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The model you linked in the question will do the job. You just set $a_{jt}=0$ if a worker on shift $j$ would be taking a break at time $t$.


I am not sure of the bounds of the problem, but I'll try to provide an answer. Let's consider the following two sets: $$ V = \{v: vehicles\} \\ T = \{t: days\} $$ Now, we have the parameters you have provided, which I understand are the following: $$ VCAP_v: \text{capacity of vehicle v} \\ VCOST_v: \text{cost of vehicle v}\\ D_t: \text{demand of day t} $$ ...

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