Throughout the past decade, there has been an extensive research on scheduling the hospital resources such as the operation theatre(s) (OTs) and the experts (such as nurses, doctors etc.) inside the hospitals. With the technological growth, mainly advancement in communication media (such as smart phones, video conferencing, smart watches etc.) one may think of taking the expertise by the doctors (distributed around the globe) from outside the in-house hospitals. Earlier this interesting situation of hiring doctors from outside the hospitals has been studied from monetary (with patient having infinite budget) and non-monetary perspectives in strategic setting. In this paper, the more realistic situation is studied in terms of hiring the doctors from outside the hospital when a patient is constrained by budget. Our proposed mechanisms follow the two pass mechanism design framework each consisting of allocation rule and payment rule. Through simulations, we evaluate the performance and validate our proposed mechanisms.