Byung-Cheon Choi

Approximation algorithms for multi-agent scheduling to minimize total weighted completion time

We consider a multi-agent scheduling problem on a single machine in which each agent is responsible for his own set of jobs and wishes to minimize the total weighted completion time of his own set of jobs. It is known that the unweighted problem with two agents is NP-hard in the ordinary sense. For this case, we can reduce our problem to a Multi-Objective Shortest-Path (MOSP) problem and this reduction leads to several results including Fully Polynomial Time Approximation Schemes (FPTAS). We also provide an efficient approximation algorithm with a reasonably good worst-case ratio.

Two-stage production scheduling with an outsourcing option

This paper considers a two-stage production scheduling problem in which each activity requires two operations to be processed in stages 1 and 2, respectively. There are two options for processing each operation: the first is to produce it by utilizing in-house resources, while the second is to outsource it to a subcontractor. For in-house operations, a schedule is constructed and its performance is measured by the makespan, that is, the latest completion time of operations processed in-house. Operations by subcontractors are instantaneous but require outsourcing cost. The objective is to minimize the weighted sum of the makespan and the total outsourcing cost. This paper analyzes how the models computational complexity changes according to unit outsourcing costs in both stages and describes the boundary between NP-hard and polynomially solvable cases. Finally, this paper presents an approximation algorithm for one NP-hard case.

Complexity of single machine scheduling subject to nonnegative inventory constraints

This paper focuses on single machine scheduling subject to inventory constraints. Jobs either add items to an inventory or remove items from that inventory. Jobs that have to remove items cannot be processed if the required number of items is not available. We consider scheduling problems on a single machine with the minimization of the total weighted completion time, the maximum lateness, and the number of tardy jobs, respectively, as objective and determine their computational complexity. Since the general versions of our problems turn out to be strongly NP-hard, we consider special cases by assuming that different jobs have certain parameter values in common. We determine the computational complexity for all special cases when the objective is either to minimize total completion time or to minimize maximum lateness and for several special cases when the objective is either to minimize total weighted completion time or to minimize the number of tardy jobs.

Two-machine flow shop scheduling problem with an outsourcing option

We consider a two-machine flow shop problem in which each job is processed through an in-house system or outsourced to a subcontractor. A schedule is established for the in-house jobs, and performance is measured by the makespan. Jobs processed by subcontractors require paying an outsourcing cost. The objective is to minimize the sum of the makespan and total outsourcing costs. We show that the problem is NP-hard in the ordinary sense. We consider a special case in which each job has a processing requirement, and each machine a characteristic value. In this case, the time a job occupies a machine is equal to the jobs processing requirement plus a setup time equal to the characteristic value of that machine. We introduce some optimality conditions and present a polynomial-time algorithm to solve the special case.

A vector space approach to tag cloud similarity ranking

One of the most exciting recent developments in web science is social tagging that enables users to easily annotate web content using free form keywords. Well known examples include Delicious, Flickr, and YouTube which respectively allow users to tag web pages, images, and videos. A tag cloud represents an aggregation of tags to characterize some entity of interest, and it has many potential applications particularly in the context of multimedia information retrieval and recommendation. In this paper, we present a novel method that computes the similarity between tag clouds through effectively incorporating tag similarity information. The considered problem has several unique characteristics mainly due to the informal nature of tag descriptions as well as the frequent tag updates, making it difficult to apply existing approaches in the information retrieval literature. Experimental results on Delicious data show that the proposed scheme can effectively utilize the tag similarity to improve the performance of tag cloud similarity ranking.

Outsourcing and scheduling for two-machine ordered flow shop scheduling problems☆

This paper considers a two-machine ordered flow shop problem, where each job is processed through the in-house system or outsourced to a subcontractor. For in-house jobs, a schedule is constructed and its performance is measured by the makespan. Jobs processed by subcontractors require paying an outsourcing cost. The objective is to minimize the sum of the makespan and the total outsourcing cost. Since this problem is NP-hard, we present an approximation algorithm. Furthermore, we consider three special cases in which job j has a processing time requirement pj, and machine i a characteristic qi. The first case assumes the time job j occupies machine i is equal to the processing requirement divided by a characteristic value of machine i, that is, pj/qi. The second (third) case assumes that the time job j occupies machine i is equal to the maximum (minimum) of its processing requirement and a characteristic value of the machine, that is, max{pj,qi} (min{pj,qi}). We show that the first and the second cases are NP-hard and the third case is polynomially solvable.

Complexity of a scheduling problem with controllable processing times

We consider the problem of scheduling a set of independent jobs on a single machine so as to minimize the total weighted completion time, subject to the constraint that the total compression cost is less than or equal to a fixed amount. The complexity of this problem is mentioned as an open problem. In this note we show that the problem is NP-hard.

Flow shops with machine maintenance: Ordered and proportionate cases

We consider the m-machine ordered flow shop scheduling problem with machines subject to maintenance and with the makespan as objective. It is assumed that the maintenances are scheduled in advance and that the jobs are resumable. We consider permutation schedules and show that the problem is strongly NP-hard; it remains NP-hard in the ordinary sense even in the case of a single maintenance. We show that if the first (last) machine is the slowest and if maintenances occur only on the first (last) machine, then sequencing the jobs in the LPT (SPT) order yields an optimal schedule for the m-machine problem. As a special case of the ordered flow shop, we focus on the proportionate flow shop where the processing times of any given job on all the machines are identical. We prove that the proportionate flow shop problem with two maintenance periods is NP-hard, while the problem with a single maintenance period can be solved in polynomial time. Furthermore, we show that the optimal algorithm for the single maintenance case is a -approximation algorithm for the two maintenance case. In our conclusion we discuss also the computational complexity of other objective functions.

Two-agent single-machine scheduling problem with just-in-time jobs

Abstract We consider two scheduling problems on a single machine with two agents. The objective is to optimize the performance measure for agent 1 while maintaining the weighted number of just-in-time jobs for agent 2 at or above a given threshold. The performance measures for agent 1 are the total weighted completion times and the weighted number of tardy jobs. We analyze how the complexities of the two problems change, depending on the conditions of processing times and weights.

Minimizing makespan in an ordered flow shop with machine-dependent processing times

We consider a generalization of the proportionate flow shop problem with the makespan objective. Each job has a processing requirement and each machine has a characteristic value. In our case, we assume that the time a job occupies a machine is equal to the processing requirement of the job plus a setup time that is equal to the characteristic value of that machine. In this paper, we consider permutation schedules and show that the problem is solvable in polynomial time when the number of machines is fixed.