Discrete-continuous project scheduling problems with positive discounted cash flows andthe maximization of the NPV are considered. We deal with a class of theseproblems with an arbitrary number of discrete resources and one continuous, renewableresource. Activities are nonpreemptable, and the processing rate of an activity is acontinuous, increasing function of the amount of the continuous resource allotted to theactivity at a time. Three common payment models – Lump Sum Payment, Payments at ActivityCompletion times, and payments in Equal Time Intervals are analyzed. Formulations ofmathematical programming problems for an optimal continuous resource allocation for eachpayment model are presented. Applications of two local search metaheuristics – Tabu Searchand Simulated Annealing are proposed. The algorithms are compared on a basis ofcomputational experiments. Some conclusions and directions for future research are pointedout.

Optimization is an important tool widely used in formulation of the mathematical modeland design of various decision making problems related to the science and engineering.Generally, the real world problems are occurring in the form of multi-criteria andmulti-choice with certain constraints. There is no such single optimal solution existwhich could optimize all the objective functions simultaneously. In this paper,ϵ-constraint method along with Karush−Kuhn−Tucker (KKT) condition has been used tosolve multi-objective Geometric programming problems(MOGPP) for searching a compromisesolution. To find the suitable compromise solution for multi-objective Geometricprogramming problems, a brief solution procedure using ϵ-constraint method hasbeen presented. The basic concept and classical principle of multi-objective optimizationproblems with KKT condition has been discussed. The result obtained by ϵ-constraint method withhelp of KKT condition has been compared with the result so obtained by Fuzzy programmingmethod. Illustrative examples are presented to demonstrate the correctness of proposedmodel.

In this paper we give necessary and sufficient optimality conditions for a vectoroptimization problem over cones involving support functions in objective as well asconstraints, using cone-convex and other related functions. We also associate a unifieddual to the primal problem and establish weak, strong and converse duality results. Anumber of previously studied problems appear as special cases.

This work aims to fill a lacunae in the project-oriented production systems literatureproviding a formal analytic description of the rework effects formulae and thedetermination of the extended design time due to a certain degree of overlapping in a pairof activities. It is made through the utilization of concepts of workflow constructionwith hidden (semi) Markov models theory and establishing a way to disaggregate activitiesinto sub-activities, in order to determine the activity parameters used by the projectscheduling techniques. With the aim to make a correlation between the entropy of the statetransitions and the probability of changes, the information theory is also used, and theconcept of impact caused by the probability of changes is provided. Numerical examples areshown for the purpose to demonstrate the applicability of the concepts developed, and oneexample of overlapping of two activities is shown. The original contributions of this workare shown on the last section.

The present paper addresses the class of two-stage robust optimization problems which canbe formulated as mathematical programs with uncertainty on the right-hand sidecoefficients (RHS uncertainty). The wide variety of applications and the fact that manyproblems in the class have been shown to be NP-hard, motivates the search for efficientlysolvable special cases. Accordingly, the first objective of the paper is to provide anoverview of the most important applications and of various polynomial or pseudo-polynomialspecial cases identified so far. The second objective is to introduce a new subclass ofpolynomially solvable robust optimization problems with RHS uncertainty based on theconcept of state-space representable uncertainty sets. A typicalapplication to a multi period energy production problem under uncertain customer loadrequirements is described into details, and computational results including a comparisonbetween optimal two-stage solutions and exact optimal multistage strategies arediscussed.

A concept of an Orderly Colored Longest Path (OCLP) refers to the problem of finding the longest path in a graph whose edges are colored with a given number of colors, under the constraint that the path follows a predefined order of colors. The problem has not been widely studied in the previous literature, especially for more than two colors in the color arrangement sequence. The recent and relevant application of OCLP is related to the interpretation of Nuclear Magnetic Resonance experiments for RNA molecules. Besides, an employment of this specific graph model can be found in transportation, games, and grid graphs. OCLP models the relationships between consecutive edges of the path, thus it appears very useful in representing the real problems with specific ties between their components. In the paper, we show OCLP’s correlation with similar issues known in graph theory. We describe the applications, three alternative models and new integer programming algorithms to solve OCLP. They are formulated by means of max flow problems in a directed graph with packing constraints over certain partitions of nodes. The methods are compared in a computational experiment run for a set of randomly generated instances.

