Abstract: With the problems of task assignment,cost calculation and maximum benefit in the modern integrated enterprises of oil/gas exploration,exploitation,refining,transportation and marketing,it is presented for a new algorithm to determine the optimal solution of assignment problem,i.e.the least increment method.By the method,the least value in every column is firstly selected (if there are at least two in some column,then any one may be chosen).If the only one value is selected in each row,then the optimal plan of assignment is obtained.If more than two values are selected in some row,then the row must be adjusted according to the least increment or the least summation of increment,which is computed by choosing the second least value or the third least value etc.in the column corresponding to these values in the row.Generally,this method can find out the optimal solution of assignment problem quickly and easily.The case study and comparison with other methods show that it is simple and easily understandable;And it is an alternative method of task assignment and cost calculation.

Key words: assignment problem, the least increment, summation of increment, optimal solution, cost calculation