Enumeration Approach

The complete method of enumeration involves listing all the possible assignments that are in a given problem then selecting one with the minimum cost or have the least profit. This method is useful when applied in the right ways and therefore for it to be effective there have to be the least number or few numbers of rows and columns. There is a possibility of the user increases the number of rows and columns. This action may cause the method to be impractical, and hence it is not advisable to increase the number of rows or columns. Too many rows and columns may take too much time to list all the available assignments. Integer linear program (ILP) is said to be symmetric when it can be permutated, and the structure of the problem will not be changed (Margot, 2010).

If an assignment problem has let say (n) columns and (n) rows, then the assignment has (m!) different assignment problems. An assignment problem, therefore, is a linear programming (LP) problem whereby the undependable variable (X) can be assigned an assignment one or zero. Example of this explanation is if the employee (e) in an organization is assigned a project say project (p). Thus the undependable variable X will be Xep. In other words, an assignment problem is an integer problem of zero to one.

An enumeration approach is therefore described to be an integer programming whereby all the possible solutions for an objective function are laid out in a list and then the best solution chosen from the list. Enumeration helps to identify the most appropriate solution when rounding off after working out the problem. An example of this case is if a company predicts it will produce X1=5.36 products say tables and offer X2=8.56 services. Problems involving integers programming optimization entails finding an optimal solution to a problem which can be a hard task which can be algorithmically hard to solve (Genova & Guliashki, 2011).

This is not realistic since there cannot be a fraction number of products and services. The values have to round off to whole numbers, and they will be 5 and nine respectively. However, rounding off may affect the company’s profit; it may increase or lower the profit depending on the side affected by rounding off. The organization works on an optimal solution, solutions that maximize the profit gained and minimizes the cost

A company applying the integer programming problem as the products cannot be fractions then it can use the enumeration problem approach to address or aid in finding the best solution to the problem which cannot be detected by simply rounding off the numbers which cannot give a feasible answer to the question.

While applying the enumeration problem approach, the feasible solution can be tedious as it produces large and cumbersome procedures to solve a simple problem such as a 5-row problem. A problem with five rows means the problem has 120 feasible solutions 5! =(5x4x3x2x1). This approach can be difficult once done manually, but with the help of other computer spreadsheet programs such as Excel, the enumeration approach can be efficient to solve a 5-row x 5 columns problem.

The same would apply to the 7-row problem. This problem has 5040 feasible solutions obtained as 7! =(7x6x5x4x3x2x1). This would be impractical do work by hand, but spreadsheet in Microsoft excel would facilitate and make the work easier. There are different empirical methods applied to data and situations which does not provide the researcher with substitute judgment as long as the method provides an answer to the question asked (Bettis, Gambardella, Helfat & Mitchell, 2014).



Margot, F. (2010). Symmetry in integer linear programming. In 50 Years of Integer Programming 1958-2008 (pp. 647-686). Springer, Berlin, Heidelberg.

Genova, K., & Guliashki, V. (2011). Linear integer programming methods and approaches–a survey. Journal of Cybernetics and In

Bettis, R., Gambardella, A., Helfat, C., & Mitchell, W. (2014). The quantitative empirical analysis in strategic management. Strategic Management Journal35(7), 949-953.