Nonlinear integer programming problem

Question

Explain Nonlinear integer programming problem with an example ?

Answer 1

The nonlinear integer programming problem in this optimal staffing problem can be highlighted as below:

With service-level constraints over a time interval, suppose there are K call types, I skill groups, P periods and Q types of work schedules. We have the following definition of parameters:

The cost vector can be defined as c^→=(c_1,1,…,c_1,Q,……,c_I,1,……,c_I,Q)' where ci,Q is the cost of agent of skill group i having shift q. The decision variables can be defined as this vector x^→=(x_1,1,…,x_1,Q,……,x_I,1,……,x_I,Q)', where xi,Q is the number of agents with skill group i having shift q. The paper defines a vector of auxiliary variable y^→=(y_1,1,…,y_1,Q,……,y_I,1,……,y_I,Q)', where y_i,Q is the number of agents with skill group i in period p.

The vector satisfies the matrix equation y^→=Ax^→ , where the element (p,q) of matrix A is 1 and other elements are zero. By defining the service level for call type g_k,p(y^→) as the ratio of expected value of number of calls answered within sk,p seconds in period p and number of calls in period p, the single-stage steady problem solved in this paper can be formulated as: