Rescheduling unrelated parallel machines with total flow time and total disruption cost criteria

In this paper, we consider a rescheduling problem where a set of jobs has already been assigned to unrelated parallel machines. When a disruption occurs on one of the machines, the affected jobs are rescheduled, considering the efficiency and the schedule deviation measures. The efficiency measure is the total flow time, and the schedule deviation measure is the total disruption cost caused by the differences between the initial and current schedules. We provide polynomial-time solution methods to the following hierarchical optimization problems: minimizing total disruption cost among the minimum total flow time schedules and minimizing total flow time among the minimum total disruption cost schedules. We propose exponential-time algorithms to generate all efficient solutions and to minimize a specified function of the measures. Our extensive computational tests on large size problem instances have revealed that our optimization algorithm finds the best solution by generating only a small portion of all efficient solutions.     

Complexity,algorithms and applications of the integer network flow with fractional supplies problem

We consider here the integer minimum cost network flow when some of the supplies are fractional. In the presence of fractional supplies it is impossible to satisfy the flow balance constraints, creating an imbalance. We present here a polynomial time algorithm for minimizing the total cost of flow and imbalance penalty. We also show that in the presence of a constraint that bounds the imbalance the problem is NP-hard, but efficiently solvable for a fixed number of fractional supplies.     

Single-machine scheduling with time-and-resource-dependent processing times

We consider single-machine scheduling problems in which the processing time of a job is a function of its starting time and its resource allocation. The objective is to find the optimal sequence of jobs and the optimal resource allocation separately. We concentrate on two goals separately, namely, minimizing a cost function containing makespan, total completion time, total absolute differences in completion times and total resource cost; minimizing a cost function containing makespan, total waiting time, total absolute differences in waiting times and total resource cost. We show that the problems remain polynomially solvable under the proposed model.     

Fast approximation schemes for Boolean programming and scheduling problems related to positive convex Half-Product

We address a version of the Half-Product Problem and its restricted variant with a linear knapsack constraint. For these minimization problems of Boolean programming, we focus on the development of fully polynomial-time approximation schemes with running times that depend quadratically on the number of variables. Applications to various single machine scheduling problems are reported: minimizing the total weighted flow time with controllable processing times, minimizing the makespan with controllable release dates, minimizing the total weighted flow time for two models of scheduling with rejection.     

Parallel-machine scheduling with non-simultaneous machine available time

We consider a problem of scheduling n independent jobs on m parallel identical machines. The jobs are available at time zero, but the machines may not be available simultaneously at time zero. We concentrate on two goals separately, namely, minimizing a cost function containing total completion time and total absolute differences in completion times; minimizing a cost function containing total waiting time and total absolute differences in waiting times. In this paper, we present polynomial time algorithm to solve this problem.     

Asymptotically optimal schedules for single-server flow shop problems with setup costs and times

We consider the processing of M jobs in a flow shop with N stations in which only a single server is in charge of all stations. We demonstrate that for the objective of minimizing the total setup and holding cost, a class of easily implementable schedules is asymptotically optimal.     

带有拒绝的单机和同型机排序问题

研究了带有拒绝的单机和同型机排序问题. 对于单机情形, 工件的惩罚费用是对应加工时间的\alpha倍.如果工件有到达时间, 目标为最小化时间表长与惩罚费用之和, 证明了这个问题是可解的.如果所有工件在零时刻到达, 目标为最小化总完工时间与惩罚费用之和, 也证明了该问题是可解的.对于同型机排序问题, 研究了工件分两批在线实时到达的情形, 目标为最小化时间表长与惩罚费用之和.针对机器台数2和m, 分别给出了竞争比为2和4-2/m的在线算法.     

Single machine scheduling problems with financial resource constraints: Some complexity results and properties

We consider single machine scheduling problems with a non-renewable resource. These types of problems have not been intensively investigated in the literature so far. For several problems of these types with standard objective functions (namely the minimization of makespan, total tardiness, number of tardy jobs, total completion time and maximum lateness), we present some complexity results. Particular attention is given to the problem of minimizing total tardiness. In addition, for the so-called budget scheduling problem with minimizing the makespan, we present some properties of feasible schedules.     

Scheduling problems in master-slave model

We consider scheduling problems in the master slave model, which was introduced by Sahni in 1996. The goal is to minimize the makespan and the total completion time. It has been shown that the problem of minimizing makespan is NP-hard. Sahni and Vairaktarakis developed some approximation algorithms to generate schedules whose makespan is at most constant times the optimal. In this paper, we show that the problem of minimizing total completion time is NP-hard in the strong sense. Then we develop algorithms to generate schedules whose total completion time and makespan are both bounded by some constants times their optimal values. Research supported in part by the National Science Foundation through grant DMI-0300156.     

Scheduling unit-length jobs with machine eligibility restrictions

We consider uniform parallel machine scheduling problems with unit-length jobs where every job is only allowed to be processed on a specified subset of machines. We develop efficient methods to solve problems with various objectives, including minimizing a total tardiness function, a maximum tardiness function, total completion time, the number of tardy jobs, the makespan, etc.     

Two-machine flow-shop scheduling with equal processing time on the second machine for minimizing total weighted completion time

We consider the classical two-machine flow-shop scheduling for minimizing the total weighted completion time. For this problem, the computational complexity of a version in which the jobs have a common processing time on the second machine, has not been addressed. We show that the problem is unary NP-hard, answering an open problem posed in Zhu et al. (2016). Then we present an approximation algorithm for the problem with worst-case performance ratio at most 2.     

