Computer Simulation/Modelling Approaches

Computer simulation approaches can be divided into two distinct categories: those that assume processes are continuous and those that are concerned with events and timings that are discreet and punctuate the continuum of time. There is arguably a third type of computer simulation which has generally been labelled as operational research or optimisation, and these approaches are mathematical and deterministic or stochastic and are generally concerned with supporting decisions such as the location of warehouses, level of inventory batch sizing, or inventory management practices.

The following sections describe the various computer modelling/simulation approaches and their application to supply chains/networks.

4.6.5.1 System Dynamics

System dynamics is founded on the pioneering work of Jay Forester (1958) who used computer simulation to show how demand can become amplified as it flows upstream in a supply chain: a retailer batches their orders to a supplier, and the supplier then batches their orders to their supplier, and in so doing the original demand can be shown to oscillate with increasing amplitude and periodicity as it moves up the supply chain.

Forrester (1958) was extremely careful in the specification of his computer model, to quote directly:

“To determine the behaviour of a system by simulating the performance of its parts requires that one describe exactly, and in detail, the characteristics which are to be included. The

validity of the outcome of the system studies depends on the judgment of what is pertinent to include in the system

description.”

This not only serves to emphasise the importance of correct specification, but also how one of the most significant insights into supply chain operations was developed - not from empirical observations but from computer simulations. Forrester recognised that the supply chain system was one of continuous flows and control through various feedback mechanisms and his conceptualisation is presented in Figure 4—1.

Figure 4—1: Continuous flows and feedback of a supply chain system

Source: Forrester (1958)

This elegant model captures the essence of parsimonious specification: a computer simulation to explore the impact of delays, ordering practices, and inventory management processes on the dynamic response of a system. In so doing Forrester (1958) accepted (at least in his first specification) that effects such as marketing, promotions and competitive action did not need to be considered.

The systems dynamic approach to computer simulation has proved extremely valuable in developing our understanding of many issues related to demand amplification, such as the impact of information sharing, inter-organisational collaboration and inventory management practices. Indeed it secured the central axiom that supply chain management is primarily concerned with: flows of material, information and cash.

Interestingly, Forrester’s (1958) first computer models fell into the category of models that were not validated using real world data, and were primarily concerned with developing or extending the simple theory that already existed to describe decisions of how much a firm needs to order and when to place an order. Forrester merely extended this concept across organisational boundaries.

4.6.5.2 Discrete Event Simulation

Discrete event simulation assumes that the phenomenon of interest is not continuous but is captured in specific events. These events may persist in time and at the level of the event may well assume continuous characteristics.

In supply chain simulation terms it is hard to differentiate between discrete events and system dynamics, this is probably because of the fundamental nature of a supply chain which is concerned with the flows of material from one organisation to another. However, there is an established place for discrete events within this continuum, for instance the availability of capacity, disruptions, changes in cost parameters (Rosenfield et al., 1985), and time compression (Chang and Makatsoris, 2001).

The combination of discrete events with system dynamics has proved useful in the understanding of external events (Lee et al., 2002)such as disruptions and catastrophes, and in the timing of decisions such as supplier switching. This combination of approaches comes close to mimicking the real world and is conceptually similar to ABM described later.

4.6.5.3 Optimisation Methods

If simulation is about understanding relationships between variables, there exists another set of computer models that are primarily concerned with optimisation. Whilst these computational methods may seem inappropriate to an ontology where local optimisation is prioritised over system optimisation, the findings of such models are often operationalised heuristically, and it is therefore worth considering them if only to establish computer simulation as a feasible means of establishing supply chain and network theory.

Optimisation approaches can be characterised as having an objective function which can be expressed as the minimisation or maximisation of a dependent variable subject to various constraints. The general form of approaching optimisation problems can be demarked by whether or not the problem can be defined as either mathematically resolvable (linear programming, integer/mixed integer programming and non-linear programming) or only resolvable by searching through a range of potential solutions to find the best (gradient- based, meta-model, statistical and random search/heuristics).

Mathematical optimisation methods have been extensively applied to answering strategic, tactical and operational supply chain problems, such as where to locate warehouses, how to minimise transport costs, and how best to organise picking within a warehouse. The search methods of optimisation have been used to address phenomena where there are a number of interrelated independent variables, such as the establishment of an optimal inventory policy given uncertainty in demand and supply and where demand is modified by availability (Spall, 1998; Zadeh, 1999; Zhao and Melamed, 2009) .

4.6.5.4 Agent Based Modelling

ABM is an organisation of code and processing that allows multitudinous simultaneous actions to take place within a computer simulation. This organisation of code simulates real world social phenomena much more adequately than other code and processing organisations that are more orientated to processing actions sequentially. This facility has been widely adopted in computer simulations of social systems as it allows system

behavioural characteristics to emerge and avoids arguments of tautology much more easily than with other computer simulation approaches. It is this aspect of ABM that makes it suitable for exploratory computer simulations of complex phenomena designed to expose emergent relationships between variables. ABM differs from the other forms of modelling previously mentioned in that the design is focused on individual action which is formatted as a set of simple generic rules that each agent applies using its state variables as inputs, thus giving a general rule a specific interpretation. This contrasts with other forms of simulation which reflect an abstraction of an observed system.

ABM has been commonly applied in the understanding of highly dynamic ecological systems, such as social networks (Gilbert and Doran, 1994), and other time series evolutionary problems including supply network behaviour. In this context ABM simulations have developed some traction in efforts to understand networks that have a scale (population, temporal, geographical or relational) which precludes the collection of empirical data from which to inductively develop theory.

The importance of Choi et al.’s (2001a) conceptualisation of supply networks as CASs becomes clear in the consideration of how research into CASs, and in particular supply networks, can be carried out as they provide the basic structure and components from which a model of a supply network as a CAS can be constructed, thereby adding to the case for the incorporation of autonomous parallel action into any computer simulation.