Parameterized complexity of machine scheduling: 15 open problems

Machine scheduling problems are a long-time key domain of algorithms and complexity research. A novel approach to machine scheduling problems are fixed-parameter algorithms. To stimulate this thriving research direction, we propose 15 open questions in this area whose resolution we expect to lead to the discovery of new approaches and techniques both in scheduling and parameterized complexity theory.Comment: Version accepted to Computers & Operations Researc

A new lower bound approach for single-machine multicriteria scheduling

The concept of maximum potential improvement has played an important role in computing lower bounds for single-machine scheduling problems with composite objective functions that are linear in the job completion times. We introduce a new method for lower bound computation; objective splitting. We show that it dominates the maximum potential improvement method in terms of speed and quality

A Novel Approach to the Common Due-Date Problem on Single and Parallel Machines

This paper presents a novel idea for the general case of the Common Due-Date (CDD) scheduling problem. The problem is about scheduling a certain number of jobs on a single or parallel machines where all the jobs possess different processing times but a common due-date. The objective of the problem is to minimize the total penalty incurred due to earliness or tardiness of the job completions. This work presents exact polynomial algorithms for optimizing a given job sequence for single and identical parallel machines with the run-time complexities of $O(n \log n)$ for both cases, where $n$ is the number of jobs. Besides, we show that our approach for the parallel machine case is also suitable for non-identical parallel machines. We prove the optimality for the single machine case and the runtime complexities of both. Henceforth, we extend our approach to one particular dynamic case of the CDD and conclude the chapter with our results for the benchmark instances provided in the OR-library.Comment: Book Chapter 22 page

Minimizing weighted total earliness, total tardiness and setup costs

The paper considers a (static) portfolio system that satisfies adding-up contraints and the gross substitution theorem. The paper shows the relationship of the two conditions to the weak dominant diagonal property of the matrix of interest rate elasticities. This enables to investigate the impact of simultaneous changes in interest rates on the asset demands.

Common Due-Date Problem: Exact Polynomial Algorithms for a Given Job Sequence

This paper considers the problem of scheduling jobs on single and parallel machines where all the jobs possess different processing times but a common due date. There is a penalty involved with each job if it is processed earlier or later than the due date. The objective of the problem is to find the assignment of jobs to machines, the processing sequence of jobs and the time at which they are processed, which minimizes the total penalty incurred due to tardiness or earliness of the jobs. This work presents exact polynomial algorithms for optimizing a given job sequence or single and parallel machines with the run-time complexities of $O(n \log n)$ and $O(mn^2 \log n)$ respectively, where $n$ is the number of jobs and $m$ the number of machines. The algorithms take a sequence consisting of all the jobs $(J_i, i=1,2,\dots,n)$ as input and distribute the jobs to machines (for $m>1$) along with their best completion times so as to get the least possible total penalty for this sequence. We prove the optimality for the single machine case and the runtime complexities of both. Henceforth, we present the results for the benchmark instances and compare with previous work for single and parallel machine cases, up to $200$ jobs.Comment: 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computin

Permutation Flowshop Scheduling with Earliness and Tardiness Penalties

We address the permutation flowshop scheduling problem with earliness and tardiness penalties (E/T) and common due date of jobs. Large number of process and discrete parts industries follow flowshop type of production process. There are very few results reported for multi-machine E/T scheduling problems. We show that the problem can be sub-divided into three groups- one, where the due date is such that all jobs are necessarily tardy; the second, where the due date is such that it is not tight enough to act as a constraint on scheduling decision; and the third is a group of problems where the due date is in between the above two. We develop analytical results and heuristics for problems arising in each of these three classes. Computational results of the heuristics are reported. Most of the problems in this research are addressed for the first time in the literature. For problems with existing heuristics, the heuristic solution is found to perform better than the existing results.

Multi-Period Cell Loading and Job Sequencing in a Cellular Manufacturing System

In this paper, a multi-period cell loading problem is addressed, where the objectives are to minimise the number of tardy jobs (nT) in a multi-period planning horizon and optimise the scheduling of tardy jobs. Three cell loading and job scheduling strategies are proposed and tested with two newly developed mixed integer programming models. Additionally, three types of due dates (tight, medium and loose) and three different demand levels were considered. Finally, two tardy job assignment methods were proposed to observe the impact on nT. Case problems were solved based on minimising nT, Tmax and total tardiness (TT) objectives and cost sensitivity analysis was performed. Results indicated that, the first strategy, (early start allowance and tardy job assignment after each period) performed better in terms of nT. For the secondary objectives, tradeoffs were observed among different strategies depending on the type of due date, demand level and tardy job assignment method

Single-machine scheduling with stepwise tardiness costs and release times

We study a scheduling problem that belongs to the yard operations component of the railroad planning problems, namely the hump sequencing problem. The scheduling problem is characterized as a single-machine problem with stepwise tardiness cost objectives. This is a new scheduling criterion which is also relevant in the context of traditional machine scheduling problems. We produce complexity results that characterize some cases of the problem as pseudo-polynomially solvable. For the difficult-to-solve cases of the problem, we develop mathematical programming formulations, and propose heuristic algorithms. We test the formulations and heuristic algorithms on randomly generated single-machine scheduling problems and real-life datasets for the hump sequencing problem. Our experiments show promising results for both sets of problems