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APPLICATION OF THE MODEL TO MANAGEMENT AND PUBLIC-SECTOR PLANNING PROBLEMS

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RISE is an optimization package where a number of regulatory/competitive 

environment and institutional factors have been abstracted and quantified in 

the model.  One of the advantages of the model is that it serves as a 

`simulation' laboratory in which the consequences of managerial and 

regulatory decisions can be readily tested. The source code is provided to 

allow the research community to extend the software?s current capabilities to 

other applications as outlined below.



PRIVATE-SECTOR APPLICATIONS



RISE would be a convenient tool in the planning level (such as the corporate-

planning department) of an airline, which is responsible for strategic

decisions on market entry and exit.  Specifically, it helps to re-examine

existing route structure, fleet requirements and route frequency.  In this

regard, it holds promise to make the best out of the routes an airline has. 

By a careful channelization of the traffic flow in a system of feeders and

long-haul operations, formerly short-hop, thin-density, uneconomical segments

could become profitable to serve--since a traffic-flow pattern that results 

in high-route-density operations would bring about cost savings to the 

carrier. In short, systematic route-planning minimizes the profit 

disadvantages of low-density and short-hop operations.



The next level of the application of RISE is obtained through sensitivity

analysis.  Suppose an airline is considering the merits of a new route.  The

"graph-theoretic" way in which the route specification is encoded can be 

parametrically changed to represent the inclusion of the route under

consideration into the network system. (See Chan [2005]- Location, Transport 

& Land-Use ?Section 4.7.) Analysis can then be carried out to assess the 

cost/effectiveness of the new route.



Further application can be made to the timely subject of mergers. Obviously,

RISE cannot help merger decision in its entirety.  It can, however, serve as 

a tool to predict the routing/scheduling implications when two sets of routes

merge into a conglomerate network.  Since route-structure complementarily is 

one of the prime considerations in a merger case, the graph-theoretic way of 

encoding the combined route systems expedites merger analysis.  RISE may 

assist in answering the following questions:  

"Could economies-of-scale in routing/scheduling be expected from the merger?" 

"Would there be diminishing marginal-returns?"



PUBLIC-SECTOR APPLICATIONS



The above-mentioned route awards and merger decisions obviously concern a

regulatory agency like the US Dept. of Transportation besides the carriers in

consideration.  The regulatory agency can conceivably find RISE useful.  Many

economists have used econometric models to assess whether air transportation

should be further de-regulated or re-regulated, where there are stipulations

that the existing competition between carriers is introducing inefficiency.



To supplement these studies, RISE can be used as a descriptive `simulation,'

experimental tool in this regard to predict the effect of different degrees 

of route-competition. This is readily performed by parametrically varying the

model inputs which represent the route-competition pressure exerted on the

airline under consideration by the rest of the industry. Where the total

picture of all the domestic route carriers is wanted, RISE can be applied in

the following pair-wise manner. RISE is run on airline A given the existing

competition pressure from the rest of the carriers, then RISE is run on

airline B with airline A now grouped into the rest of the industry. This

repetitive application of RISE is a way to empirically trace out the

trajectory of the partial equilibrium points for an oligopolistic competition

industry.



Obviously, RISE can be used for other scheduled transportation services aside

from airlines. In fact all three datasets included here in the folder are 

drawn from a bus system for downtown York, Pennsylvania. A transit authority 

in this case will find RISE useful in route configuration which is the 

essential component of any service. An example set of runs, complete with 

inputs and outputs is documented in RISE1.OUT. Similar output data can be 

generated from RISE2.DAT and RISE3.DAT. As mentioned in the README file, 

RISE1.DAT contains a test dataset intended to generate a star-shape route 

network, RISE2.DAT contains a test dataset intended to generate a two-loop 

route network, and RISE3.DAT contains a test dataset intended to generate an 

open-loop route network. Sample output files are also accommodated here by 

RISE1.OUT, RISE2.OUT and RISE3.OUT.





FUTURE EXTENSIONS



If RISE is to be used by a regulatory agency such as the US Department of

Transportation (DOT), there should be an additional measure of effectiveness

besides profit to the carriers. One of the chief guidelines has been "public

convenience and necessity".  DOT is concerned with the well-being, or 

welfare, of the users of air transportation.  Travel demand is modeled in 

RISE only as a function of whether the level-of-service is non-stop, multi-

stop, or connection; no price/fare policy is addressed. Such a formulation of 

the demand function, while serviceable for planning the operations of 

individual carriers, has to be used in conjunction with parallel analyses in 

order to address the question of public-sector policy. Given these 

extensions, RISE can be useful not only to the domestic air-transportation 

industry, but also in evaluating policy issues on a national level.



