C.T. Ng

Due-date assignment and single machine scheduling with deteriorating jobs

We study a scheduling problem with deteriorating jobs, that is, jobs whose processing times are an increasing function of their start times. We consider the case of a single machine and linear job-independent deterioration. The problem is to determine an optimal combination of the due-date and schedule so as to minimize the sum of due-date, earliness and tardiness penalties. We give an O(n log n) time algorithm to solve this problem.

Paired domination on interval and circular-arc graphs

We study the paired-domination problem on interval graphs and circular-arc graphs. Given an interval model with endpoints sorted, we give an O(m+n) time algorithm to solve the paired-domination problem on interval graphs. The result is extended to solve the paired-domination problem on circular-arc graphs in O(m(m+n)) time.

Due-date assignment and parallel-machine scheduling with deteriorating jobs

In this paper we study the problem of scheduling n deteriorating jobs on m identical parallel machines. Each jobs processing time is a nondecreasing function of its start time. The problem is to determine an optimal combination of the due-date and schedule so as to minimize the sum of the due-date, earliness and tardiness penalties. We show that this problem is NP-hard, and we present a heuristic algorithm to find near-optimal solutions for the problem. When the due-date penalty is 0, we present a polynomial time algorithm to solve it.

Flowshop scheduling of deteriorating jobs on dominating machines

In this paper we consider the general, no-wait and no-idle permutation flowshop scheduling problem with deteriorating jobs, i.e., jobs whose processing times are increasing functions of their starting times. We assume a linear deterioration function with identical increasing rates for all the jobs and there are some dominating relationships between the machines. We show that the problems to minimize the makespan and the total completion time remain polynomially solvable when deterioration is considered, although these problems are more complicated than their classical counterparts without deterioration.

A graph-theoretic approach to interval scheduling on dedicated unrelated parallel machines

We study the problem of scheduling n non-preemptive jobs on m unrelated parallel machines. Each machine can process a specified subset of the jobs. If a job is assigned to a machine, then it occupies a specified time interval on the machine. Each assignment of a job to a machine yields a value. The objective is to find a subset of the jobs and their feasible assignments to the machines such that the total value is maximized. The problem is NP-hard in the strong sense. We reduce the problem to finding a maximum weight clique in a graph and survey available solution methods. Furthermore, based on the peculiar properties of graphs, we propose an exact solution algorithm and five heuristics. We conduct computer experiments to assess the performance of our and other existing heuristics. The computational results show that our heuristics outperform the existing heuristics.

Finite dominating sets for the multi-facility ordered median problem in networks and algorithmic applications

We identify a finite dominating set (FDS) for a special case of the multi-facility ordered median problem in networks, in which the @l-weights can take at least two different values. This FDS result not only includes the FDS research for the p-center problem, but also extends the case of a

MULTI-FACILITY ORDERED MEDIAN PROBLEMS IN DIRECTED NETWORKS

This paper uses a finite dominating set (FDS) to investigate the multi-facility ordered median problem (OMP) in a strongly connected directed network. The authors first prove that the multi-facility OMP has an FDS in the node set, which not only generalizes the FDS result provided by Kalcsics, et al. (2002), but also extends the FDS result from the single-facility case to the multiple case, filling an important gap. Then, based on this FDS result, the authors develop an exact algorithm to solve the problem. However, if the number of facilities is large, it is not practical to find the optimal solution, because the multi-facility OMP in directed networks is NP-hard. Hence, we present a constant-approximation algorithm for the p-median problem in directed networks. Finally, we pose an open problem for future research.

Scheduling to minimize makespan with time-dependent processing times

In this paper we study the scheduling problem of minimizing makespan on identical parallel machines with time-dependent processing times. We first consider the problem with time-dependent processing times on two identical machines to minimize makespan, which is NP-hard. We give a fully polynomial-time approximation scheme for the problem. Furthermore, we generalize the result to the case with m machines.