The term, dynamic programming, was first used by Bellman to represent the mathematical theory of a multistage decision process. Dynamic programming is applied to allocate expenditures so that maximum benefits result. Three types of applications of dynamic programming are single-stage, multistage, and multistage with a time factor. Single-stage programming is used to evaluate a single project having several alternatives. Multistage programming involves selection of several projects having several alternatives. Multistage dynamic programming with a time factor is used where several projects and alternatives are considered and where various time periods are involved.

The Alabama Highway Department did considerable work on the application of dynamic programming to the optimization of budget allocation for the spot-safety- improvement program. Significant modifications were incorporated into the Alabama procedures to make it applicable to the spot-safety-improvement program in Kentucky (3). That procedure was adapted to Kentucky's needs and has been used periodically to select projects for the safety improvement program.

Another application of dynamic programming in Kentucky has been for the selection of projects for resurfacing. With hundreds of candidate projects recommended for resurfacing each year, it is difficult to select projects that will yield the greatest benefits to the driving public. Prior to the application of dynamic programming to resurfacing projects, it was necessary to develop reliable means of calculating benefits derived from roadway resurfacing.

Further use of the dynamic programming process in Kentucky has been for the development of a means to priority rank safety improvements for interstate and toll road facilities. Separate reports were prepared to document the procedures used for the interstate system and the toll road system. As was the case with other applications of dynamic programming, the major task was determination of benefits expected from each improvement. For both the interstate and toll road programs, all benefits were estimated to be the result of accident reductions associated with the improvements.

The program described herein is designed specifically for highway projects. Program development was done in 1974 and several modifications have been made since then. Additional modifications were performed during the preparation of this user's manual to make the program easier to use. A current listing of the program is in Appendix A.

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The contents of this report reflect the views of the authors, who are responsible for the facts and accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the University of Kentucky or the Kentucky Department of Highways. This report does not constitute a standard, specification, or regulation.