Eishi Chiba

Collision probability in an in-line machines model

This paper presents a simple model of the manufacturing line which focuses on the performance of collision probability, and a method of application to the manufacture of Flat Panel Displays (FPDs) and semiconductors. We derive an approximate formula of the collision probability. When the processing time follows a normal distribution, we also did simulations to evaluate the exact probabilities and confirm that our approximation approach yields reasonable results compared to the simulated results. Moreover, we simplify our approximate formula of the collision probability. Concretely speaking, we derive a closed form formula when the processing time follows an exponential distribution. Finally, we present an optimization problem with the collision probability and show a method to solve it.

Collision Probability in an Automated Production Line under Erlang Distribution

Flat panel displays (FPDs) are manufactured through many different processing equipments arranged sequentially in a line. Although the constant inter-arrival time (i.e., the tact time) of glass substrates in the line should be kept as short as possible, the collision probability between glass substrates increases as the time becomes shorter. Since the glass substrate is expensive and fragile, the collision should be avoided. In this paper, we derive a closed form formula of the collision probability for a model, in which the processing time on each equipment is assumed to follow the Erlang distribution. We also show some numerical results and computer simulation results of the collision probability.

Resolution of resource conflicts in the CCPM framework using a local search method

We propose approximate methods for resolving resource conflicts in the Critical Chain Project Management (CCPM) method. The CCPM method consists of five processes. Effective approaches for four of the five processes already exist. For the remaining unresolved process, namely the resolving of resource conflicts, an effective method has yet to be proposed. Hence, we develop three simple approximate solving methods, and improve these using a local search. Methods based on the earliest and latest start times are used. The local search method undertakes a basic search by swapping the processing order of two arbitrary tasks. Through numerical experimentation, we found that these solving methods are practical if the number of outputs is one. In addition, the average value of the solutions obtained by the three simple methods was improved by up to approximately 10% when a local search was used if the number of tasks was 50.

Maximizing the total weight value of just-in-time jobs in identical parallel machines with periodic time slots

We address the processing of jobs in an environment with periodic due dates. Every job must be completed exactly on a due date, the situation of which shall be referred to as just-in-time. Each job is associated with a weight which is non-increasing with time. The problem we address is to maximize the total weight of just-in-time jobs. We prove that this class of problem is NP-hard. The key idea is a reduction from the Hamiltonian path problem, known as strongly NP-hard. Moreover, we discuss some special cases where the problem is solvable. If no set-up times exist, there are cases where the problem is solvable, we then present a method to solve the problems. To achieve this, we derive partition and union procedures, and use network flow algorithms.

A heuristic algorithm for maximizing the total weight of just-in-time jobs under multi-slot conditions

Maximizing the total weight of just-in-time jobs under multi-slot conditions was proven recently to be NP-hard. We consider a heuristic algorithm for this problem. First, we compute a schedule that minimizes the number of time slots. Next, we make a new set of jobs by merging existing jobs in the schedule. Then, we compute a minimum cost flow for the network constructed from this new set of jobs. Finally, we obtain a feasible schedule from the flow. Moreover, we implement the heuristic algorithm, and consider its features and performance from the computational experimentation.

On the Redundancy of Delivery Time in an In-Line Machine Model

In this paper, we focus on an in-line machine model. This model represents systems for the manufacturing of a product in large quantities. Recently, studies relating to the collision probability between jobs have been conducted in such models. In this paper, we extend the known models to a generalized version by considering delivery time between machines. We first present a method for computing a schedule of jobs in the generalized model. Then, we show that the collision probability for the generalized model is the same as that for the model without delivery time. We call this property the redundancy of delivery time. Next, we introduce two optimization problems with collision probability for the generalized model. Using the redundancy of delivery time, it is shown that these optimization problems are equivalent to simpler problems. This finding may prove to be very useful when considering optimization problems with collision probability.

A heuristic algorithm for the prize collecting Steiner Tree problem

The Prize Collecting Steiner Tree (PCST) problem is one of the most important problems in the field of combinatorial optimization. In this paper, we consider new heuristics for the PCST problem. The heuristics consists of two stages. The first stage of the heuristics is to compute a spanning tree, which is based on the greedy approach. In the second stage of the heuristics, each arc in the spanning tree is checked. Throughout this checking, if the deletion of arcs improves the objective function value, then such arcs are deleted from the spanning tree. Next, we implement the heuristics for computational experimentation. In computational experimentation, we use approximation ratio as a key to evaluation values. From our computational experimentation, we confirm that the heuristics method is very fast.