Network Modeling

Network Modeling

Describe the characteristics of network flow problems , the decision variables for network flow problems , objective function of network flow problems , constraints for network flow problems , implementing the model in a spreadsheet , and analyzing the solution

Network Modeling

Introduction

Many problems in business are decisions that concern network flow problems . Although these problems vary , they all have one characteristic in common they can be illustrated or presented in a graphical form known as a network (Ragsdale ,

. 185 . There are several types of network flow problems , including transshipment

, shortest path , maximal flow problems , transportation assignment , and generalized flow problems These problems can be formulated and solved as LP problems (Ragsdale ,

. 185

Characteristics of network flow problems

In a model of a network , the amount of flow that occurs on arcs in network is symbolized by a decision variable . A flow balance constraint is composed for each node in the network : Net flow (node ) - (node , the the source (Breese , 1991

Transshipment

An understanding of the transshipment problem is important , because most of the other types of network flow problems can be viewed as simple variations of the transshipment problem (Ragsdale ,

. 186 . Figure 5 .1 on

. 186 is a network model of a transshipment problem . It displays many of the characteristics shared by network flow problems (Ragsdale br

. 186 . All network flow problems can be shown as a collection of nodes connected by arcs . An arc is a line that joins two nodes to each other A node is a circle . The two main types of nodes are supply nodes and demand nodes . Supply nodes are the sending nodes , and demand nodes are the receiving nodes (Hossein , 2005

As shown in Figure 5 .1 , the nodes representing the port cities of Newark and Jacksonville are both supply nodes because each has a supply of cars to send to other nodes in the network . Richmond represents a demand node because it demands to receive cars from the other nodes . All the other nodes in this network are transshipment nodes . Transshipment nodes can both send to and receive from other nodes in the network (Ragsdale ,

. 187 . The the node representing Atlanta in figure 5 .1 is a transshipment node because it can receive cars from Jacksonville Mobile , and Columbus , and it can send cars to Columbus , Mobile , and Richmond (Ragsdale ,

. 187 . The net supply or demand for each node in the network is indicated by a positive or negative number next to each node . Positive numbers represent the demand at a given node , and negative numbers represent the supply available at a given node . For example , the value 80 next to the node for Richmond indicates that the number of cars needs to increase by 80 , or that Richmond has a demand for 80 cars . The value -200 next to the node for Newark indicates that the number of cars can be reduced by 200 , or that Newark has a supply of 200 cars . A transshipment node...