Simulation of the linear programming problem associated to the optimization of the sales force efforts assignment in an insurance company

Resource allocation may be decided by using computer programs applied to a specific domain to automatically and dynamically distribute resources to applicants. It may be considered as a specialized case of automatic scheduling.

With computers able to solve linear programming easily, the challenge is the problem formulation – translating the problem statement into a system of linear equations to be solved by the computer. The information required to write the objective function is derived from the problem statement.

We carried out a simulation on a concrete situation specific to the life insurances in order to emphasize the way in which the method of the linear programming can be applied in the optimization processes of the resources assignment. We focused our attention on a multinational company specialized in the life insurances domain that wants to reach the Romanian insurances market, offering two types of services packages of private life insurances according to the first paid by the clients: Life Insurance Standard (a short term insurance that covers exclusively events resulted from an accident and offers financial protection in case of death as a consequence of an accident, total or partial invalidity as a result of an accident, hospitalizing or operation as a result of an accident) and Life Insurance Premium (a product of life financial protection on a medium and long term to which the client can choose the contract period that best suits his financial plans - 5,10, 20 years and offers the protection to the diagnosis of critical illnesses, the protection in case of death and invalidity, as a result of an accident, the protection in case of total or temporary incapacity of work and the possibility to increase the benefits along the contract without evaluating the health condition).

The insurance company’s manager must decide the appropriate assignment of the sales force efforts in order to maximize the profit. The company’s specialists in the financial plans domain estimate that a sales agent of the Life Insurance Standard (LIS) package will have a medium profit of 1.100 EURO, while a sales agent of the Life Insurance Premium (LIP) package will have a medium profit of 650 EURO. The training for the sales operations of the

Life Insurance Standard package will require 230 hours while for the Life Insurance

Premium, it will involve 410 hours; the company’s manager decides the assignment of a maximum 1.650.000 EURO budget for all the training operations that support the sales of the two insurance packages. The contribution margin is 530 EURO for a Life Insurance

Standard sold package and 320 EURO for a Life Insurance Premium sold package. The

contribution margin is determined as a difference between the incomes resulted from the sale of a life insurance package and the afferent variable costs. The optimization of the company’s total contribution margin requires the exceeding of the minimum level of 1.480.000 EURO. The maximum number of sales agents for the Life Insurance Standard basic package who will be recruited from the persons with university studies in the sales management domain is of 5000 in order to fit the budget assigned to human resources by the company’s manager.

In order to solve this problem of linear programming, we must identify the decisional variables in a first stage which are represented by the two life insurance packages: Life Insurance

Standard and Life Insurance Premium. We will assign the X1 symbol to the sales team of the Life Insurance Standard services package and the X2 symbol to the sales team of the Life

Insurance Premium services package. The next stage involves the setting of the objective

function by means of the linear programming method, which is thus formulated:

Maximization π (profit) = 1.100 X1 + 650 X2 (1)

After the setting of the objective function, it is necessary to define the set of constraints: the budget assigned to the sales agents’ training, the contribution margin and the maximum number of sales agents. The conversion in formulae of the three types of constraints will be carried out according to the two decisional variables.

The formulation of the constraint referring to the budget assigned to the sales agents’ training (1.650.000 EURO maximum) will take into account the number of hours for the development of the communication and sales abilities (230 hours in the case of the Life Insurance

Standard package, respectively 410 hours in the case of the Life Insurance Premium

package):

230 X1 + 410 X2 ≤1.650.000 (2)

The second constraint of the decisional problem must ensure, according to the objective imposed by the insurance society’s manager, a minimum contribution margin of 1.480.000 EURO by means of the contributions brought by the unitary contribution margins (530 EURO in case of selling a Life Insurance Standard package, respectively 320 EURO in case of selling a Life Insurance Premium package).

530 X1 + 320 X2 ≥1.480.000 (3)

The third constraint refers to the maximum number of the sales agents who will be recruited in order to accomplish the sales objective; we will assign the coefficient 1 to the sales team of the Life Insurance Standard package and the coefficient 0 to the sales team of the

Life Insurance Premium package because the share of the first team must be bigger than the

one of the second team.

1 X1 + 0 X2 ≤ 5.000 (4)

Due to the fact that none of the decisional variables can have negative values, we will impose their constraint too: X1, X2 ≥0. We will appeal to the Linear and Integer Programming function of the WinQSB software (The free trial version of the WinQSB software was downloaded from the website: http://www.asecib.ase.ro/soft.htm) in order to solve quickly this problem of linear programming.

The access of the linear programming application from the WINQSB software menu imposes the introduction of the entry data basis, the user specifying the number of decisional variables (the two packages of private life insurances Life Insurance Standard LIS and Life Insurance Premium LIP) and the number of constraints (the budget designed for the training of the sales team, the contribution margin and the number of sales agents). The arguments of the objective function are introduced in the first line and the coefficients specific to the three constraints will be introduced in the next lines. The values in the R.H.S. (right-hand side) field are represented by the optimization functions of the resources assignment under the conditions of the two decisional variables and the three constraints (the equations (1), (2) and (3), while the Direction field indicates the sign corresponding to the optimization functions. (figure no.1)

Figure no. 1 – Entry database for the problem concerning the optimization of the sales force efforts assignment in order to maximize the profit in an insurance company using WinQSB

software

The Solve the Problem function from the Solve and Analyze menu of the WinQSB software

provides the results of the problem that we will analyze and interpret in detail. The value of the solution for each decisional variable, the value of the unitary profits and the total contribution to the objective function are presented in the columns of the results data basis. (figure no. 2)

Figure no. 2 – The results of the problem concerning the optimization of the sales force efforts assignment in order to maximize the profit in an insurance company using WinQSB software

In many organizations the sales force is the company’s most expensive promotional resource, and too often companies fail to maximize return on that investment. Numerical measurements will always dominate any measure of sales force effectiveness, but a manager must look beyond that to drive superior performance. The linear programming problem concerning the sales force optimization can be equally important as the quantitative factors.