A bicriterion approach to common flow allowances due window assignment and scheduling with controllable processing times

Abstract

Abstract:We investigate a single-machine scheduling problem for which both the job processing times and due windows are decision variables to be determined by the decision maker. The job processing times are controllable as a linear or convex function of the amount of a common continuously divisible resource allocated to the jobs, where the resource allocated to the jobs can be used in discrete or continuous quantities. We use the common flow allowances due window assignment method to assign due windows to the jobs. We consider two performance criteria: (i) the total weighted number of early and tardy jobs plus the weighted due window assignment cost, and (ii) the resource consumption cost. For each resource consumption function, the objective is to minimize the first criterion, while keeping the value of the second criterion no greater than a given limit. We analyze the computational complexity, devise pseudo-polynomial dynamic programming solution algorithms, and provide fully polynomial-time approximation schemes and an enhanced volume algorithm to find high-quality solutions quickly for the considered problems. We conduct extensive numerical studies to assess the performance of the algorithms. The computational results show that the proposed algorithms are very efficient in finding optimal or near-optimal solutions.

Optimization for Due-Window Assignment Scheduling with Position-Dependent Weights

“…Ji et al [13] considered the single-machine SLK-DW assignment scheduling problem with group technology. Yin et al [14], Yin et al [15], and Wang et al [16] considered SLK-DW assignment scheduling problems with resource allocation (controllable processing time). Mor and Mosheiov [17] considered SLK-DW assignment proportionate flow-shop scheduling problems.…”

Two‐agent scheduling with linear resource‐dependent processing times

“…The authors show that the problem to minimize an integrated criterion is polynomially solvable, while the other three variants of the problem are ‐hard, and develop an FPTAS for the three ‐hard versions of the problem with the discrete type of resource. D. Wang, Yin, and Cheng (2017) investigate a bicriterion approach to common flow allowances due window assignment and scheduling with linear or convex resource‐dependent processing times, where the two criteria studied are the total weighted number of early and tardy jobs plus the weighted due window assignment cost, and the resource consumption cost. The authors analyze the computational complexity, devise pseudo‐polynomial time dynamic programming algorithms, and provide FPTASs for the problems they consider.…”

“…The authors analyze the computational complexity, devise pseudo‐polynomial time dynamic programming algorithms, and provide FPTASs for the problems they consider. It is crucial to note that the idea for designing the algorithms for the problems in D. Wang, Yin, et al (2017) can be applied to solve an open problem left in Leyvand et al (2010). Compare the works of Leyvand et al (2010) and D. Wang, Yin, et al (2017) with our problem, the due date or time window of a job is part of the decision process rather than an input parameter in their models, and thus their method for devising a polynomial‐time (1 + ϵ )‐approximation algorithm with ϵ < + ∞ cannot also be applied for our problem.…”

A unified approach for single machine scheduling with position-dependent workloads and positional penalties

“…Generally, each of the due-dates is defined as the sum of its processing time and a job-independent constant. Significant papers considering different SLK objective functions include: [4,12,14,22,30,31,33,35,37,40].…”