The Impact of Nonlinear Dynamics on the Resilience of a Grocery Supply Chain

Purpose of this paper The resilience of supply chain replenishment systems is an performance important attribute and especially so in the retail sector where initiatives such as Efficient Consumer Response have led to lower inventory holding while attempting to maintain high levels of on-shelf availability. A common approach to testing for resilience of such systems would be through simulation modelling, especially where batching of orders occurs, for example. However, with developments in non-linear control theory, there is an opportunity to use more sophisticated analytical approaches to evaluate and improve resilience. The aim of this paper is to demonstrate the value of an analytical approach with empirical testing on a replenishment system used by a grocery retailer. Design/methodology/approach An Industrial Dynamics (ID) approach is used for framing and building a credible representation of the grocery retailer’s replenishment system. Initially a nonlinear causal loop and block diagram representations of the actual system were developed based on empirical data collection. Mathematical analysis of the model, based on nonlinear control engineering techniques in combination with ID simulation, have been used to understand the behaviour of stock and shipment output responses in the distribution centre given step and periodic demand signals. Findings Mathematical analysis through nonlinear control theory techniques has led to insights into the dynamic behaviour of the replenishment control model. This allowed the identification of specific behavioural changes in the supply chain stock and shipment responses, which are key indicators for assessing supply chain resilience, without going through a time-consuming simulation process. Transfer function and describing function analyses served as guidelines for undertaking ID simulation. Value The integrated method we have used combines to best advantage the knowledge generated via the twin approaches of non-linear control systems engineering analysis plus ID simulation. This duality maximises insight into the resultant causal relationships output from these procedures and hence enables the engineering of the optimal design for a real-world supply chain. The consequence is the development of a robust system based approach which brings together two mutually supportive components, simulation and non-linear control theory, to enhance supply chain resilience. The approach is illustrated using data concomitantly with a comprehensive grocery supply chain case study. Research limitations/implications This research is limited to the dynamics of single-echelon supply chain system. Although the electronic point of sales data and the store replenishment system have been considered in the validation process, this study has focused on analysing the resilience performance of a replenishment system only. Future research will consider a multiechelon supply chain. Practical implications 615 19th ISL, Ho Chi Minh City, Vietnam 6 – 9th July 2014 The systems based method is readily transferable to other industrial settings and environments, thereby enabling insights into resilience. A number of lessons for the case study are identified and these may also be applicable in other practical contexts. INTRODUCTION In recent years, successful businesses have moved from a product-driven strategy to a more market-driven one. In the retail environment, strong competition creates constant pressure on retailers to continually improve performance. To achieve this, grocery retailers have modernised their supply chains (Hingley et al., 2011). The distribution centre has becoming increasingly important in decrease lead-times and taking inventory out of the retail operations. Moreover, with the growth of internet ordering for groceries and the use of store-based picking strategies for e-fulfilment to home shoppers, DCs now have to deliver stock to meet demands of both store and home shoppers (Fernie and Grant, 2008). Hence, this resulting complex retail business created the necessity for DCs to have effective replenishment systems, not only to meet the requirements of the supply chain but to be resilient to disturbances. The dynamic behaviour of these systems plays a significant role in supply chain resilience performance. These dynamics are normally driven by the application of different control system policies and can be considered as a source of supply chain disruption depending on the control system design (Mason-Jones and Towill, 1998). More often than not, such resilience may be evaluated through simulation, given the complexity of the system. However, developments in computing capabilities allow non-linear control theory to now be effectively used instead. In this paper, we aim to analyse the resilience performance of a DC replenishment system within one of the largest grocery retailers in the UK, using an approach that combines nonlinear control theory and simulation modelling. SUPPLY CHAIN RESILIENCE AND SYSTEM DYNAMICS In the supply chain literature, the idea of resilience has recently emerged (Christopher and Peck, 2004), and is defined as “the adaptive capability of