Approximation of the supply scheduling problem

The supply scheduling problem consists in finding a minimum cost delivery plan from a set of providers to a manufacturing unit, subject to given bounds on the shipment sizes and subject to the demand at the manufacturing unit. We provide a fully polynomial time approximation scheme for this problem.     

A branch-and-bound algorithm of the single machine schedule with sequence-dependent setup times for minimizing maximum tardiness

This paper addresses the NP-hard problem of scheduling N jobs on a single machine with due dates, sequence-dependent setup times and no preemption where the objective is to minimize the maximum tardiness. An algorithm based on branch-and-bound permutation schemes is developed including the implementation of lower and upper bounding procedures, and three dominance rules. Computational experiments demonstrate the effectiveness of the algorithm. In the experiments, the impacts of control parameters to generate test instances on algorithm performance (CPU times) are studied by statistics methods.     

Location-routing: Issues,models and methods

This paper is a survey of location-routing: a relatively new branch of locational analysis that takes into account vehicle routing aspects. We propose a classification scheme and look at a number of problem variants. Both exact and heuristic algorithms are investigated. Finally, some suggestions for future research are presented.     

Multi-component reactions between 2-aminopyrimidine, aldehydes and isonitriles: the use of a nonpolar solvent suppresses formation of multiple products

A reliable and convenient protocol for MCRs between 2-aminopyrimidine, aldehydes and isonitriles is described. Toluene was chosen as the reaction solvent based on mechanistic reasoning. The product mixtures were found to contain a single imidazo[1,2-a]pyrimidine product in each case, which were isolated and purified by precipitation and crystallization. Chromatographic recovery from filtrates raised the total yields to 49-66%. The procedure provides a practical alternative to hitherto reported methods in which formation of multiple products was observed.     

A mathematical programming model and solution for scheduling production orders in Shanghai Baoshan Iron and Steel Complex

In this paper, we investigate the production order scheduling problem derived from the production of steel sheets in Shanghai Baoshan Iron and Steel Complex (Baosteel). A deterministic mixed integer programming (MIP) model for scheduling production orders on some critical and bottleneck operations in Baosteel is presented in which practical technological constraints have been considered. The objective is to determine the starting and ending times of production orders on corresponding operations under capacity constraints for minimizing the sum of weighted completion times of all orders. Due to large numbers of variables and constraints in the model, a decomposition solution methodology based on a synergistic combination of Lagrangian relaxation, linear programming and heuristics is developed. Unlike the commonly used method of relaxing capacity constraints, this methodology alternatively relaxes constraints coupling integer variables with continuous variables which are introduced to the objective function by Lagrangian multipliers. The Lagrangian relaxed problem can be decomposed into two sub-problems by separating continuous variables from integer ones. The sub-problem that relates to continuous variables is a linear programming problem which can be solved using standard software package OSL, while the other sub-problem is an integer programming problem which can be solved optimally by further decomposition. The subgradient optimization method is used to update Lagrangian multipliers. A production order scheduling simulation system for Baosteel is developed by embedding the above Lagrangian heuristics. Computational results for problems with up to 100 orders show that the proposed Lagrangian relaxation method is stable and can find good solutions within a reasonable time.     

The one dimensional Compartmentalised Knapsack Problem: A case study

The Compartmentalised Knapsack Problem (CKP) is similar to the ordinary Knapsack Problem except that items to be packed belong to separate classes, and items can only be packed, in knapsack compartments, amongst items in their own class. This paper addresses a case study in the cutting of steel rolls in which the CKP arises. The rolls are cut in two-phases: the first phase produces sub-rolls (compartments) which are, after reducing the thickness, cut in a second phase to produce ribbons (a class consists of ordered items with the same thickness). Finally, two methods of solving CKP are presented, and these are used to generate columns in the classical linear optimisation model of Gilmore and Gomory. Results of computational experiments are presented.     

Applications of residues to combinatorial identities

A concrete aspect of Grothendieck Duality is used to give local cohomology proofs of combinatorial identities including MacMahon's master theorem, Grosswald identity, identity of Shoo, Tepper identity, and others.

     

Xanthines as a scaffold for molecular diversity

Summary Xanthines represent a new, versatile scaffold for combinatorial chemistry. A five-step solid-phase synthesis of xanthine derivatives is described which includes alkylations, a nucleophilic displacement reaction at a heterocycle and a ring closure reaction by condensation of a nitroso function with an activated methylene group. The selected reaction sequence allows the production of a highly diverse small-molecule combinatorial compound library.     

Solving the maximum edge weight clique problem via unconstrained quadratic programming

The unconstrained quadratic binary program (UQP) is proving to be a successful modeling and solution framework for a variety of combinatorial optimization problems. Experience reported in the literature with several problem classes has demonstrated that this approach works surprisingly well in terms of solution quality and computational times, often rivaling and sometimes surpassing more traditional methods. In this paper we report on the application of UQP to the maximum edge-weighted clique problem. Computational experience is reported illustrating the attractiveness of the approach.