机器具有准备时间的双目标平行机排序问题

本文讨论机器具有准备时间的双目标平行机排序问题，目标函数为完工时间和最优条件下极小化最大完工时间．通过对SPT排序的性质的分析，给出了最优排序的下界．在此基础上证明了SPT排序的误差界为3／2，并且是紧界．     

A modified HOL priority scheduling discipline: Performance analysis

In this paper, we introduce and analyze a modified HOL (head-of-the-line) priority scheduling discipline. The modification is incorporated to cope with the so-called starvation problem of regular HOL priority queues. We consider a discrete-time single-server queueing system with two priority queues of infinite capacity and with the introduced priority scheme. We show that the use of probability generating functions is suitable for analyzing the system contents and the packet delay. Some performance measures (such as means and variances) of these stochastic quantities will be derived. Furthermore, approximate expressions of the tail probabilities are obtained from the probability generating functions, by means of the dominant-singularity method. These expressions, together with their characteristics, constitute one of the main contributions of this paper. Finally, the impact and significance of the m-HOL (modified HOL) priority scheduling on these performance measures is illustrated by some numerical examples.     

Multi-objective time–cost trade-off in dynamic PERT networks using an interactive approach

We develop a multi-objective model for the time–cost trade-off problem in a dynamic PERT network using an interactive approach. The activity durations are exponentially distributed random variables and the new projects are generated according to a renewal process and share the same facilities. Thus, these projects cannot be analyzed independently. This dynamic PERT network is represented as a network of queues, where the service times represent the durations of the corresponding activities and the arrival stream to each node follows a renewal process. At the first stage, we transform the dynamic PERT network into a proper stochastic network and then compute the project completion time distribution by constructing a continuous-time Markov chain. At the second stage, the time–cost trade-off problem is formulated as a multi-objective optimal control problem that involves four conflicting objective functions. Then, the STEM method is used to solve a discrete-time approximation of the original problem. Finally, the proposed methodology is extended to the generalized Erlang activity durations.     

Inventory constrained maritime routing and scheduling for multi-commodity liquid bulk,Part I: Applications and model

This paper formulates a model for finding a minimum cost routing in a network for a heterogeneous fleet of ships engaged in pickup and delivery of several liquid bulk products. The problem is frequently encountered by maritime chemical transport companies, including oil companies serving an archipelago of islands. The products are assumed to require dedicated compartments in the ship. The problem is to decide how much of each product should be carried by each ship from supply ports to demand ports, subject to the inventory level of each product in each port being maintained between certain levels that are set by the production rates, the consumption rates, and the storage capacities of the various products in each port. This important and challenging inventory constrained multi-ship pickup–delivery problem is formulated as a mixed-integer nonlinear program. We show that the model can be reformulated as an equivalent mixed-integer linear program with special structure. Over 100 test problems are randomly generated and solved using CPLEX 7.5. The results of our numerical experiments illuminate where problem structure can be exploited in order to solve larger instances of the model. Part II of the sequel will deal with new algorithms that take advantage of model properties.     

Priority rule-based heuristic for multi-mode resource-constrained project scheduling problems with resource vacations and activity splitting

This paper presents a priority rule-based heuristic for the multi-mode resource-constrained project scheduling problem with the splitting of activities around unavailable resources allowed. All resources considered are renewable and each resource unit may not be available at all times due to resource vacations, which are known in advance. A new concept called moving resource strength is developed to help identify project situations where activity splitting is likely to be beneficial during scheduling. The moving resource strength concept is implemented in priority rule-based heuristics to control activity splitting when scheduling. Multiple comparisons of the performance of combination of activity–mode priority rules used in the heuristics are provided. Computational experiments demonstrate the effectiveness of the heuristic in reducing project makespan, and minimizing activity splitting.     

Improved approximation for non-preemptive single machine flow-time scheduling with an availability constraint

We study the problem of scheduling n non-preemptable jobs on a single machine which is not available for processing during a given time period. The objective is to minimize the sum of the job completion times. The best known approximation algorithm for this NP-hard problem has a relative worst-case error bound of 17.6%. We present a parametric O(nlog n)-algorithm H with which better worst-case error bounds can be obtained. The best error bound calculated for the algorithm in the paper is 7.4%. In a computational experiment, we test the algorithm with the performance guarantee set to 10.2%. It turns out that randomly generated instances with up to 1000 jobs can be solved with a mean (maximum) error of 0.31% (3.18%) and a mean (maximum) computation time of 0.8 (9.7) seconds.     

A genetic algorithm for resource investment project scheduling problem,tardiness permitted with penalty

In this paper a genetic algorithm for solving a class of project scheduling problems, called Resource Investment Problem, is presented. Tardiness of project is permitted with defined penalty. Elements of algorithm such as chromosome structure, unfitness function, crossover, mutation, immigration and local search operations are explained.     

A branch-and-price algorithm for scheduling parallel machines with sequence dependent setup times

We consider the problem of scheduling n independent jobs on m unrelated parallel machines with sequence-dependent setup times and availability dates for the machines and release dates for the jobs to minimize a regular additive cost function. In this work, we develop a new branch-and-price optimization algorithm for the solution of this general class of parallel machines scheduling problems. A new column generation accelerating method, termed “primal box”, and a specific branching variable selection rule that significantly reduces the number of explored nodes are proposed. The computational results show that the approach solves problems of large size to optimality within reasonable computational time.     

关于排序模型1｜·｜ri≥0｜ ∑n i=1 to n vi的注记

设J={J1,…,Jn}是n个工件的集合,M是一台机器.每个工件Ji要在机器M上加工一次,而且是相继只加工一次,即加工不能够中断.Ji的加工时间是pi,准备时间是ri,即Ji不能在ri之前加工,要求完工的期限是di,即工件Ji的加工应该在di之前完成.否则,这个工件将被拒绝放在一旁.我们的目的是寻找排序算法A,当使用到给定的J上时,使被拒绝的工件个数为最少. 1978年Kise，Ibaraki，Mine等在条件ri〈rj蕴涵di≤dj（对于任何1≤i，j≤n）下，对于任何给定的J找到算法A他们在论文[1]中“证明”算法A是最优算法．最近，李杉林给出一个例子说明他们的证明中的一个关键引理是错误的．本文作者在书[2]中也沿用了这个错误的“证明”．对于算法A的最优性，本文给出一个新的简单的证明．     

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.