Bi-level programming for home health care supply chain considering outsourcing

Home Health Care Supply Chain (HHCSC) is an interesting and widespread topic in developed countries due to an aging population's care. Home care services aim to provide general hygiene care and nursing considering dependency for older people. One of the real circumstances in such systems is that the two parties, caregivers and patients, adopt their decisions at different decision levels. From the perspective of HHCSC companies, the position of pharmacies, scheduling and routing of nurses, and the quantity of releasing drugs have been important and open issues. Another real supposition in HHCSC networks is that the patients choose their company and its services according to its cost. Contrary to previous works, here, we firstly consider outsourcing for patients' demand to receive direct services from a hospital as a real assumption. Besides, this work develops a bi-level programming model as a static Stackelberg game between nurses and patients within the framework of HHCSC. Another novelty of this work is to utilize capable meta-heuristics reported in the literature as well as hybrid ones. To validate the application of meta-heuristics in small sizes, a solution procedure combining a heuristic and exact method is utilized. Finally, comparative analysis of the algorithm, probing the model using a real-case study, and some sensitivity analyses are done.