Sharif Digital Repository

In the project scheduling literature, nonrenewable resources are assumed to be available in full amount at the beginning of the project. However, in practice, it is very common that these resources are procured along the project horizon according to some pre-scheduled plan. In this paper, we study an extended form of the resource-constrained project scheduling problem that is subject to this type of nonrenewable resources in addition to the renewable resources. In order to solve this problem, we propose a branch and cut algorithm. We incorporate with the algorithm some technics and fathoming rules to shorten the solving process. The algorithm is capable of specifying lower bounds for the... 

In Mobile Ad hoc Networks (MANETs), nodes depend on each other for routing and forwarding their packets. However, to save power and other resources, nodes belonging to independent authorities may behave selfishly, and not cooperate in network activities. Such selfish behaviour poses a real threat to the proper functioning of MANETs. To cope with this situation, a motivation stimulation mechanism is required to provide sufficient incentives for nodes to forward other nodes' packets. One appropriate approach is to have network nodes pay in order to motivate them to cooperate with the protocol. To achieve truthfulness, the payment should be based on the cost of transmission of packets. Since... 

A lot of projects in real life are subject to some kinds of nonrenewable resources that are not exactly similar to the type defined in the project scheduling literature. The difference stems from the fact that, in those projects, contrary to the common assumption in the project scheduling literature, nonrenewable resources are not available in full amount at the beginning of the project, but they are procured along the project horizon. In this paper, we study this different type of nonrenewable resources. To that end, we extend the resource constrained project scheduling problem (RCPSP) by this resource type (RCPSP-NR) and customize four basic branch and bound algorithms of RCPSP for it,... 

We introduce a multimode resource-constrained project scheduling problem with finish-to-start precedence relations among project activities, considering renewable and nonrenewable resource costs. We assume that renewable resources are rented and are not available in all periods of time of the project. In other words, there is a mandated ready date as well as a due date for each renewable resource type so that no resource is used before its ready date. However, the resources are permitted to be used after their due dates by paying penalty costs. The objective is to minimize the total costs of both renewable and nonrenewable resource usage. This problem is called multimode resource-constrained... 

Scheduling under nonrenewable resources is one of the challenging issues in project scheduling problems. There are many cases where the projects are subject to some nonrenewable resources. In most of the literature, nonrenewable resources are assumed to be available in full amount at the beginning of the project. However, in practice, it is prevalent that these resources are procured along the project horizon. This paper studies the generalized resource-constrained project scheduling problem (RCPSP) where, in addition to renewable resources, nonrenewable resources are considered, such as budget or consuming materials by the project activities. As the problem is NP-hard, some sub-algorithm... 

In this paper we introduce some general necessary conditions for the existence of graph homomorphisms, which hold in both directed and undirected cases. Our method is a combination of Diaconis and Saloff–Coste comparison technique for Markov chains and a generalization of Haemers interlacing theorem. As some applications, we obtain a necessary condition for the spanning subgraph problem, which also provides a generalization of a theorem of Mohar (1992) as a necessary condition for Hamiltonicity. In particular, in the case that the range is a Cayley graph or an edge-transitive graph, we obtain theorems with a corollary about the existence of homomorphisms to cycles. This, specially, provides... 

In this paper we introduce a chromatic parameter, called the fixing chromatic number, which is related to unique colourability of graphs, in the sense that it measures how one can embed the given graph G in G∪Kt by adding edges between G and Kt to make the whole graph uniquely t-colourable. We study some basic properties of this parameter as well as its relationships to some other well-known chromatic numbers as the acyclic chromatic number. We compute the fixing chromatic number of some graph products by applying a modified version of the exponential graph construction  

In this paper, we apply some new algebraic no-homomorphism theorems in conjunction with some new chromatic parameters to estimate the circular chromatic number of graphs. To show the applicability of the general results, as a couple of examples, we generalize a well known inequality for the fractional chromatic number of graphs and we also show that the circular chromatic number of the graph obtained from the Petersen graph by excluding one vertex is equal to 3. Also, we focus on the Johnson–Holroyd–Stahl conjecture about the circular chromatic number of Kneser graphs and we propose an approach to this conjecture. In this regard, we introduce a new related conjecture on Kneser graphs and we... 

We introduce two necessary conditions for the existence of graph homomorphisms based on the concepts of density and power graph. As corollaries, we obtain a lower bound for the fractional chromatic number, and we set forward elementary proofs of the facts that the circular chromatic number of the Petersen graph is equal to three and the fact that the Coxeter graph is a core  

The effect of temperature on the noncontact atomic force microscopy (NC-AFM) surface imaging is investigated with the aid of molecular dynamics (MD) analysis based on the Sutton-Chen (SC) interatomic potential. Particular attention is devoted to the tip and sample flexibility at different temperatures. When a gold coated probe is brought close to the Au (001) surface at high temperatures, the tip and surface atoms are pulled together and their distance becomes smaller. The tip and sample atoms displacement varies in the different environment temperatures and this leads to the different interaction forces. Along this line, to study the effect of temperature on the resulting images, we have...