Staff optimization for time-dependent acute patient flow

The emergency department is a key element of acute patient flow, but due to high demand and an alternating rate of arriving patients, the department is often challenged by insufficient capacity. Proper allocation of resources to match demand is, therefore, a vital task for many emergency departments.Constrained by targets on patient waiting time, we consider the problem of minimizing the total amount of staff-resources allocated to an emergency department. We test a matheuristic approach to this problem, accounting for both patient flow and staff scheduling restrictions. Using a continuous-time Markov chain, patient flow is modeled as a time-dependent queueing network where inhomogeneous behavior is evaluated using the uniformization method. Based on this modeling approach, we recursively evaluate and allocate staff to the system using integer linear programming until the waiting time targets are respected in all queues of the network. By comparing to discrete-event simulations of the associated system, we show that this approach is adequate for both modeling and optimizing the patient flow. In addition, we demonstrate robustness to the service time distribution and the associated system with multiple classes of patients.     

A branch-and-cut-and-price algorithm for the cumulative capacitated vehicle routing problem

In this paper we consider the Cumulative Capacitated Vehicle Routing Problem (CCVRP), which is a variation of the well-known Capacitated Vehicle Routing Problem (CVRP). In this problem, the traditional objective of minimizing total distance or time traveled by the vehicles is replaced by minimizing the sum of arrival times at the customers. We propose a branch-and-cut-and-price algorithm for obtaining optimal solutions to the problem. To the best of our knowledge, this is the first published exact algorithm for the CCVRP. We present computational results based on a set of standard CVRP benchmarks and investigate the effect of modifying the number of vehicles available.     

Single machine scheduling problems with controllable processing times and total absolute differences penalties

In this paper, we consider single machine scheduling problem in which job processing times are controllable variables with linear costs. We concentrate on two goals separately, namely, minimizing a cost function containing total completion time, total absolute differences in completion times and total compression cost; minimizing a cost function containing total waiting time, total absolute differences in waiting times and total compression cost. The problem is modelled as an assignment problem, and thus can be solved with the well-known algorithms. For the case where all the jobs have a common difference between normal and crash processing time and an equal unit compression penalty, we present an O(n log n) algorithm to obtain the optimal solution.     

Single machine scheduling with exponential learning functions

In this paper we consider the single machine scheduling problem with exponential learning functions. By the exponential learning functions, we mean that the actual job processing time is a function of the total normal processing times of the jobs already processed. We prove that the shortest processing time (SPT) rule is optimal for the total lateness minimization problem. For the following three objective functions, the total weighted completion time, the discounted total weighted completion time, the maximum lateness, we present heuristic algorithms according to the corresponding problems without exponential learning functions. We also analyse the worst-case bound of our heuristic algorithms. It also shows that the problems of minimizing the total tardiness and discounted total weighted completion time are polynomially solvable under some agreeable conditions on the problem parameters.     

A note on parallel-machine scheduling with deteriorating jobs

We consider a parallel-machine scheduling problem of minimizing the total completion time. The processing time of a job is a linear function of its starting time and deterioration rate. This problem is known to be NP-hard, even for the case with two machines. In this note, we generalize an existing lower bound for the two-machine case to the general case with an arbitrary number of machines. Despite the generalization concerning machine number, our bound has one extra term that makes our bound tighter than the existing one.     

No-wait scheduling of position dependent jobs and adjustable processing intervals

In this paper, we consider a single machine no-wait scheduling model whereby job processing times are general functions of their position in the job sequence. We assume that the single machine must operate at a certain cycle, which can be determined by the scheduler. Furthermore, exactly one job has to be completed by the end of each cycle. Using different variations of the Linear Assignment Problem formulation, we develop polynomial time algorithms for minimizing the following objectives: makespan, total completion time, maximum earliness and total earliness.     

极小化加权完工时间和的Flowshop问题的算法

本文讨论了极小化加权完工时间和的Flowshop问题.我们给出了一个最坏情况误差界为m的启发式算法,对于m=2的情况,如果工件具有一致权因子,即pi相似文献   

Flow shop scheduling algorithms for minimizing the completion time variance and the sum of squares of completion time deviations from a common due date

We consider two problems of m-machine flow shop scheduling in this paper: one, with the objective of minimizing the variance of completion times of jobs, and the other with the objective of minimizing the sum of squares of deviations of job completion times from a common due date. Lower bounds on the sum of squares of deviations of job completion times from the mean completion time of jobs for a given partial sequence are first presented. Using these lower bounds, a branch and bound algorithm based on breadth-first search procedure for scheduling n jobs on m-machines with the objective of minimizing completion time variance (CTV) is developed to obtain the best permutation sequence. We also present two lower bounds and thereafter, a branch and bound algorithm with the objective of minimizing the sum of squares of deviations of job completion times from a given common due date (called the MSD problem). The computational experience with the working of the two proposed branch and bound algorithms is also reported. Two heuristics, one for each of the two problems, are developed. The computational experience on the evaluation of the heuristics is discussed.     

Minimizing maximum lateness in a flow shop subject to release dates

We consider the problem of minimizing the maximum lateness in a m-machine flow shop subject to release dates. The objective of this paper is to develop a new branch-and-bound algorithm to solve exactly this strongly NP-hard problem. The proposed branch-and-bound algorithm encompasses several features including a procedure for adjusting heads and tails, heuristics, and a lower bounding procedure, which is based on the exact solution of the two-machine flow shop problem with time lags, ready times, and delivery times. Extensive computational experiments show that instances with up to 6000 operations can be solved exactly in a moderate CPU time.