Research On Optimization Models Of Facility Location Problem With Collection Depots

Facility location decisions are critical elements in strategic planning fora wide range of private and public firms. The branches of locating facilities are broadand long-lasting, influencing numerous operational and logistical decisions, and the results in intense market competition. Facility location problems locate a set of facilitie to achieve the optimal objective with respect to some set ofconstraints. Certain facilities need an existing collection depot, such as a garbage disposal center or a warehouse, when serving their customers, where the depot chosen minimizes the cost for the customer. The objective of locating this kind of facility is minimizing the cost for all customers. Facility location problemwith collection depots is an extension of some classical location models including Weber problem and center problem. Research on facility location problem withcollection depots not only enriches and develops locationtheory but also deepens the research on Weber problem and center problem.Distance metric is one of critical factors in facility location problem. Different kind of facility usually uses different distance metric. In most cases, the distance metric is assumed to be symmetric, which means that the journey or time from one point to anotheris equal to the one back. However, in reality they are different due to some factors. Thus it is of a great significance both in theory and reality to introduce distances without symmetry in facility location problems.On the other hand, the demand of a customer can be represented by its weights. The demands of customers usually are not fixed after the facility is located, which results changing weights. When the weight is a stochastic variate from some probability distribution and so is the service cost, the minimum expected cost may be refered to be the limit of cost budget. However, in the process of location, the real cost would exceed this threshld, and over-run situation happens. When this situation is allowed, the objective of locating a facility is minimizing the over-run probability. Thus the minimization of over-run probability is realistic in facility location problems.On account of asymmetry of distance metric and randomness of demand weights, facility location problem withcollection depots is systematically studied in this thesis, aiming to enrich the research on facility location problem withcollection depots and provide theories and methods for locating facilities with this kind of service characteristic.First, some distance metric common in continuous facility location problems are summarized, most of which are special cases of convex distance function induced by a gauge metric. Models based on probabilistic method and scenario planningmethod for location problem with randomness are introduced. For facility location problem withcollection depots, models with different objective and service path are analyzed. On this basis overall framework for optimization models of facility location problem withcollection depots is presented.When the distance metric fails the symmetric property, minimax and minisum models of facility location problem withcollection depotsunder convex distance are formulated, respectively, and is divided into round-trip case and one-way cases according to the service path pattern. Based on theories of geometry and convex analysis, properties of bisectors and existence of dominant solution are studied, from which it follows the existence of optimal solution of location models with convex distance. With help of subgradient and construction of effect lowerbound of the objective function, solving methods based on the Big Triangle Small Triangle method are presented.For the case that demand weights are independent random variates from some probability distributions, the service cost is expressed as the maximum weighted distance of all demand points, and round-trip minimax model and one-way minimax models of over-run probability minimization problem are formulated. Properties of the optimization models are studied and existence of optimal solution in the convx hull of demand points and collection depots is shown. By obtaining upper bounds and lower bounds of round-trip and one-way distances and objective functions, methods are presented to solve random minimax models. Numerical examples show the feasibility of our methods.When demand weights are drawn from some probability distributions, the service cost is represented as the total weighted distances of all demand points and models of over-run probability minimization problem with minisum objective are formulated according to different service path patterns. On one hand, for each service path pattern, the minimization problem is transferred equivalently to a normalized threshold maximization problem, some properties of the equivalent model are found and a sufficient condition for existence of optimal solution is presented. On the other hand, when the over-run probability is given, models of threshold minimization problem are formulated based on the upper quantile of standard normal distribution, and sufficient conditions for existence of optimal solutions are shown. By obtaining upper bounds and lower bounds of objective functions, methods are presented to solve presented models. Numerical examples show the feasibility of our methods.Optimization models and solving methods of facility location problem withcollection depotsunder convex distance and random weights are applied to the First Environmental Sanitation Transportation Center in Xiangfang District in Harbin. Based on analysis of collection and transportation service of municipal solid waste, optimal locations are found for the transportation center to cope with increasing population, which provides reasonable foundation in theory for relocation in the future.