Introduction to the theory, benefits and uses of simulation.

The Simulation Process:

It is important for us to outline the process of simulation. There are a number of steps that need to be taking to successfully apply this technique. These steps are as follows:

• Data collection
• Random- number assignment
• Model Formulation
• Analysis.

Data Collection:

“Simulation requires extensive data gathering on costs, productivities, capacities, and probability distributions”. Usually there are two approaches to data collection that can be used by analysts. Either a Statistical sampling procedure or a Historical search can be used in the data collection process. A  Statistical approach is used when there isn’t enough published data on the topic or the costs of data collection are high, a Historical approach is used when there is enough published data available, e.g. government reports, journals or company records.

Random- number assignment:

A random-number table is used to determine the supply and demand for each week in a company. A random number is a number that has an equal probability of being selected as any other number.  An unbiased generation of events can be simulated if random numbers are assigned to the events in the same proportion as their probability of occurrence.

Model Formulation:

To formulate a simulation model, the analyst involved must specify the relationships between the variables. Simulation models are made up of 3 different variables:

1. Decision variables: these are controlled by the decision maker and change each time different events are simulated.
2. Uncontrolled variables: these are random events to which the decision maker is unable to control.
3. Dependant variables: “reflect the values of the decision variables and uncontrollable variables.”

Analysis:

Simulation Analysis can be compared to hypothesis testing, i.e. sample data is produced that can be statistically analysed. The results of the sample runs provide the analyst with data, so that all of the results of the sample runs can be compared so as the best possible out come can be picked. A Statistical test can help to outline whether the differences in the operating characteristics are of importance. The most commonly used statistical methods are:

• Analysis of a variance
• Regression Analysis
• T-tests.

Again an important fact needs to be addressed when looking at the topic of analysis, in relation to simulation; the differences that may occur when conducting simulation experiments maybe statistically significant, but this does not mean that they are managerially significant.

Introduction to the theory, benefits and uses of Waiting Lines

A waiting line can be described as when one or more customers are waiting to be served. It is important to outline that “customers” are not always people, when discussing waiting lines, a customer can be describing inventory items that are waiting to be used, or machines that need maintenance.  

“A waiting line forms because of a temporary imbalance between the demand for service and the capacity of the system to provide the service.”

It is obvious that both demand and supply change over time to suit both the companies and customers’ needs.

The fact that the number customers arriving into a waiting line on any given day varies and the time it takes to process each customer also may vary, so therefore a waiting line will obviously develop. It is however, important to realise that even if the process time of each customer is constant a waiting line may also develop. In this case it can be said that the variability of the demand rate determines the size of the waiting lines. “In general, if there is no variability in the rate of demand or service rates and enough capacity has been provided, no waiting lines form.”

What are the uses of Waiting Line Theory?

Waiting Line theory applies to a number of different categories of firms. Waiting Line theory relates customer arrivals and the processing characteristics of the service- system to service-system output characteristics. It can relate to both service firms and manufacturing firms. Service system maybe satisfying customer complaints, production of a machine etc.

One of the most effective waiting line management is that of Disney world. Each day the number of visitors to the attraction can vary greatly. Waiting Lines for each of the separate attractions are kept to reasonable levels through their expert analysis of the process flows, people moving equipment and layout.

The analysis of waiting lines is of great use to managers as it affects inventory management, layout planning, design, capacity planning and scheduling.

How are Waiting –Line problems structured?

A description of the elements of the problem, is how waiting line problems begin. Each situation will obviously be different, but yet there are four main elements that are present in each problem. The four main elements are:

1. The generation of potential customers. This can be an input or customer population.
2. A waiting line of customers.
3. A service facility, this is a person/ or people, machines.
4. A priority rule, this is how the selection of the next customer for service is selected.

Customer Population:

The source of input for a service system is the customer population. The customer population can be put into 2 categories, finite and infinite.  The input source is said to be finite when the potential number of new customers is affected by the number of customers that are already in the system. An infinite customer population is the opposite, so the number of potential new customers entering the system is not affected by the number of existing customers in the system.

Customers in the waiting line can also be described as being patient or impatient. When examining the customers in a waiting line, a patient customer is one who enters the system and stays there until they are served. On the other hand an impatient customer is one which leaves the system before they are served, or decides not to join the system at all.

The Service System:

The service system is said to be the arrangement of facilities ( people and machines), and the number of lines ,i.e. single or multiple.  An example of a single line would be in banks, and multiple lines would be present in supermarkets.

The arrangement of facitities can also be put into different categories.

• Single-channel, single phase system: this is when all the services required by the customers can be provided by a single server facility.
• Single- channel, multiple-phase system: this is used when the services are provided by more than one service facility.
• Multiple- channel, single- phase : this is used when there is a high demand and the same service is provided at more than one facility, or when the services offered at each facility is different.
• Multiple-channel, multiple-phase : this is when the customers need to be serviced at the first facility , then have to move to the second facility etc.
• Mixed arrangement : this is the most complex form of waiting line. This is when customers require a unique sequence of required services.

Priority Rule :

The priority rule helps to determine which customer is going to be served next.

The pre-emptive discipline is a rule which allows a higher priority customer to interrupt the service of another customer.

Using Waiting-Line Models to Analyse Operations

Waiting Line Models can be used by managers to balance the gains against the costs of increasing the efficiency of the service line. Managers should be aware of the following operating characteristics of a system.

• Line Length
• Number of Customers in the System
• Waiting Time in Line
• Total Time in System
• Service Facility Utilization.