Abstract    This paper presents a multi-objective and multi-service location-allocation model with capacity planning to design a healthcare facilities network through considering a referral system. Therefore, a mixed integer nonlinear programming (MINLP) model containing two objective functions is proposed. The first objective function is relates to minimization of total opening cost, minimization of total set up cost of different types of services and minimization of total traveled distance by patients to reach each facility. The second objective function in the model aims to minimize maximum normalized workload between opened facilities in each level. Specifying location of different facilities, allocating patients zones to family physician centers, establishing an optimal flow between different levels in the network and determining the optimal capacity for different specialized and super specialty facilities are main strategic and tactical decisions in the proposed model. In order to solve the proposed model and arrive at Pareto solutions, a primary nonlinear integer program is transformed to linearize the model and then, an augmented -constraint method is applied on numerical examples. Finally, the results obtained by sensitivity analysis on the main parameters are reported to show that the presented model can be used to design a multi-level healthcare facility network.

Keywords    Healthcare network design, Location-allocation, Referral system, Capacity planning, Family physician centers, Augmented ε-constraint.

چکیده    دراین مقاله، یک مدل مکان­یابی-تخصیص چندهدفه و چندخدمته سلسله مراتبی به همراه برنامه­ریزی ظرفیت برای طراحی شبکه سلامت با در نظرگرفتنن نظام ارجاع ارائه شده است. بدین منظور یک مدل برنامه­ریزی غیرخطی دوهدفه پیشنهاد شده است. تابع هدف اول مربوط به حداقل کردن مجموع هزینه­های تاسیس تسهیلات ، هزینه­های راه­اندازی انواع خدمات در تسهیلات و مجموع مسافت طی شده توسط بیماران برای رسیدن به هر تسهیل می­باشد. در تابع هدف دوم، حداکثر بارکاری در میان تسهیلات بازشده درهرسطح حداقل می شود. در مدل پیشنهاد شده، تعیین مکان بهینه­ی تسهیلات مختلف، تخصیص مناطق بیماران به مراکز پزشک خانواده، تعیین جریان بهینه بین سطوح مختلف شبکه، وتعیین ظرفیت بهینه­ی تسهیلات تخصص و فوق­تخصصی جز تصمیمات مهم تاکتیکی و استراتژیکی است. به منظور حل مدل پیشنهادی و بدست آوردن نقاط پارتویی، ابتدا مدل ارائه شده به مدل خطی تبدیل شده، سپس از روش محدودیت اپسیلون توسعه یافته بر روی مثال­های عددی استفاده شده است. نتایج حاصل از آنالیز حساسیت برروی پارامترهای اساسی نشان می­دهد که مدل ارائه شده می­تواند برای طراحی شبکه سلامت چندسطحه به کار رود.

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