Jeffrey B. Sidney

Scheduling with general job-dependent learning curves

Abstract Several recent papers focused on the effect of learning on the optimal solution of scheduling problems. We extend the setting studied so far to the case of job-dependent learning curves, that is, we allow the learning in the production process of some jobs to be faster than that of others. Our learning curve approach, which assumes learning takes place as a function of repetition of the production process, is otherwise completely general, and is not based upon any particular model of learning acquisition. We show that in the new, possibly more realistic setting, the problems of makespan and total flow-time minimization on a single machine, a due-date assignment problem and total flow-time minimization on unrelated parallel machines remain polynomially solvable.

Decomposition Algorithms for Single-Machine Sequencing with Precedence Relations and Deferral Costs

A one-machine deterministic job-shop sequencing problem is considered. Associated with each job is its processing time and linear deferral cost. In addition, the jobs are related by a general precedence relation. The objective is to order the jobs so as to minimize the sum of the deferral costs, subject to the constraint that the ordering must be consistent with the precedence relation. A decomposition algorithm is presented, and it is proved that a permutation is optimal if and only if it can be generated by this algorithm. Four special network structures are then considered, and specializations of the general algorithm are presented.

Optimal Single-Machine Scheduling with Earliness and Tardiness Penalties

We consider a single-machine job shop scheduling problem in which penalties occur for jobs that either commence before their target start times or are completed after their due dates. The objective is to minimize the maximum penalty, subject to restrictive assumptions on the target start times, the due dates, and the penalty functions. We present an algorithm for solving this problem, along with a method for generating alternative optima. The algorithm is generalized to cover the case in which the machine is available for only a limited time span.

Sequencing with Series-Parallel Precedence Constraints

One of the most important ideas in the theory of sequencing and scheduling is the method of adjacent pairwise job interchange. This method compares the costs of two sequences which differ only by interchanging a pair of adjacent jobs. In 1956, W. E. Smith defined a class of problems for which a total preference ordering of the jobs exists with the property that in any sequence, whenever two adjacent jobs are not in preference order, they may be interchanged with no resultant cost increase. In such a case the unconstrained sequencing problem is easily solved by sequencing the jobs in preference order. In this paper, a natural subclass of these problems is considered for which such a total preference ordering exists for all subsequences of jobs. The main result is an efficient general algorithm for these sequencing problems with series-parallel precedence constraints. These problems include the least cost fault detection problem, the one-machine total weighted completion time problem, the two-machine maximum completion time flow-shop problem and the maximum cumulative cost problem.

Scheduling a deteriorating maintenance activity on a single machine

We study a problem of scheduling a maintenance activity on a single machine. Following several recent papers, the maintenance is assumed to be deteriorating, that is, delaying the maintenance increases the time required to perform it. The following objective functions are considered: makespan, flowtime, maximum lateness, total earliness, tardiness and due-date cost, and number of tardy jobs. We introduce polynomial time solutions for all these problems.

Note on scheduling with general learning curves to minimize the number of tardy jobs

Several research studies have confirmed that people and organizations become better at their tasks as the tasks are repeated. The effect of this learning phenomenon on classical scheduling problems has been studied recently. One of the single-machine scheduling problems which seems to become nontrivial when learning effects are introduced is that of minimizing the number of tardy jobs. In this note, we study the special case where all jobs share a common due-date. We show that even when the learning process is assumed to be general and job-dependent, the problem remains polynomially solvable.

Scheduling in dual gripper robotic cells for productivity gains

We consider single part-type problems. Since all parts produced are identical, it is sufficient to determine the sequence of moves performed by the robot. The processing constraints define the cell to be a flowshop. The objective is the minimization of the steady-state cycle time to produce a part, or equivalently the maximization of the throughput rate. We study the problem of scheduling robot moves in dual gripper robot cells functioning in a bufferless environment. We develop an analytical framework for studying dual gripper robotic cells and examine the cycle time advantage of using a dual gripper rather than a single gripper robot. It is shown that an m-machine dual gripper robot cell can have at most double the productivity of its single gripper counterpart. We also propose a practical heuristic algorithm to compare productivity for given cell data. Computational testing of the algorithm on realistic problem instances is also described.

Distributed Sorting

The problem of sorting a file distributed over a number of sites of a communication network is examined. Two versions of this problem are investigated; distributed solution algorithms are presented; and their communication complexity analyzed both in the worst and in the average case. The worst case bounds are shown to be sharp, with respect to order of magnitude, for large files.

Optimal Sequencing by Modular Decomposition: Polynomial Algorithms

We show that the combination of dynamic programming with partial-order decomposition algorithms enables us to solve sequencing problems in polynomial time for substantially larger classes of precedence constraints than previously realized. The algorithms efficiency depends on the maximum number of jobs that are not related by the precedence constraints in certain subsets of the jobs. We also demonstrate how to modify this general algorithm lo take advantage of special problem characteristics.

The Two-Machine Maximum Flow Time Problem with Series Parallel Precedence Relations

The n-job 2-machine flow shop problem with series-parallel precedence constraints is considered with the objective to minimize makespan. Recent results of Kurisu are utilized in the development of a polynomial bounded optimal algorithm.