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Nonlinear integer programming problem

Explain Nonlinear integer programming problem with an example ?

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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→=(c1,1,…,c1,Q,……,cI,1,……,cI,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→=(x1,1,…,x1,Q,……,xI,1,……,xI,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→=(y1,1,…,y1,Q,……,yI,1,……,yI,Q)', where yi,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 gk,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:

350_nonlinear progg.jpg

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