Resource constrained scheduling with general truncated job-dependent learning effect

Abstract

Scheduling with general truncated job-dependent learning effect and resource-dependent processing times is studied on a single machine. It is assumed that the job processing time is a function of the amount of resource allocated to the job, the general job-dependent learning effect and the job-dependent control parameter. For each version of the problem that differs in terms of the objective functions and the processing time functions, the optimal resource allocation is provided. Polynomial time algorithms are also developed to find the optimal schedule of several versions of the problem.

Resource allocation scheduling with deteriorating jobs and position-dependent workloads

“…Example 1. There are n = 5 jobs, where α = 3, (3,6,5,4,7), (ξ 1 , ξ 2 , ξ 3 , ξ 4 , ξ 5 ) = (4,8,10,6,3), and the values of w j,r are given as follows (see Table 1): 30)-(33), the optimal sequence is J 2 → J 1 → J 3 → J 5 → J 4 . For the problem 1 p j,r (u j , s j ) = wj,r uj η + bs j αV + β n j=1 v j u j , according to Lemma 2, the optimal resource allocation u j of job J j can be obtained as: u 1 = αη n r=1 Ξr(w1,r) η x1,r β n r=1 v1x1,r…”

“…For details on the scheduling problems with deterioration effect (time-dependent processing times), we refer the reader to the recent papers Huang [6], Sun and Geng [19], Huang et al [7], Gawiejnowicz [2], and Qian and Han [17]. The papers about controllable processing times (resource allocation), the reader is referred to articles Shabtay and Steiner [18], Wang and Wang [27], Wang and Wang [26], Lu et al [13], He et al [5], Wang et al [24], Liu and Jiang [10], Lv et al [14], and Zhao [31].…”

Single-Machine Maintenance Activity Scheduling with Convex Resource Constraints and Learning Effects

“…Therefore, in previous studies, Ji et al [22] considered a single machine due date assignment scheduling problem with job-dependent aging effects and a deteriorating maintenance activity, where due dates are assigned using the SLK due date determination method. He et al [23] studied the single-machine sequencing problem of resource allocation with general truncated learning effects. A convex resource allocation model under the condition of finite resource consumption cost is proposed, and various optimal algorithms are given for different cases of the problem.…”

Single machine and flowshop scheduling problems with sum-of-processing time based learning phenomenon

“…They showed that minimizing makespan problem is NP-hard, and provided a (1 + ε) fully polynomial-time approximation scheme in O( n 3m+1 L 2m+1 ε 2m ) time, where m denotes the number of the machines and L is a given constant. He et al [5] studied that the processing time of a job is a function of the amount of allocated resource, the general jobdependent learning effect and the job-dependent control parameter. The bounded linear and convex resource consumption functions.…”