up and service levels down. In practice, an example of uninformed replenishment policy was evidenced by Spiegler et al (2016b), who noticed that the replenishment system of a DC in a grocery retailer was set to have WIP target values equal to zero, causing inventory o↵sets. Although in this example, this uninformed policy did not cause periodicity in the supply chain system (rogue seasonality), it contributed to the bullwhip and ripple e↵ect.…”

“…In the supply chain literature, a plethora of studies have made e↵orts to understand system dynamics and design production and inventory control systems that reduce demand amplification (Chen et al, 2000;Dejonckheere et al, 2003;Disney and Towill, 2003;Chen and Lee, 2012;Wang et al, 2015b) and decrease risk of stock-out (Wang et al, 2015a;Spiegler et al, 2016b), consequently improving transport and production operations (Bicheno et al, 2001;Potter and Lalwani, 2008;Juntunen and Juga, 2009;Cannella and Ciancimino, 2010;Spiegler and Naim, 2014) and service and financial performance (Torres and Maltz, 2010;Ivanov and Sokolov, 2013;Dai et al, 2016).…”

“…Similarly, Spiegler et al (2016b) used the describing function method to analyse the resilience performance of a grocery supply chain under non-negative batching constraints in the ordering rule and backlog situations in the shipment estimation. In both the works of Wang et al (2015b) and Spiegler et al (2016b), the describing function method enabled understanding of the nonlinear impact of di↵erent demand signals, with di↵erent means, amplitudes and frequencies, on supply chain performance.…”

“…In this paper, we expand on the works of Wang et al (2015b) and Spiegler et al (2016b) and follow the recommendations of Spiegler et al (2016a) on the application of describing function method to not only understand the impact of di↵erent demand signals passing through replenishment constraints but also to use it as a design tool to control and avoid sustained oscillations or limit cycles that are intrinsic to some nonlinear systems and, therefore, managing rogue seasonality. We also complement the works of Wang and Disney (2012) and Wang et al (2014) whose methods, despite enabling the identification of oscillatory re-gions in the production and inventory control system, did not reveal the characteristics of the limit cycling behaviour.…”

“…By inserting CLIP functions ( to avoid order rates reaching negative values (also referred to as forbidden return constraint) and shipments being made without any on-hand inventory, the model in Figure 1 has been used to replicate the Beer Game (Spiegler and Naim, 2014). Other OUT systems that consider some of these nonlinearities include Laugesen and Mosekilde (2006); Mosekilde and Laugesen (2007); Wang and Disney (2012); Hwarng and Yuan (2014); Wang et al (2015b) More recently, a similar model has been identified in the replenishment system of a grocery retailer (Spiegler et al, 2016b), but, in addition to the non-negativity constraint, orders were also batched based on the buying quantities and truckload limits.…”