how to handle semi continuous constraints by using the optimization toolbox?

bold VRP is a mixed integer problem, just like this.

where g_i is the demand of customer i, q is the capacity of vehicle.

but when we consider VRP with time windows, dependent variables are coming, we should add constraints like this

In the above formulations,

where s_i is the time spot when a vehicle arrives at customer i, and a_i,b_i ,are time windows of customer i

how should I handle constraint (10) which is not continuous by using the Matlab optimization toolbox?

Answer 1

[Alan Weiss]

Take a look at this example and others in the Mixed-Integer Linear Programming Examples.

Alan Weiss

MATLAB mathematical toolbox documentation

[qing WU]

what confused me is how to handle constraint (10), not the relationship between x and y or t