Solving a bi-criterion cutting stock problem with open-ended demand: a case study

We consider a real-life cutting stock problem with two types of orders. All orders have to be cut from a given number of raws (also known as stock unit, master reel or jumbo). For each order the width of the final (also known as reels or units) and the number of finals is given. An order is called an exact order when the given number of finals must be produced exactly. An order is called an open order when at least the given number of finals must be produced. There is a given maximum on the number of finals that can be produced from a single raw which is determined by the number of knives on the machine. A pattern specifies the number of finals of a given width that will be produced from one raw. A solution consists of specifying a pattern for each raw such that in total the number of finals of exact orders is produced exactly and at least the number of finals of open orders is produced. There are two criteria defined for a solution. One criterion is the cutting loss: the total width of the raws minus the total width of the produced finals. The second criterion is the number of different patterns used in the solution. We describe a branch-and-bound algorithm that produces all Pareto-optimal solutions.     

Round robin tournaments and three index assignments

Scheduling a sports league can be seen as a difficult combinatorial optimization problem. We study some variants of round robin tournaments and analyze the relationship with the planar three-index assignment problem. The complexity of scheduling a minimum cost round robin tournament is established by a reduction from the planar three-index assignment problem. Furthermore, we introduce integer programming models. We pick up a popular idea and decompose the overall problem in order to obtain two subproblems which can be solved sequentially. We show that the latter subproblem can be casted as a planar three-index assignment problem. This makes existing solution techniques for the planar three-index assignment problem amenable to sports league scheduling.     

Scheduling a non-professional indoor football league: a tabu search based approach

This paper deals with a real-life scheduling problem of a non-professional indoor football league. The goal is to develop a schedule for a time-relaxed, double round-robin tournament which avoids close successions of games involving the same team in a limited period of time. This scheduling problem is interesting, because games are not planned in rounds. Instead, each team provides time slots in which they can play a home game, and time slots in which they cannot play at all. We present an integer programming formulation and a heuristic based on tabu search. The core component of this algorithm consists of solving a transportation problem, which schedules (or reschedules) all home games of a team. Our heuristic generates schedules with a quality comparable to those found with IP solvers, however with considerably less computational effort. These schedules were approved by the league organizers, and used in practice for the seasons 2009–2010 till 2016–2017.

     

On structural properties of the value function for an unbounded jump Markov process with an application to a processor sharing retrial queue

The derivation of structural properties for unbounded jump Markov processes cannot be done using standard mathematical tools, since the analysis is hindered due to the fact that the system is not uniformizable. We present a promising technique, a smoothed rate truncation method, to overcome the limitations of standard techniques and allow for the derivation of structural properties. We introduce this technique by application to a processor sharing queue with impatient customers that can retry if they renege. We are interested in structural properties of the value function of the system as a function of the arrival rate.     

One-step multi-electron transfer mechanism of polynuclear copper complexes for molecular conversions

The oxidative coupling reaction of 2,6-dimethylphenol may result in either a desired polymeric substance (i.e. the polyphenylene ether, PPE) or the undesired “dimeric” species diphenoquinone, DPQ. The relative amounts of each product depend on the experimental conditions and the used catalytic system. Usually copper amine compounds are used as a catalyst for the oxidative coupling reactions. They have the advantage of easy access and produce high yields of high molecular PPE; however, other metal coordination compounds, like those of Mn, may also be used as catalysts. The present paper focuses on mechanistic studies with various copper (aliphatic and aromatic) amine compounds as catalysts. Owing to the steric constraints of the amine ligands, dinuclear Cu(II) compounds, with small bridging anionic ligands, are easily formed. Such species are believed to be the catalyst precursors. Upon addition of a base (1:1 on copper) and excess phenol, phenolate ligands coordinate as bridging ligands to copper. After a two-electron transfer reaction, the resulting phenoxonium ligand, which is a rather poor ligand, remains attached to the Cu(I), probably coordinating via its aromatic ring. Nucleophilic attack by a phenol to the phenoxonium ion at the 4-position is likey to be most important to the coupling reaction. In the beginning of the reaction the undesired side product DPQ is also formed via a C–C coupling reaction. With copper(II) compounds containing imidazole-type chelating ligands, good activity was obtained; in the case of pyrazole-based and bridging S-donor chelating ligands, that no or very weak activity was found. In a study of the mechanism of the propagation reaction the rate-determining reaction was thought to be probably a one-step, two-electron transfer, during which the two Cu(II) ions in the dinuclear complex oxidize the phenolate to phenoxonium. After the phenoxium ion is formed the bonding with the (then) Cu(I) species is weakened and the reactions with phenolic end groups can take place. The effect of the amine ligands appears to be both steric and electronic. With certain ligands the reoxidationof the reduced catalyst is not possible.     

Determination of Vapor Liquid Equilibrium from the Kovats Retention Index on Dimethylsilicone using the Wilson Mixing Model

Non-ideal mixing in a dimethylsilicone stationary phase is modeled according to the Wilson activity coefficient. Pure liquid vapor pressures of alkylated compound series are calculated from capillary GLC retention with the functional group heat of solution in a polymer solvent. The new method uses the Kovats index, molar mass, and functional group to determine the bubble line of a compound. Boiling points at reduced and normal pressure are compared to literature values of 194 gasoline components. An unlike molecular pair interaction parameter is derived, using only bubble line data of the pure liquids. Binary phase diagrams are constructed and compared to vapor liquid equilibrium data.     

Asymptotic behavior ofL-statistics for a large class of time series

In this paper we derive the asymptotic normality ofL-statistics with unbounded scores for a large class of time series. To handle the dependence structure, we use the concept ofm(n)-decomposability as an alternative to classical mixing concepts.Research supported by the Office of Naval Research Contract N00014-91-J-1020.Part of this work was done while the author was at the Department of Mathematics, KUN, Nijmegen, The Netherlands.