الفهرس 
Shortest path using max-plus algebra
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Abstract
The field of Operations Research (OR) emerged in the 1950s as a scientific approach to decision making. Most problems in OR involve a 2search for optimality.3 Most often, problems in OR is solved by the development of algorithmic procedures that lead to optimal solutions. OR uses many suitable techniques or tools available such as Linear Programming, Non-linear Programming, Integer Programming, Networks, Dynamic Programming, Goal Programming, Game Theory, Inventory Control, Simulation, Queuing Theory{u2026}etc. Network is a graphical representation of a project. Network analysis considers a practical way to monitor the progress of the project till its accomplishment in the minimum time; it can also be used to assist in allocating resources and to minimize total cost.The max-plus algebra uses the operation of taking a maximum, thus making it an ideal candidate for mathematically describing problems in OR. Max-plus algebra is a class of discrete algebraic systems, known as an effective tool for modeling and analyzing several types of discrete event systems in which the max and plus operations are defined as addition and multiplication in conventional algebra. Using this system, the behavior of a class of discrete event systems can be represented by simple linear equations, by which modeling, analysis, and control of the systems can be realized This thesis considers solving some problems such as shortest path and critical path method using a mathematical theory called the max-plus algebra, which affords a uniform treatment of many problems that arise in the field of OR. We illustrate the suggested method of applying this theory with detailed examples on critical path and shortest path of network