Tu consulta optimizada sería asi:
Cita: "SELECT clientes.nombres, opertation.deliveryday, opertation.nrodoc, opertation.status, opertation.respons, opertation.view, opertation.dateprocess
FROM clientes inner join operation on clientes.idclie=opertation.idclie
Where opertation.idclie =$customer
AND nrodoc LIKE '$nrodoc%'
OR DATE_FORMAT(deliveryday ,'%Y-%m-%d') >= '$deliveryday'
and DATE_FORMAT(deliveryday ,'%Y-%m-%d') <= '$dateprocess'
"
Esto no te digo que funcione, si no que es más optimo si el idclie es númerico