We study an uncapacitated facility location model where customers are served byfacilities of level one, then each level one facility that is opened must be assigned toan opened facility of level two. We identify a polynomially solvable case, and study somevalid inequalities and facets of the associated polytope.

This paper addresses the problem of managing a waiting list for elective surgery todecide the number of patients selected from the waiting list and to schedule them inaccordance with the operating room capacity in the next period. The waiting listprioritizes patients not only by their initial urgency level but also by their waitingtime. Selecting elective surgery patients requires a balance between the waiting time forurgent patients and that for less urgent patients. The problem is formulated as aninfinite horizon Markov Decision Process. Further, the study proposes a schedulingprocedure based on structural properties of an optimal policy by taking a sampling-basedfinite horizon approximation approach. Finally, we examine the performance of the policyunder various conditions.

We present a non-cooperative union-firm wage bargaining model in which the union mustchoose between strike and holdout if a proposed wage contract is rejected. The innovativeelement that our model brings to the existing literature on wage bargaining concerns theparties’ preferences which are not expressed by constant discount rates, but by sequencesof discount factors varying in time. First, we determine subgame perfect equilibria if thestrike decision of the union is exogenous. We analyze the case when the union is committedto strike in each disagreement period, the case when the union is committed to strike onlywhen its own offer is rejected, and the case of the never strike exogenous decision. Acomparison of the results is provided, among the cases of the exogenous strike decisions.Next, we consider the general model with no assumption on the commitment to strike. Wefind subgame perfect equilibria in which the strategies supporting the equilibria in theexogenous cases are combined with the minimum-wage strategies, provided that the firm isnot less patient than the union. If the firm is more impatient than the union, then thefirm is better off by playing the no-concession strategy. We find a subgame perfectequilibrium for this case.

We study the pricing problem between two firms when the manufacturer’s willingness to pay(wtp) for the supplier’s good is not known by the latter. We demonstrate that it is in theinterest of the manufacturer to hide this information from the supplier. The precision ofthe information available to the supplier modifies the rent distribution. The risk ofopportunistic behaviour entails a loss of efficiency in the supply chain. The model isextended to the case of a supplier submitting offers to several manufacturers. Somemanagerial insight through a numerical illustration is provided.

In this article we study the realistic network topology of Synchronous Digital Hierarchy(SDH) networks. We describe how providers fulfill customer connectivity requirements. Weshow that SDH Network design reduces to the Non-Disjoint m-Ring-Star Problem (NDRSP). Wefirst show that there is no two-index integer formulation for this problem. We thenpresent a natural 3-index formulation for the NDRSP together with some classes of validinequalities that are used as cutting planes in a Branch-and-Cut approach. We propose apolyhedral study of a polytope associated with this formulation. Finally, we present ourBranch-and-Cut algorithm and give some experimental results on both random and realinstances.

A Content Distribution Network (CDN) can be defined as an overlay system that replicatescopies of contents at multiple points of a network, close to the final users, with theobjective of improving data access. CDN technology is widely used for the distribution oflarge-sized contents, like in video streaming. In this paper we address the problem offinding the best server for each customer request in CDNs, in order to minimize theoverall cost. We consider the problem as a transportation problem and a distributedalgorithm is proposed to solve it. The algorithm is composed of two independent phases: adistributed heuristic finds an initial solution that may be later improved by adistributed transportation simplex algorithm. It is compared with the sequential versionof the transportation simplex and with an auction-based distributed algorithm.Computational experiments carried out on a set of instances adapted from the literaturerevealed that our distributed approach has a performance similar or better to itssequential counterpart, in spite of not requiring global information about the contentsrequests. Moreover, the results also showed that the new method outperforms thebased-auction distributed algorithm.

