工件加工时间增加的排序问题(1‖Cmax)

讨论了工件加工时间随工件开工时间线性增加的排序问题,考虑的目标函数是最大完工时间,证明了加工时间是简单线性增加情况下最大完工时间问题是多项式时间可解的,对于加工时间是一般线性增加情况,研究了最优排序的性质,同时证明了两种特殊情况下最大完工时间问题也是多项式时间可解的。     

Minimizing makespan on a single batching machine with release times and non-identical job sizes

We consider the problem of scheduling jobs with release times and non-identical job sizes on a single batching machine; our objective is to minimize makespan. We present an approximation algorithm with worst-case ratio 2+ε, where ε>0 can be made arbitrarily small.     

A branch and bound algorithm for the one-machine scheduling problem with minimum and maximum time lags

We consider the one-machine scheduling problem with minimum and maximum time lags while minimizing the makespan. This problem typically arises in a manufacturing environment where the next job has to be carried out within a specific time range after the completion of the immediately preceding job. We describe a branch and bound algorithm, based on the input and output of a clique and the relevant propositions, for finding the optimal waiting times. The computational experiments give promising results, showing whether a given instance is feasible or infeasible. With the proposed branch and bound algorithm we can either find an optimal schedule or establish the infeasibility within an acceptable run time.     

A note on single-machine group scheduling problems with position-based learning effect

In many situations, the skills of workers continuously improve when repeating the same or similar tasks. This phenomenon is known as the “learning effect” in the literature. However, most studies considering the learning effect ignore the fact that production efficiency can be increased by grouping various parts and products with similar designs and/or production processes. This phenomenon is known as “group technology” in the literature. In this paper, we propose a new group scheduling learning model where the learning effect not only depends on the job position, but also depends on the group position. We then show that the makespan and the total completion time problems remain polynomially solvable under the proposed model.     

Single machine scheduling subject to precedence delays

A single-machine scheduling problem with precedence delays is analyzed. A set of n tasks is to be scheduled on the machine in such a way that the makespan is minimized. The executions of the tasks are constrained by precedence delays, i.e., a task can start its execution only after any of its predecessors has completed and the delay between the two tasks has elapsed. In the case of unit execution times and integer lengths of delays, the problem is shown to be NP-hard in the strong sense. In the case of integer execution times and unit length of delays, the problem is polynomial, and an O(n²) optimal algorithm is provided. Both preemptive and non-preemptive cases are considered.     

A hybrid imperialist competitive algorithm for minimizing makespan in a multi-processor open shop

In this paper a new mixed-integer linear programming (MILP) model is proposed for the multi-processor open shop scheduling (MPOS) problems to minimize the makespan with considering independent setup time and sequence dependent removal time. A hybrid imperialist competitive algorithm (ICA) with genetic algorithm (GA) is presented to solve this problem. The parameters of the proposed algorithm are tuned by response surface methodology (RSM). The performance of the algorithm to solve small, medium and large sized instances of the problem is evaluated by introducing two performance metrics. The quality of obtained solutions is compared with that of the optimal solutions for small sized instances and with the lower bounds for medium sized instances. Also some computational results are presented for large sized instances.     

Some scheduling problems with time-dependent learning effect and deteriorating jobs

Although machine scheduling problems with learning and deteriorating effects consideration have received increasing attention in the recent years, most studies have seldom considered the two phenomena simultaneously. However, learning and deteriorating effects might co-exist in many realistic scheduling situations. Thus, in this article, a model which takes the effects of time-dependent learning and deterioration simultaneously is proposed and applied into some scheduling problems. Under the proposed model, the processing time of a job is determined by a function of its corresponding starting time and positional sequence in each machine. We show that some single machine and flowshop scheduling problems are polynomially solvable with the certain performance measures such as makespan, total completion time, and weighted completion time.     

The “least flexible job first” rule in scheduling and in queueing

We consider an environment with m$m$ machines in parallel operating at different speeds. The processing requirements of all jobs are independent and have the same exponential distribution. Job j$j$ may only be processed on a specific subset of the m$m$ machines, referred to as its restricted set. The restricted sets are nested and preemptions are allowed. We show that the Least Flexible Job to the Fastest Machine (LFJ-FM) minimizes the expected makespan and the total expected completion time.     

A note on the complexity of flow-shop scheduling with deteriorating jobs

This paper is a note on “Complexity analysis of job-shop scheduling with deteriorating jobs” [G. Mosheiov, Complexity analysis of job-shop scheduling with deteriorating jobs, Discrete Applied Mathematics 117 (2002) 195-209]. A proportional deterioration rate is assumed and the objective is the minimization of the makespan. Mosheiov presents NP-hardness results for flow-shops and open-shops with three or more machines and for job-shops with two or more machines. The proof of NP-hardness for the flow-shop case is however not correct. This paper provides a correct proof.     

Coordination mechanisms with hybrid local policies

We study coordination mechanisms for scheduling n jobs on m parallel machines where agents representing the jobs interact to generate a schedule. Each agent acts selfishly to minimize the completion time of his/her own job, without considering the overall system performance that is measured by a central objective. The performance deterioration due to the lack of a central coordination, the so-called price of anarchy, is determined by the maximum ratio of the central objective function value of an equilibrium schedule divided by the optimal value. In the first part of the paper, we consider a mixed local policy with some machines using the SPT rule and other machines using the LPT rule. We obtain the exact price of anarchy for the problem of minimizing the makespan and some bounds for the problem of minimizing the total completion time. In the second part of the paper, we consider parallel machine scheduling subject to eligibility constraints. We devise new local policies based on the flexibilities and the processing times of the jobs. We show that the newly devised local policies outperform both the SPT and the LPT rules.