Chapter Contents Previous Page Next Page

Network and Optimization Models

For example, we can define and analyze a network of project activities using project management software. Project management is a popular category of off-the-shelf decision support software. The best selling package is Microsoft Project. It is a powerful application that you can use to efficiently plan, manage, and communicate project information. Project managers can enter actual costs for tasks and assignments. Check http://www.microsoft.com/ office/project. While many computer users are familiar with project management software not everyone realizes it is based on network flow models. These models are specially structured linear programming problems.

DSS Analysts can define other networks. For example, one can develop a network of possible airline routes and schedules and compare costs. A set of routes or paths can be analyzed using a number of heuristic or quantitative tools. It has been estimated that 70% of all linear programming applications are network flow problems or have a substantial network structure. In addition to project management and aircraft routing, applications include: production planning and aggregate scheduling, personnel planning and scheduling, land use allocation, classroom scheduling, plant location, multinational cash flow management, and integrated production-inventory-distribution. Often a network model can be depicted as a set of nodes and arcs. Nodes may be sources of product and or demanders of product. Units of product can move from one node to another across arcs. For more information check Richard Barr’s Survey of Network Models at www.seas.smu.edu/~barr/ip/ch0/ch0.html.

Linear programming is the most widely known technique in a family of tools called mathematical programming. There are many possible uses of mathematical programming, especially of linear programming, in organizations. Many books have been written for courses in Management Science, Quantitative Analysis and Operations Research. Managers and DSS specialists are usually not experts in using optimization or simulation tools. Small-scale optimization DSS can be built using a spreadsheet program like Microsoft Excel. An on-line Web-based tutorial on Using MS Excel Solver for Spreadsheet Optimization is at the Frontline Systems Web site (http://frontsys.com/).

Decision Variables. These variables are unknown values that are searched for by applying the model. Usually decision variables are designated by X₁, X₂, …, X_N .

Figure 9.5 An Example Optimization Model developed in Microsoft Excel

In Figure 9.5 the decision variables are the quantities of TVs, stereos and speakers to build. The objective function is to maximize total profits. The constraints are from the parts inventory. Managers should be able to build a simple Model-Driven DSS like Figure 9.5 in Excel. A support person may need to help in conceptualizing the problem or in testing the end user application. For more information on Optimization and Linear Programming check Harvey Greenberg's excellent Mathematical Programming glossary at URL http://www.cudenver.edu/~hgreenbe/glossary/intro.html and Michael Trick's Operations Research Page at URL http://mat.gsia.cmu.edu/index.html.

Most often optimization models are included in a DSS to assist in resource allocation. Managers are often required to allocate productive resources like raw materials, people, money or time, which can be used in a variety of different ways. The problem is to determine the best way to use the resources. Managers need to determine what "best" means, but usually it implies maximizing profits, minimizing costs, maximizing quality or minimizing the risk of failure (cf., http://frontsys.com/tutorial.htm).