The object of this research in the queueing theory is a theorem about theStrong-Law-of-Large-Numbers (SLLN) under the conditions of heavy traffic in a multiserveropen queueing network. SLLN is known as a fluid limit or fluid approximation. In thiswork, we prove that the long-term average rate of growth of the queue length process of amultiserver open queueing network under heavy traffic strongly converges to a particularvector of rates. SLLN is proved for the values of an important probabilisticcharacteristic of the multiserver open queueing network investigated as well as the queuelength of jobs.

In this paper, we develop a divide-and-conquer approach, called block decomposition, tosolve the minimum geodetic set problem. This provides us with a unified approach for allgraphs admitting blocks for which the problem of finding a minimum geodetic set containinga given set of vertices (g-extension problem) can be efficiently solved. Ourmethod allows us to derive linear time algorithms for the minimum geodetic set problem in(a proper superclass of) block-cacti and monopolar chordal graphs. Also, we show that hullsets and geodetic sets of block-cacti are the same, and the minimum geodetic set problemis NP-hard in cobipartite graphs. We conclude by pointing out several interesting researchdirections.

Dynamic Cell Formation Problem (DCFP) seeks to cope with variation in part mix anddemands using machine relocation, replication, and removing; whilst from practical pointof view it is too hard to move machines between cells or invest on machine replication. Tocope with this deficiency, this paper addresses Reconfigurable Dynamic Cell FormationProblem (RDCFP) in which machine modification is conducted instead of their relocation orreplication in order to enhance machine capabilities to process wider range of productiontasks. In this regard, a mixed integer nonlinear mathematical model is proposed, which isNP-hard. To cope with the proposed model’s intractability, an Imperialist CompetitiveAlgorithm (ICA) is developed, whose obtained results are compared with those of GeneticAlgorithm’s (GA’s), showing superiority and outperformance of the developed ICA.

In this paper, we develop the concept of almost stochastic dominance for higher orderpreferences and investigate the related properties of this concept.

In this paper, we show how optimization methods can be used efficiently to determine theparameters of an oscillatory model of handwriting. Because these methods have to be usedin real-time applications, this involves that the optimization problems must be rapidelysolved. Hence, we developed an original heuristic algorithm, named FHA. This code wasvalidated by comparing it (accuracy/CPU-times) with a multistart method based on TrustRegion Reflective algorithm.

In this short note, we investigate the framework where agents or players have some uncertainties upon their payoffs or losses, the behavior (or the type, number or any other characteristics) of other players. More specifically, we introduce an extension of the concept of Nash equilibria that generalize different solution concepts called by their authors, and depending on the context, either as robust, ambiguous, partially specified or with uncertainty aversion. We provide a simple necessary and sufficient condition that guarantees its existence and we show that it is actually a selection of conjectural (or self-confirming) equilibria. We finally conclude by how this concept can and should be defined in games with partial monitoring in order to preserve existence properties.

The problem of finding structures with minimum stabbing number has received considerableattention from researchers. Particularly, [10]study the minimum stabbing number of perfect matchings (mspm), spanning trees(msst) and triangulations (mstr) associated to set of points in theplane. The complexity of the mstr remains open whilst the other two are known tobe 𝓝𝓟-hard. This paper presents integer programming(ip) formulations for these three problems, that allowed us to solve them tooptimality through ip branch-and-bound (b&b) or branch-and-cut(b&c) algorithms. Moreover, these models are the basis for the developmentof Lagrangian heuristics. Computational tests were conducted with instances taken from theliterature where the performance of the Lagrangian heuristics were compared with that ofthe exact b&b and b&c algorithms. The results reveal that theLagrangian heuristics yield solutions with minute, and often null, duality gaps forinstances with several hundreds of points in small computation times. To our knowledge,this is the first computational study ever reported in which these three stabbing problemsare considered and where provably optimal solutions are given.