In this research, critical infrastructure protection against intentional attacks is modeled as a discrete simultaneous game between the protector and the attacker, to model the situation that both players keep the information of their resource allocation secret. We prove that keeping the...

Let P be an undirected path graph of n vertices. Each edge of P has a positive length and a constant capacity. Every vertex has a nonnegative supply, which is an unknown value but is known to be in a given interval. The goal is to find a point on P to build a facility and move all vertex...

Pisinger et al. introduced the concept of ‘aggressive reduction’ for large-scale combinatorial optimization problems. The idea is to spend much time and effort in reducing the size of the instance, in the hope that the reduced instance will then be small enough to be solved by an exact...

The design of distribution systems raises hard combinatorial optimization problems. For instance, facility location problems must be solved at the strategic decision level to place factories and warehouses, while vehicle routes must be built at the tactical or operational levels to supply...

In today’s retail business many companies have a complex distribution network with several national and regional distribution centers. This article studies an integrated facility location and inventory allocation problem for designing a distribution network with multiple distribution centers...

In this paper, we present a cut-and-solve (CS) based exact algorithm for the Single Source Capacitated Facility Location Problem (SSCFLP). At each level of CS’s branching tree, it has only two nodes, corresponding to the Sparse Problem (SP) and the Dense Problem (DP), respectively. The SP,...

The two-echelon location-routing problem (LRP-2E) arises from recent transportation applications like city logistics. In this problem, still seldom studied, first-level trips serve from a main depot a set of satellite depots, which must be located, while second-level trips visit customers from...

In this paper, we discuss two challenges of long term facility location problem that occur simultaneously; future demand change and uncertain number of future facilities. We introduce a mathematical model that minimizes the initial and expected future weighted travel distance of customers. Our...

The location set covering problem continues to be an important and challenging spatial optimization problem. The range of practical planning applications underscores its importance, spanning fire station siting, warning siren positioning, security monitoring and nature reserve design, to name...

The inequality measure “Quintile Share Ratio” (QSR or sometimes S80/S20) is the primary income inequality measure in the European Union’s set of indicators on social cohesion. An important reason for its adoption as a leading indicator is its simplicity. The Quintile Share Ratio is “The...