In spite of our genuine attempt to make RISE a general scheduled-

transportation package--as to be distinguished from an airline package--the 

field testing on public transportation has not been as complete as for an 

airline. For that reason, a lot of the institutional factors have been left 

out in such applications. It is an area that can benefit from additional 

development.





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			SOFTWARE SYSTEM CONFIGURATION

			-----------------------------



For those interested in further developing RISE, let us sketch out the 

technical specifications and  main algorithm below. RISE is coded in FORTRAN.  

The software system consists of a total of 40 routines (not counting system 

programs and output interpretation programs). Programs are organized in a 

"modular" design so that future extension to the system can be implemented 

with minimal difficulty.



SIZE



The object or executable code of RISE takes up approximately 120-thousand

bytes, including all the systems routines called and the COMMON area.  The

array size required for a 25-city system is about 35-thousand bytes, and is

projected to be about 353-thousand bytes for an 80-city system and so on.  

The storage requirement of RISE for most scheduled-transportation networks

therefore falls well within the primary-storage capacity of a PC.  RISE

requires negligible secondary-storage support, which is used merely to store

the programs and to handle approximately N*N/2 (where N is the number of

terminals [nodes] in the system) pieces of input records.  This means about 

300 input-records for a 25-node system and 3200 input records for an 80-node 

system etc.)



RUN TIMES



A number of computer runs have been performed to assess how fast the 

algorithm executes.  The observed computational speeds have been quite 

encouraging. Execution times are in seconds.



SUMMARY OF THE ALGORITHM



While documented mathematically as a recursive program in the Chan (2005) 

book, the whole algorithm can be summarized in the flow chart of the 

following figure.  The algorithm consists of two parts -- (i) intra state-

stage-space instructions, and (ii) inter state-stage-space instructions.  The 

former pertains to the steps executed at the grid points of the state-stage 

space while the latter pertains to loops through the whole state-stage space. 

Here is a schematic of the algorithm:



                     Start

                       |

                       |

                       v

             ____________ Initial

             | No            feasible

             |               solution

             |               exists

             |               ?

             |              /

             v             /

           Impose         / Yes 

           penalty       /

           method       /

             \         /  

              v       v           

              SYNTHESIS *------> ANALYSIS

                   ^             ^  /   ^

                    \        **//  /    |

                     \ *      //  / *   |

                      \      //  v      |

                       IMPROVEMENT      |

                         |              |

                         |              |

                         |              |

                         v              |

                      labels            | No

                    unchanged   ________|

                  over two cycles?

                         |  

                         |

                         |  yes

                         |

                         v

                    Local Optimum

      

LEGEND:



Intra state-stage space flow

*    1st intra-flow

**  subsequent intra-flow

             





Intra State-stage Space Iteration

*********************************



These instructions again consist of two parts:  (a) the first loop through 

the state-stage space, and (b) the subsequent loops through the state-stage 

space. The first loop (a) requires the execution of the synthesis, analysis 

and improvement steps.  The subsequent loops (b) requires only the execution 

of analysis and improvement.  The set of instructions can be formalized as

follows:



Step 1.  Synthesize a route/routing at an uncovered grid point of the

state-stage space.



Step 2.  Analyze/evaluate the route/routing at the grid point.



Step 3.  Improve the routing and reliability if the marginal revenue from the

new routing is larger than that from the existing; otherwise, proceed.



Step 4.  If it is the first loop through the state-stage space, go to Step l;

otherwise go to Step 2.



Inter State-stage Space Iteration

*********************************



Let us now march through the entire algorithm by viewing the algorithm from

one state-stage space iteration to another:



Step 1.  If no initial feasible solution exists, impose the penalty method 

for the first loop through the state-stage space; otherwise proceed.



Step 2.  Execute intra state-stage space instructions.



Step 3.  If the labels in the state-stage space remain unchanged over two

successive, stop--a local optimum has been obtained; otherwise go to Step 2.





For a more formal explanation, refer to the Chan (2005) book under "Location 

Routing" Chapter, where the theory of recursive programming has been 

detailed, and a couple of numerical examples have been worked out for 

illustration.

