A graph coloring approach to scheduling of multiprocessor tasks on dedicated machines with availability constraints

We address a generalization of the classical 1- and 2-processor unit execution time scheduling problem on dedicated machines. In our chromatic model of scheduling machines have non-simultaneous availability times and tasks have arbitrary release times and due dates. Also, the versatility of our approach makes it possible to generalize all known classical criteria of optimality. Under these stipulations we show that the problem of optimal scheduling of sparse tree-like instances can be solved in polynomial time. However, if we admit dense instances then the problem becomes NP-hard, even if there are only two machines.     

On the choice of explicit stabilizing terms in column generation

Column generation algorithms are instrumental in many areas of applied optimization, where linear programs with an enormous number of columns need to be solved. Although successfully employed in many applications, these approaches suffer from well-known instability issues that somewhat limit their efficiency. Building on the theory developed for nondifferentiable optimization algorithms, a large class of stabilized column generation algorithms can be defined which avoid the instability issues by using an explicit stabilizing term in the dual; this amounts at considering a (generalized) augmented Lagrangian of the primal master problem. Since the theory allows for a great degree of flexibility in the choice and in the management of the stabilizing term, one can use piecewise-linear or quadratic functions that can be efficiently dealt with using off-the-shelf solvers. The practical effectiveness of this approach is demonstrated by extensive computational experiments on large-scale Vehicle and Crew Scheduling problems. Also, the results of a detailed computational study on the impact of the different choices in the stabilization term (shape of the function, parameters), and their relationships with the quality of the initial dual estimates, on the overall effectiveness of the approach are reported, providing practical guidelines for selecting the most appropriate variant in different situations.     

An approach to the valuation and decision of ERP investment projects based on real options

The risks and uncertainties inherent in most enterprise resources planning (ERP) investment projects are vast. Decision making in multistage ERP projects investment is also complex, due mainly to the uncertainties involved and the various managerial and/or physical constraints to be enforced. This paper tackles the problem using a real-option analysis framework, and applies multistage stochastic integer programming in formulating an analytical model whose solution will yield optimum or near-optimum investment decisions for ERP projects. Traditionally, such decision problems were tackled using lattice simulation or finite difference methods to compute the value of simple real options. However, these approaches are incapable of dealing with the more complex compound real options, and their use is thus limited to simple real-option analysis. Multistage stochastic integer programming is particularly suitable for sequential decision making under uncertainty, and is used in this paper and to find near-optimal strategies for complex decision problems. Compared with the traditional approaches, multistage stochastic integer programming is a much more powerful tool in evaluating such compound real options. This paper describes the proposed real-option analysis model and uses an example case study to demonstrate the effectiveness of the proposed approach.     

Integration of generative and evaluative models for production scheduling of lube oil plants in a petroleum refinery

A study was made on the existing practices of production planning, scheduling and prevailing constraints in the six plants of a lube oil section in a petroleum refinery. Based on the data collected from these plants, some generative and evaluative models were developed. The generative models developed were flow network optimisation (FNO) model and binary integer linear programming (BILP) model. The evaluative model developed was simulation. The optimal results obtained from the generative model were fed to the evaluative model to derive the measure of performance. This integration of generative and evaluative models offers an opportunity for better understanding of the subsystem and appropriate decision making.     

A hybrid genetic algorithm with dominance properties for single machine scheduling with dependent penalties

In this paper, a hybrid genetic algorithm is developed to solve the single machine scheduling problem with the objective to minimize the weighted sum of earliness and tardiness costs. First, dominance properties of (the conditions on) the optimal schedule are developed based on the switching of two adjacent jobs i and j. These dominance properties are only necessary conditions and not sufficient conditions for any given schedule to be optimal. Therefore, these dominance properties are further embedded in the genetic algorithm and we call it genetic algorithm with dominance properties (GADP). This GADP is a hybrid genetic algorithm. The initial populations of schedules in the genetic algorithm are generated using these dominance properties. GA can further improve the performance of these initial solutions after the evolving procedures. The performances of hybrid genetic algorithm (GADP) have been compared with simple genetic algorithm (SGA) using benchmark instances. It is shown that this hybrid genetic algorithm (GADP) performs very well when compared with DP or SGA alone.     

单机最优分批排序的结构性质

A batch is a subset of jobs which must be processed jointly in either serial or parallel form. For the single machine, batching, total completion time scheduling problems, the algorithmic aspects have been extensively studied in the literature. This paper presents the optimal batching structures of the problems on the batching ways: all jobs in exactly N(arbitrary fix batch number and 1 < N < n) batches.     

最小化加权误工工件数的多代理平行分批排序

考虑多代理的平行分批排序,不同代理的工件不能放在同一批中加工,目标函数是最小化加权误工工件数.本文考虑两种模型,证明了甚至当所有工件具有单位权时,这两个模型都是强NP困难的.但当代理数给定时,这两个问题都可在拟多项式时间解决,并且当工件具有单位权时,可在多项式时间解决.进一步证明当代理数固定时,两个问题都有FPTAS算法.     

基于一般学习效应下的单机排序问题

近来具有学习效应的机器排序问题收到广泛的关注.对于机器排序中工件的实际加工来说,与工件加工位置有关的学习模型更具有现实性.本文研究了工件加工位置和与已经加工过的工件之和有关的一般学习效应模型.首先证明文献中与位置和已经加工过的工件加工时间之和有关的学习模型是本模型的特殊情形.其次对于单机排序问题我们提出一般解法.     

带固定工件的单机排序问题1｜FB, rj,pmtn｜∑j Uj的多项式算法

研究具有若干固定工件和自由工件,其中固定工件必须在指定时间窗内加工,而自由工件具有不同交工的时间,并且其加工可以中断的单机排序问题,其目标是极小化工件的误工数.该问题可以表示为1|FB,rj,pmtn|∑j Uj.首先讨论了问题的几个重要性质,以此为基础建立了求解该问题的动态规划算法,其时间复杂度为O(n4+m log m),其中m和n分别是固定工件数和自由工件数.     

Single machine scheduling with forbidden start times

This paper addresses a single machine scheduling problem in which the following simple constraint is added: a set of time slots is forbidden for starting a task, that is no task can start at any forbidden time point. We show that the single machine problem with makespan minimization is strongly -complete and we give polynomial algorithms to solve the problems with a small number of forbidden start times.