A multiobjective routing model for Multiprotocol Label Switching networks with multiple service types and traffic splitting is presented in this paper. The routing problem is formulated as a multiobjective mixed-integer program, where the considered objectives are the minimization of the bandwidth routing cost and the minimization of the load cost in the network links with a constraint on the maximal splitting of traffic trunks. Two different exact methods are developed for solving the formulated problem, one based on the classical constraint method and another based on a modified constraint method. A very extensive experimental study, with results on network performance measures in various reference test networks and in randomly generated networks, is also presented and its results are discussed.

A series of studies demonstrate that consumers have fairness judgments about the retailer’s price which will impact their shopping decisions. Thus, it is necessary for the retailer to take consumers’ fairness concerns into account when setting his pricing policies. We assume that when the retailer’s price is lower than a consumer’s justice reference price, the consumer is likely to sense a positive price unfairness that will lead to increased consumer utility, and when the retailer’s price is higher than a consumer’s justice reference price, the consumer is likely to sense a negative price unfairness that will have a negative effect on consumer utility. According to the information conditions of the consumers’ justice reference price, the retailer should consider three situations: certain information, random information and partial information. In all situations, we show that the retailer has a unique optimal pricing strategy. Finally, through numerical examples, we find that our distribution-free policies perform almost the same as the results under the distributions that maximize the entropy. Our results reveal that it is important for the retailer to consider consumers’ fairness concerns, otherwise he may suffer losses when p _c is very small.

A novel approach for assessing the robustness of an equilibrium in conflict resolution is presented. Roughly, an equilibrium is robust if it is resilient, or resistant to deviation. Robustness assessment is based on a new concept called Level of Freedom, which evaluates the relative freedom of a decision maker to escape an equilibrium. Resolutions of a conflict can be affected by changes in decision makers’ preferences, which may destabilize an equilibrium, causing the conflict to evolve. Hence, a conflict may become long-term and thereby continue to evolve, even after reaching an equilibrium. The new robustness measure is used to rank equilibria based on robustness, to facilitate distinguishing equilibria that are relatively sustainable. An absolutely robust equilibrium is a special case in which the level of freedom is at an absolute minimum for each individual stability definition.

It is not usually independent among criteria in multi-criteria decision making (MCDM), and various dependences of criteria greatly influence the results of decision making. If an exact decision is desired, we must make clear the role of the dependences of criteria. Prioritizations, a new kind of dependences of criteria proposed recently, imply that the importance weights of criteria with lower priority for an alternative rely on whether the alternative satisfies the decision maker under criteria with higher priority. It has been validated that there exist lots of relevant applications in our daily activities. However, most existing literatures focus on how to deal with the problems of MCDM with ordered prioritizations among criteria (a special form of prioritizations). The characteristics of prioritizations are not dug deep. This paper constructs a new form of prioritizations, called paired prioritizations, so as to reduce or even avoid imperfect rationality of decision makers hidden in the ordered prioritizations. We first represent binary paired prioritizations as a digraph, based on which we discover two kinds of imperfect rationality (inconsistency and incompleteness) produced in the period that the decision maker supplies the binary paired prioritizations. After the given paired prioritizations are consistent and complete, we develop an approach to transform the paired prioritizations to ordered prioritizations. The latter can be used to handle prioritized MCDM problems. Moreover, uncertainty, another kind of imperfect rationality, is considered when the decision maker provides the fuzzy paired prioritizations based on a set of linguistic labels. We construct a fuzzy digraph whose fuzzy relations are just the fuzzy paired prioritizations. The ordered prioritizations can then be derived with the aid of the fuzzy digraph. Two use cases are taken to show the process of transformations from binary/fuzzy paired prioritizations to ordered prioritizations.

Increased globalization, as well as the ability to have virtual supply chain partners, has had numerous effects on supply chains. While some of these effects are positive, making more resilient supply chains, there are also the negative effects of scale and complexity, making these supply chains more challenging than ever to manage. Having a means to measure the complexity is crucial for today’s managers to make more informed decisions. This measure must not only account for the number of arcs, but the amount of information and material carried on it, as well as incorporate the benefit that virtual arcs add to the network by increasing efficiency and reducing information, product and financial transfer costs and time. This research utilizes newer models in network clustering and complexity theory to make them applicable to supply chains and creates a new, practical approach to measuring supply chain complexity which can be easily implemented by practitioners.

Path determination is a fundamental problem of operations research. Current solutions mainly focus on the shortest and longest paths. We consider a more generalized problem; specifically, we consider the path problem with desired bounded lengths (DBL path problem). This problem has extensive applications; however, this problem is much harder, especially for large-scale problems. An effective approach to this problem is equivalent simplification. We focus on simplifying the problem in acyclic networks and creating a path length model that simplifies relationships between various path lengths. Based on this model, we design polynomial algorithms to compute the shortest, longest, second shortest, and second longest paths that traverse any arc. Furthermore, we design a polynomial algorithm for the equivalent simplification of the DBL path problem. The complexity of the algorithm is O(m), where m is the number of arcs.