7.2

Types of Simulation and Process

7.2.1

Types of Simulation

Simulations can be classified as discrete or continuous, fixed-interval or next-event, and deterministic or probabilistic. (1)

Discrete versus Continuous Simulations Most business simulation models involve variables with integer outcomes, for instance the number of items sold (i.e. the outcomes are discrete). They are many situations that involve discrete variables. Such situations can be described by a count of the number of occurrences (e.g., number of customers arrived, number of cars serviced, number of unit demanded, number of calls received, and so on). In certain instances, the variable of interest is continuous. It can assume both integer and non-integer values over a range of values. The quantities that are measured rather than counted have this characteristic, such as time, weight, distance, and length. The distinction between discrete and continuous variables is important for simulation design. However, in this chapter we will consider only the discrete-variable simulations.

(2)

Fixed-Interval versus Next-Event Simulations In certain instances, an analyst will be interested in simulating the value of a variable over a given or fixed interval. For example, the situation may involve sales of a product, and the analyst may want to simulate the number of units sold per day, or per week. Hence, the analyst would design the simulation to indicate the sales over one of these intervals. Although time intervals are the most typical intervals, distance and area are two other possible intervals. For instance, a problem may involve the number of defects per mile of roadways, or the number of breaks per square yard of cloth. In such cases interest usually centres on how many occurrences there are rather than the where or when of an occurrence. When interest centres on the accumulated value of a variable over a length of time or other interval, we say that the simulation is a fixed-interval simulation. Another type of simulation focuses on when something happens, or how much time is required to perform a task. For instance, a simulation of machine breakdowns may involve information on how long a machine operated before a breakdown and, perhaps, on how much time was required to repair the machine. When interest centres on an occurrence of an event, we refer this as a next-event simulation.

(3)

Deterministic versus Probabilistic Simulations Another important aspect of a simulation is whether it involves deterministic or probabilistic situation. The former pertains to cases in which a specific outcome is certain, given a set of inputs; the latter pertains to cases that involve random variables and, therefore, the exact outcome cannot be predicted with certainty, given a set of inputs. This chapter focuses exclusively on probabilistic simulations, which both tend to

have broad application and commonly encountered in managerial environments. All probabilistic simulations have a certain feature in common; they incorporate some mechanism for mimicking random behaviour in one or more variables. 7.2.2

The Simulation Process

In designing a simulation, an analyst is typically guided by this basic principle; of necessity, the simulation model will be a simplification of reality. Simulation is the process of experimenting or using a model and noting the results that occur. In a business context, the process of experimenting with a model usually consists of inserting different input values and observing the resulting output values. Simulation is used where analytical techniques are not available or would be overly complex. Typical business examples are queuing systems, inventory controls, production planning problems, corporate planning etc. Simulation often provides an insight into a problem that would be unobtainable by other means. Fundamental to simulation is the concept of a model. The success of a simulation exercise is related to the predictive quality of the underlying model, so that considerable care should be taken with model construction. Let us turn our attention to how to conduct a simulation. Simulation typically involves these steps, as illustrated in Figure 7.1: 1. 2. 3. 4. 5. 6. 7. 8. 9.

Defining the problem and setting objectives. Gathering data. Introducing the variables associated with the problem. Developing the (numerical) model. Validating the model. Designing experiments. Performing simulation runs. Analyzing and interpreting the results (modify model / change data). Selecting best course of action.

Figure 7.1

Define Problem & Set Objectives

The Simulation Process

Gather Data

Introduce Variables

Develop Model

Validate Model

Design Experiments

Run Simulations

Analyze & Interpret Results

Select Best Course of Action