a pattern of necessitation of subs titution management (a mathematical model)

substitution management planning, as one of the important issues in manpower planning, is referred to as a process of filling the gaps and fulfilling the needs of very crutial and key elements of organization in managerial levels. meeting the needs by means of using external and internal manpower of the organization seems to be rational. however, it has some advantages and disadvantages. this paper will put the most emphasis on getting benefit from internal powers within the organization (qualified and talented individuals for taking managerial positions) by enforcing a mathematical model for responding to the requirements. in addition to having explained the matter, the structure of the mathematical model (from the type of ideal linear planning patterns) will be analyzed by forming function of goal and the limits. goal function is a ballanced add - up of the deviated variants that can be attributed to selected variants such as resumed manpower, categorizing of manpower, and the rate of upgrading. there are many different limitations taken into account, including objective or non objective limitations that are demonstrated by general modeling parameters and the ways of calculation. the other important matter is the parameters and the method of the designation. there are some parameters including resumed manpower, rate of upgrading, catagorization of manpower, jobs and jobs classifications and also the scale of deviated variants of -goal function and the way they are selected, will be discussed in this paper. in calculation of the scale of deviated variants of goal functions - regarding it's importance of selecting them towards personnel and organizational measures -, we use ahp methods (the method of analysis of the hierarchy process) by selecting and designating mathematical model for necessity of the managerial substitution in regard of method of the calculation of parameters.