Study On The Home Care Center Location Problem Under Uncertain Demand

The rapid aging of Chinese population makes the medical andnursing care institutions full loaded. Home care services, which areprovided by its staff going to the customers’ houses, including homehealth care and routine home care, can reduce the burden on theseinstitutions and provide convenient services to the elderly on a largescale. Home care center location problem is not only related to thequality of elders’ lives and the development of home care serviceenterprises, but also related to the distribution of social resources. Onthe basis of existing studies, this thesis focuses on the home care centerlocation problem, models, verifies and analyses the location problemunder certainty and uncertainty, takes into account the combination oflocation and path optimization problem and takes the family care centerslocation problem of Yangpu District, Shanghai city as an example. Theoverall study can be divided into three parts.Firstly, home care center location problem under deterministicdemand is studied. Taking the type of multi-service multi-facility, timevalue of money and response time limit into consideration, and treatingthe minimization of the total cost (including the cost of opening servicecenters and their services, labor cost and distance cost) as the objective,this thesis builds a multi-stage mixed integer programming model anduses C#to call Cplex to solve and verify the model. Comparativeanalysis of the impact on the model results with and without responsetime limit constraints is done. The conclusion is that the response timelimit constraint can greatly reduce the average response time, improve the service efficiency and customer satisfaction, while causing a slightincrease in the total cost; The total cost will reduce as the response timelimit is increased, and it will (almost) linearly increase as the time valueof money, investment cost and the value of other parameters increase.Secondly, the location problem under stochastic demand is studied.Taking the uncertain demand and uncertain travel time due to theuncertain road conditions, weather, vehicle condition and other factorsinto consideration and treating the minimization of the total cost(including the cost of opening service centers and their services andlabor cost) as the objective, a multi-stage stochastic probabilisticconstraint model of location problem is provided. The probabilisticconstraints are translated into deterministic constraints. A local searchheuristic is used to solve the model. The conclusion is that these twoprobabilistic constraints cause the total cost down, but the averageresponse time is extended. As for the determination of the initial solutionof the heuristic algorithm, two solutions are given. One is substitutingthe mean of demand into the model to solve it. The other one iscalculating the capacity needed for each single home care center to meetthe demand, and then substitute the result into the model and solve it.Numerical results show that the first method is better than the secondone. On the basis of the better one, this thesis studies the impact of threeparameters, which are the response time limit U, the probability ofmeeting total demand and the probability of offering services withintime limit U, on the model result. The conclusion is that the total costincreases as U increases and decreases as, increase. The averageresponse time increases as U increases, decreases as increases andkeeps the same no matter how changes.Thirdly, the joint optimization of home care center location andservice routing is concerned, with consideration of constraints onresponse time to customer’s demand and on service level. A multi-stagejoint optimization model is proposed to minimize the total cost consisting of facility open cost, service open cost and capacity cost. Inorder to reduce the computational complexity, a traveling time operatoris introduced to decompose the joint model into two sub-models(location and routing), and a heuristic and C-W saving algorithm areproposed to solve these two sub-models respectively. finally, a localsearch algorithm based on traveling time operator is proposed to solvethe joint optimization model heuristically. The model has been validatedby a case and impacts of demand uncertainty and response timeconstraint on the result are evaluated and analyzed.