Robust Research On Network Facility Location Based On Uncertain Factors

Facility location decisions are long-term strategic issues. The facility will perform for a long time horizon once it is located, and the decisions have a far-reaching impact on the daily operational decisions. During the operational lifetime of a facility, it is inevitably to be influenced by various uncertain factors, any parameters (transportation costs, locations of the demand points, and demands) may change. The classical facility location models assume that the input datas are precisely known. During the time when design decisions are in effect and the parameters change, the optimal solution derived from the classical facility location models may no longer be optimal or even feasible, which will lead to operational inefficiency, a lower service level, and squandering of resources. Therefore, it is important to consider uncertainty in facility location modeling. This dissertation considers robust facility location problem facing uncertainty when the probability distribution of the parameter is unknown, and analyzes the optimal location decisions and the location cost with uncertain factors consideration.This dissertation firstly introduces the research background, analyzes the necessities of incorporating uncertain factors into facility location literatures, and then put forward the research topics to be studied and the major innovations.Secondly, this dissertation summarizes and reviews the state-of-art of the classical facility location literatures and the facility location models under uncertainty at home and abroad.Thirdly, this dissertation examines the fix changed facility location problem with demand uncertainty. Supposing the uncertain demands take values on bounded and symmetric intervals. The cardinality constrained robust approach is employed to formulate the robust fix changed facility location model, which offers full control on the degree of the robustness of the solution by adjusting the budget of uncertainty. An algorithm based on Tabu Search is designed to solve the problem. A numerical example is used to illustrate the trade-offs between the robustness of the solution and the cost.Fourthly, this dissertation examines multi-period facility location problem facing demand uncertainty. An uncapacitated facility location problem is combined with production and inventory decisions, which generalizes the traditional facility location model by taking into consideration the initial facility location cost, as well as the production and inventory cost. Supposing the uncertain demands are within bounded and symmetric intervals, a robust multi-period facility location model is proposed. The random generated numerical results show that the different degree of robust levels lead to very different solution network topologies. The impact of the service level on the facility network design is deeply analyzed. The trade-offs between facility location cost, the operational cost, the total cost and the service level are obtained.Fifthly, this dissertation examines robust facility location problem considering supply uncertainty. Supposing the supply of the facility in the actual operation is not equal to the supply initially established, that is the supply is subject to random fluctuation. The chance constraints are introduced when formulating the robust facility location model, which guarantees the system operate properly with a certain probability when the supply fluctuate. The chance constraints are approximated safely by using Hoeffding’s inequality and the problem is transformed to a general deterministic linear programming. Finally, how the facility location cost change with confidence level is investigated through a numerical example.Sixly, this dissertation examines the covering facility location problem based on uncertain facility interdiction. Firstly, supposing the interdiction probability of the facility is known. An α-cover constraint is defined, which ensure that even if the facilities are interdicted, every demand node is covered with probability of at least α. The covering constraints in the traditional set covering problrm are replaced by chance-constraints. Then, supposing the interdiction probability of the facility is imperfect. A Γ-robust α-cover constraint is defined, which guarantee that every demand node is covered with probability of at least a on the condition that at most Γ interdiction probability realized at their worst case scenario. The Γ-robust α-cover constraints are transformed equally to linear constraints by mathematical manipulation. The random generated numerical results show how the optimal location decisions and the facility location cost change with the parameters a and ΓFinally, the dissertation concludes the research and proposes future research topics.