Chengbin Chu

A branch‐and‐bound algorithm to minimize total tardiness with different release dates

This article deals with the scheduling problem for minimizing total tardiness with unequal release dates. A set of jobs have to be scheduled on a machine able to perform only one job at a time. No preemptive job is allowed. This problem has been proven to be NP-hard. We prove some dominance properties, and provide a lower bound polynomially computed for this problem. On the basis of our previous results, we propose a branch-and-bound algorithm to solve the problem. This algorithm was tested on hard problems involving 30 jobs and also on relatively easy problems with up to 230 jobs. Detailed computational results are given.

Supply management in assembly systems

We consider the case when n components are needed to assemble a given product. Components are provided by suppliers, and the period between the order time and the time a component is available (i.e., the lead time) is a random variable with a known distribution. The due date for the assembled product is also known. The costs to be taken into account are the inventory costs of the components and the backlogging cost of the assembled product. We propose an iterative algorithm which leads to the optimal order instants of the components.

Heuristic approaches for n/m/F/ ∑Ci scheduling problems

Abstract In this paper, we address the flow shop scheduling problem, with the criterion of minimizing the sum of job completion times. Two heuristic approaches are proposed to deal with this problem. The first approach focuses on reducing machine idle times and the second one puts efforts on reducing both the machine idle times and the job queue times. The computation of a variety of numerical cases demonstrates that the heuristic approaches are quite efficient in finding the desirable solutions.

Supply management for cost minimization in assembly systems with random component yield times

This paper is concerned with inventory control in assembly systems for minimizing production costs. The system manufactures multiple products assembled from various components, and it operates according to a cyclic schedule. At the start of each cycle time, two decisions are made: the product volumes to be assembled during the current cycle, and the component-stock levels to be ordered. For a given decision, there is an associated cost incurred by backlogging of the finished products on one hand, and the component inventory holding cost, on the other hand. The objective here is to balance the two costs so as to minimize their sum. One complicating factor stems from uncertainties in both product demand levels and components yield times. These uncertainties can be modelled by probabilistic means, and hence the cost minimization problem becomes a stochastic problem. This problem can be quite difficult due to the nonlinearity of the equations involved, the mix of integer and continuous parameters, and their large number in moderate-size problems. Our approach in this paper is to first define certain control parameters and thus reduce the number of the variables involved in the optimization problem, and then solve the latter problem by using sophisticated optimization techniques in conjunction with heuristic modelling. We will demonstrate, by numerical means, the resolution of fairly difficult problems and thus establish the viability of the proposed numerical techniques.

A splitting-up approach to simplify job-shop scheduling problems

In this paper we propose a scheduling algorithm based on splitting up the problem into separate yet linked subproblems. We develop a heuristic algorithm to manage the remaining links between the scheduling subproblems obtained as a result of the splitting process. The complexity of the computation and the performance of the algorithms are examined and numerical examples are given to illustrate these algorithms.

Single machine scheduling with chain: structured precedence constraints and separation time windows

We consider a single machine scheduling problem which we studied to improve the efficiency of an automated medical laboratory. In this problem, there are not only chain structured precedence constraints, but also minimal and maximal times separating successive jobs in the same chain (separation time windows). The criterion to be minimized is the makespan. Potential applications are not restricted to medical analysis. This problem often arises in systems where chemical processes are involved. Therefore the problem studied in this paper is important in practice. We prove that the problem is nonpolynomial (NP)-complete. As a consequence, we propose three heuristics for large size problems and a branch and bound based algorithm for small size problems. Computational results are reported.

Some new efficient methods to solve the n/1/ri/ϵTi scheduling problem

Abstract In this paper, we prove a sufficient condition for local optimality to solve the n /1/ r i / ϵT i scheduling problem which is known to be NP-hard. We then define a new dominant subset of schedules on the basis of this condition and propose several new approximate algorithms to construct schedules belonging to this subset. Numerical experiments enable us to compare them with classical approximate algorithms.

Efficient heuristic and optimal approaches for n/2/F/[sigma]Ci scheduling problems

The n-job two-machine flow shop scheduling problem is studied in this paper, with the criterion of minimizing the sum of job completion times. The scheduling problem is first formulated mathematically. Three heuristic methods are then invented to find near optimal schedules. Three lower bound generation schemata are designed to compute three different lower bounds from which the tightest one is used. To further reduce the search space, some dominance properties are proved. Then a branch-and-bound algorithm is developed to obtain an optimal schedule. Finally, results and analysis of numerical computations are presented.

Sequencing of Parts in Robotic Cells

This paper considers scheduling problems in robotic cells that produce a set of part types on several machines served by one robot. We study the problem of sequencing parts of different types in a cell to minimize the production cycle time when the sequence of the robot moves is given. This problem is NP-hard for most of the one-unit robot move cycles in a robotic cell with more than two machines and producing more than two part types. We first give a mathematical formulation to the problem, and then propose a branch-and-bound algorithm to solve it. The bounding scheme of this algorithm is based on relaxing, for all of the machines except two, the constraints that a machine should be occupied by a part for a period at least as long as the processing time of the part. The lower bound obtained in this way is tight. This relaxation allows us to overcome the complexity of the problem. The lower bound can be computed using the algorithm of Gilmore and Gomory. Computational experiments on part sequencing problems in three-machine robotic cells are given.

Heuristic procedures for minimizing makespan and the number of required pallets

A heuristic procedure is developed for minimizing makespan in flow-shop scheduling problems. In comparison with current algorithms, our algorithm seems to result in an improved makespan with a small additional computational effort. An algorithm is also developed to minimize the required number of pallets for a given makespan.