Jibok Chung

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.

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.

Complexity results for the linear time–cost tradeoff problem with multiple milestones and completely ordered jobs

We consider two linear project time–cost tradeoff problems with multiple milestones. Unless a milestone is completed on time, penalty costs for tardiness may be imposed. However, these penalty costs can be avoided by compressing the processing times of certain jobs that require additional resources or costs. Our model describes these penalty costs as the total weighted number of tardy milestone. The first problem tries to minimize the total weighted number of tardy milestones within the budget for total compression costs, while the second problem tries to minimize the total weighted number of tardy milestones plus total compression costs. We develop a linear programming formulation for the case with a fixed number of milestones. For the case with an arbitrary number of milestones, we show that under completely ordered jobs, the first problem is NP-hard in the ordinary sense while the second problem is polynomially solvable.

Project Time-Cost Tradeoff Problem with Milestones under an Uncertain Processing Time

We consider a project time-cost tradeoff problem with two milestones, where one of the jobs has an uncertain processing time. Unless each milestone is completed on time, some penalty cost may be imposed. However, the penalty costs can be avoided by compressing the processing times of some jobs, which requires additional resources or costs. The objective is to minimize the expected total costs subject to the constraint on the expected project completion time. We show that the problem can be solved in polynomial time if the precedence graph of a project is a chain.

Job release scheduling problem: Complexity and an approximation algorithm

We consider the problem of releasing multiple types of jobs to a facility over a fixed period. In the problem, each type of job has its own demand for the period and the daily capacity of the facility can fluctuate. The variability of each type is defined as the total absolute deviation between the number of jobs of the corresponding type released on consecutive days. The objective is to minimize the total variability over all types. We show that the problem is strongly NP-hard. In addition, we develop an approximation algorithm and analyze its approximability according to the level of fluctuation of the daily capacity.

Cost Effective Design of TDM ADM Embedded in WDM Ring Networks

In this paper, we study a network design problem for TDM rings that are embedded in a WDM ring. We propose an optimization model based on the graph theory for the minimum use of TDM ADMs for these networks. We propose a branch-and-price algorithm to solve the suggested model to the optimality. By exploiting mathematical structure of ring networks, we develop a polynomial time column generation subroutine and a branching rule that conserves the mathematical structure for an efficient column generation. In computational experiments, the suggested model and algorithm can find not the approximation solutions but the optimal solutions for sufficient size networks within reasonable time. We also compare the solution qualities of the suggested algorithm with some known heuristics in literature.

Some Special Cases of a Continuous Time-Cost Tradeoff Problem with Multiple Milestones under a Chain Precedence Graph

We consider a time-cost tradeoff problem with multiple milestones under a chain precedence graph. In the problem, some penalty occurs unless a milestone is completed before its appointed date. This can be avoided through compressing the processing time of the jobs with additional costs. We describe the compression cost as the convex or the concave function. The objective is to minimize the sum of the total penalty cost and the total compression cost. It has been known that the problems with the concave and the convex cost functions for the compression are NP-hard and polynomially solvable, respectively. Thus, we consider the special cases such that the cost functions or maximal compression amounts of each job are identical. When the cost functions are convex, we show that the problem with the identical costs functions can be solved in strongly polynomial time. When the cost functions are concave, we show that the problem remains NP-hard even if the cost functions are identical, and develop the strongly polynomial approach for the case with the identical maximal compression amounts.

Complexity Results for the Design Problem of Content Distribution Networks

Content Delivery Network (CDN) has evolved to overcome a network bottleneck and improve user perceived Quality of Service (QoS). A CDN replicates contents from the origin server to replica servers to reduce the overload of the origin server. CDN providers would try to achieve an acceptable performance at the least cost including the storage space or processing power. In this paper, we introduce a new optimization model for the CDN design problem considering the user perceived QoS and single path (non-bifurcated) routing constraints and analyze the computational complexity for some special cases.

Optimal routing and wavelength assignment to minimize the number of SONET ADMs in WDM rings

In this study, we consider the routing and wavelength assignment problem on SONET over WDM ring networks. Our problem is the minimum ADM (add-drop multiplexer) cost problem of minimizing the number of ADM equipment instead of the minimum wavelength problem. To deal with the complexity of the problem, we create a new mathematical formulation and suggest an efficient solution method based on the branch-and-price method. We exploit the structure of the ring network to develop an efficient algorithm and show the efficiency using computer simulations.