Mathematical Model and Stochastic Multi-Criteria Acceptability Analysis for Facility Location Problem

This paper studies a real-life public sector facility location problem. The problem fundamentally originated from the idea of downsizing the number of service centres. However, opening of new facilities is also considered in case the current facilities fail to fulfil general management demands. Two operation research methodologies are used to solve the problem and the obtained results are compared. First, a mathematical programming model is introduced to determine where the new facilities will be located, and which districts get service from which facilities, as if there were currently no existing facilities. Second, the Stochastic Multi-criteria Acceptability Analysis-TRI (SMAA-TRI) method is used to select the best suitable places for service centres among the existing facilities. It is noted that the application of mathematical programming model and SMAA-TRI integration approach on facility location problem is the first study in literature. Compression of outcomes shows that mixed integer linear programming (MILP) model tries to open facilities in districts which are favoured by SMAA-TRI solution.</span

On green routing and scheduling problem

The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools

Bilevel facility location problems: theory and applications.

In this doctoral thesis we focus on studying facility location problems considering customer preferences. In these problems, there is a set of customers or users who demand a service or product that must be supplied by one or more facilities. By facilities it is understood some object or structure that offers some service to customers. One of the most important assumptions is that customers have established their own preferences over the facilities and should be taken into account in the customer-facility assignment. In real life, customers choose facilities based on costs, preferences, a predetermined contract, or a loyalty coefficient, among others. That is, they are free to choose the facilities that will serve them. The situation described above is commonly modeled by bilevel programming, where the upper level corresponds to location decisions to optimize a predefined criteria, such as, minimize location and distribution costs or maximize the demand covered by the facilities; and the lower level is associated to -customer allocation- to optimize customer preferences. The hierarchy among both levels is justified because the decision taken in the upper level directly affects the decision’s space in the lower level

Reducing mixed-integer to zero-one programs

During the last decades, there has been a lot of success in the operational research community in the development of efficient algorithms for several integer optimization programs. Unfortunately, these programs are often not sufficient to represent the environment and thus real-life applications appropriate. This challenge can only be solved by using additionally continuous variables. Then, for their optimization it is of course possible to develop always a new algorithm for each of them. But obviously, this is very expensive: On the one hand, based on the endless number of potentially occurring programs and on the other hand, based on the complexity of the problems themselves. Thus, instead of always developing a new approach, the basic idea of this thesis was to check, if it is admirable to reduce several mixed integer programs to integer ones for which approved approaches are available and that can be applied straightforward then

Modeling and analysis of the generalized warehouse location problem with staircase costs

The Capacitated Warehouse Location consists of determining the number and locations of capacitated warehouses on a set of potential sites such that demands of predefined customers are met. Two typical assumptions in modeling this problem are: the capacity of warehouses is constant and that warehouses are able to truly satisfy customer demands. However, while these kinds of assumptions define a well structured problem from the mathematical modeling perspective, they are not realistic. In this thesis we relaxed such constraints based on the fact that warehouses can be built in various sizes and also warehouses can put in orders for unsatisfied customers' demand directly to the manufacturing plant with additional costs. This flexibility can lead to best decision making ability for managers and supply chain specialists to decide between higher capacity level with higher fixed and variable costs at the warehouse or direct ordering from the manufacturing plant. A new non linear integer programming formulation with staircase costs for multiple commodities in supply chain network is presented, and new method for linearizing the model is described. Computational results indicate that reasonably good solution can be obtained by the proposed linear model. Also for solving larger problems we developed a Tabu Search algorithm. The comparisons of the result between nonlinear/linear model and the Tabu Search algorithm are also presented