Weighted Shortest Processing Time Research Articles

Single-machine scheduling with a time-dependent learning effect

In this paper we consider the single-machine scheduling problem with a time-dependent learning effect. The time-dependent learning effect of a job is assumed to be a function of the total normal processing time of the jobs scheduled in front of the job. We show by examples that the optimal schedule for the classical version of the problem is not optimal in the presence of a time-dependent learning effect for the following three objective functions: the weighted sum of completion times, the maximum lateness and the number of tardy jobs. But for some special cases, we prove that the weighted shortest processing time (WSPT) rule, the earliest due date (EDD) rule and Moore's Algorithm can construct an optimal schedule for the problem to minimize these objective functions, respectively. We use these three rules as heuristics for the general cases and analyze their worst-case error bounds. We also provide computational results to evaluate the performance of the heuristics.

Fabrication scheduling on a single machine to minimize the weighted sum of product completion time

In this paper, a fabrication scheduling problem concerning the production of components at a single manufacturing facility was studied, in which the manufactured components are subsequently assembled into a finite number of end products. Each product was assumed to comprise a common component to all jobs and a unique component to itself. Common operations were processed in batches and each batch required a setup time. A product is completed when both its two operations have been processed and are available. The optimality criterion considered was the minimization of weighted flow time. For this scheduling problem, the optimal schedules were described in a weighted shortest processing time first (WSPT) order and two algorithms were constructed corresponding to the batch availability and item availability, respectively.

Proportionate flexible flow shop scheduling via a hybrid constructive genetic algorithm

The proportionate flow shop (PFS) is considered as a unique case of the flow shop problem in which the processing times of the operations belonging to the same job are equal. A proportionate flexible flow shop (PFFS) is a machine environment with parallel identical machines at each stage. This study presents an effective hybrid approach based on constructive genetic algorithm (CGA) for PFFS scheduling with the criterion to minimize the total weighted completion time (WCT). Minimizing the WCT in a PFFS problem significantly differs from the parallel-identical-machine scheduling problem, an optimal schedule in which the jobs on each machine are in weighted shortest processing time (WSPT) order. The proposed approach incorporates two fitness functions, and a population trained by a local improvement search based on tabu search with a candidate list strategy into CGA. Simulation results are compared with those of the column generation (CG) approach to demonstrate the effectiveness of the proposed hybrid approach. In particular, the CG approach has been applied successfully to solve various parallel machine scheduling problems, and yields high-quality solutions.

Minimizing the total weighted completion time in a two-machine proportionate flow shop with different machine speeds

In this paper, we consider the problem of minimizing the total weighted completion time in an n-job, two-machine proportionate flow shop, where job processing times are inversely proportional to machine speeds. We show that the problem is NP-complete. We provide a tight lower bound to an optimal objective value and show that the worst-case performance ratio of the weighted shortest processing time rule is less than 2. We propose heuristic procedures to find an approximate solution for the problem. A computational study on randomly generated test problems is conducted to investigate the performance of the proposed heuristics.

The Least Cost Testing Sequence Problem

The Least Cost Testing Sequence (LCTS) problem is a special case of the Weighted Shortest Processing Time (SPT) sequencing problem. A manufactured item has to pass each of n-tests at the final inspection, where the ith test has an associated cost Ci of inspection and the item has a non zero probability pi of passing that test. The testing will be terminated if the item fails on any one test. When there is no constraint on the technical ordering of conducting the tests, it has been established that the optimal sequence that minimizes the expected inspection cost is obtained by sequencing the tests such that

Web server QoS models: applying scheduling rules from production planning

Most web servers, in practical use, use a queuing policy based on the Best Effort model, which employs the first-in-first-out (FIFO) scheduling rule to prioritize web requests in a single queue. This model does not provide Quality of Service (QoS). In the Differentiated Services (DiffServ) model, separate queues are introduced to differentiate QoS for separate web requests with different priorities. This paper presents web server QoS models that use a single queue, along with scheduling rules from production planning in the manufacturing domain, to differentiate QoS for classes of web service requests with different priorities. These scheduling rules are Weighted Shortest Processing Time (WSPT), Apparent Tardiness Cost (ATC), and Earliest Due Date. We conduct simulation experiments and compare the QoS performance of these scheduling rules with the FIFO scheme used in the basic Best Effort model with only one queue, and the basic DiffServ model with two separate queues. Simulation results demonstrate better QoS performance using WSPT and ATC, especially when requested services exceed the capacity of a web server.

Scheduling jobs to improve weighted on-time performance of a single machine

One of the problems faced by many manufacturers is how to improve on-time delivery (OTD). Customer orders or jobs often have different levels of importance (priorities). The levels of importance are assigned by weight numbers: the higher the weight, the more important the job. One performance measure manufacturers typically use is the total weighted number of late deliveries. This paper proposes a time-efficient scheduling heuristic, the Weighted Forward Algorithm (WFA), to reduce the weighted number of late deliveries for a single machine. A comparison between the WFA heuristic and three well-known heuristics, the Earliest Due Date (EDD), the Weighted Shortest Processing Time (WSPT), and the Forward Algorithm (FA), is then performed on two data sets, representing high and low-demand production months, for a real-world manufacturing application.The results suggest that the WFA outperforms the EDD, WSPT, and FA for this objective using both data sets. At the same time, the execution time is almost instantaneous. The WFA is also benchmarked against current practice at the same manufacturer and outperforms other heuristics and current practice.

A scheduling algorithm for time-constrained model-based diagnosis

A meta-level reasoning module for time-constrained diagnosis using hierarchical behavioural (physical “part-of”) models is proposed, its goal being to direct a model-based diagnostic engine such that the optimum trade-off between computation time and solution quality is found. The problem is defined as the task of finding the order in which to explore candidate components at differing levels within the model hierarchy, such that (a) the total repair cost of the final diagnosis is minimised, and (b) the computation is performed within the multiple deadlines attached to the suspect components. This is a bi-criterion scheduling problem; time and cost being the two factors that are taken into account during evaluation of the ordering of diagnostic jobs. A simple architecture is presented that elegantly separates the diagnostic engine from the meta-level reasoning module (termed here the Diagnostic Supervisor). A scheduler called the Time-Limited Candidate Selector (TLCS) is proposed, which forms the heart of the Diagnostic Supervisor. Its performance is compared to those of the two schedulers from which it was derived: WSPT (weighted shortest processing time) and Hodgson's algorithm. In tests using a three-layer behavioural model of a crude-oil distillation unit, the TLCS algorithm is shown to outperform both of its parents.