the supply chain to prepare for unexpected events, respond to disruptions, and recover from them by maintaining continuity of operations at desired levels of connectedness and control over structure and function” (Ponomarov and Holcomb, 2009). This definition implies achieving three properties: readiness (being prepared or available for service), response (reaction to a specific stimulus) and recovery (a return to ‘normal’ stable or steady state conditions). Despite the growing importance of the field of supply chain resilience, most existing studies are qualitative in nature. An exception is Wilson (2007), who analysed the impact caused by disruptions in transport processes on customer service levels, inventory levels and goods in transit and how a more collaborative supply chain can help to overcome this problem. Spiegler et al. (2012) investigated how different control policies and system dynamics in supply chains affect resilience, which is measured by calculating the integral of time absolute error (ITAE) of inventory and shipment responses. Both of these works are conceptual, exploratory and no empirical data were considered. However, in this study, we extend Spiegler et al.’s (2012) analytical framework for assessing supply chain resilience by enriching it with empirical research. In doing so, there is a need to consider how non-linearities have been incorporated into the analysis of dynamic systems. It has been claimed that in order to improve supply chain performance, dynamics in production-inventory control systems should be reduced (Torres and Maltz, 2010). Hence, there is plethora of literature researching the bullwhip effect and its impact on different supply chain performances, from both a quantitative modelling perspective (Fransoo and Wouters, 2000; Dejonckheere et al., 2004), either conceptually or based on empirical studies, and a descriptive perspective in the form of case studies (Lee et al., 1997; Kumar and Nigmatullin, 2011). However, so far, emphasis has been given to financial performance measures. For instance, most research focuses upon the impact of system dynamics on inventory, production and transport costs. Even when service levels and customer satisfaction are considered, these have been seen as service penalty costs. 616 19th ISL, Ho Chi Minh City, Vietnam 6 – 9th July 2014 Moreover, most of the system dynamics studies that use mathematical modelling still focus on linear models (such as Zhou et al., 2010). Forrester’s work (1968) on industrial dynamics calls attention to the importance of considering nonlinear models to represent industrial and social processes: “Nonlinearity can introduce unexpected behaviour in a system”. Such unexpected behaviour can cause instability and uncertainty. Despite many analytical methods being cited and already recommended by system dynamics scholars 30 years ago to examine nonlinear models (for example Cuypers and Rademaker, 1974; Mohapatra, 1980), they have been disregarded by recent studies where simulation techniques still dominate. Simulating complex systems without having first done some preliminary analysis can be exhaustive and unrewarding (Atherton, 1975). We use both mathematical and simulation modelling, highlighting how combining these provides greater insight than just simulation alone. RESEARCH METHOD The first stage of this research project involved developing a conceptualisation of the system through input-output and block diagrams. These were then used to create the mathematical and simulation models, with the aim of building a simple but credible representation of the real system. Nonlinear control engineering and spreadsheet simulation methods have then been used to analyse the resilience of the systems. The first stage in formulating the empirical model was defining the overall scope as well as identifying the following assumptions to be included: Store orders are aggregated, rather than being placed on store-by-store basis. Only a single product is modelled, with no promotions. The products are unaffected by unpredictable external factors (e.g. the weather). All supplier deliveries are made in full when compared with the ordered volume. The results of conceptualisation were converted into a block diagram in the Laplace domain, ‘s’ (Figure 1). Block Diagrams are a useful and simple method for analysing a system graphically. By using a block diagram, it is relatively straightforward to create the simulation model when transforming the Laplace frequency domain into difference equations by using a sampling period of Δt=1. The parameter Ti has been included in the block diagram representation and it determines the time actual and safety stocks take to balance. In the ‘As Is’ scenario this is set equal to 1. Figure 1. Block diagram of the DC replenishment system In Figure 1, the presence of CLIP and ROUNDING functions make the model nonlinear. The CLIP function denotes that shipments to the store will depend upon stock levels and deliveries from suppliers. When the shipments are not equal to the retail store orders, then backlog builds up. Hence, the desired shipment in the next replenishment period will % of Weekly Demand in Period A % of Weekly Demand in Period B Σ Σ Error Function (K)