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T his paper introduces a new neighborhood search technique, called dynasearch, that uses dynamic programming to search an exponential size neighborhood in polynomial time. While traditional local search algorithms make a single move at each iteration, dynasearch allows a series of moves to be performed. The aim is for the lookahead capabilities of dynasearch to prevent the search from being attracted to poor local optima. We evaluate dynasearch by applying it to the problem of scheduling jobs on a single machine to minimize the total weighted tardiness of the jobs. Dynasearch is more effective than traditional first-improve or best-improve descent in our computational tests. Furthermore, this superiority is much greater for starting solutions close to previous local minima. Computational results also show that an iterated dynasearch algorithm in which descents are performed a few random moves away from previous local minima is superior to other known local search procedures for the total weighted tardiness scheduling problem.

Parallel machine scheduling problems concern the scheduling of n jobs on m machines to minimize some function of the job completion times. If preemption is not allowed, then most problems are not only NP-hard, but also very hard from a practical point of view. In this paper, we show that strong and fast linear programming lower bounds can be computed for an important class of machine scheduling problems with additive objective functions. Characteristic of these problems is that on each machine the order of the jobs in the relevant part of the schedule is obtained through some priority rule. To that end, we formulate these parallel machine scheduling problems as a set covering problem with an exponential number of binary variables, n covering constraints, and a single side constraint. We show that the linear programming relaxation can be solved e ciently by column generation because the pricing problem is solvable in pseudo-polynomial time. We display this approach on the problem of minimizing total weighted completion time on m identical machines. Our computational results show that the lower bound is singularly strong and that the outcome of the linear program is often integral. Moreover, they show that our branch-and-bound algorithm that uses the linear programming lower bound outperforms the previously best algorithm.

We investigate the computational complexity of scheduling multiprocessor tasks with prespecified processor allocations. We consider two criteria: minimizing schedule length and minimizing the sum of the task completion times. In addition, we investigate the complexity of problems when precedence constraints or release dates are involved.

We address the problem of scheduling n identical jobs on m uniform parallel machines to optimize scheduling criteria that are nondecreasing in the job completion times. It is well known that this can be formulated as a linear assignment problem, and subsequently solved in O(n3) time. We give a more concise formulation for minsum criteria, and show that general minmax criteria can be minimized in O(n2) time. We present faster algorithms, requiring only O(n +mlog m) time for minimizing makespan and total completion time, O(nlogn) time for minimizing total weighted completion time, m'aximum lateness, total tardiness and the weighted number of tardy jobs, and O(nlog2n) time for maximum weighted tardiness. In the case of release dates, we propose an O(nlogn) algorithm for minimizing makespan, and an O(mn2m+') time dynamic programming algorithm for minimizing total completion time.

We study the problem of scheduling a chain-reentrant shop, a shop in which each job goes for its processing rst to a machine called the primary machine, then to a number of other machines in a xed sequence, and nally back to the primary machine for its last operation. The problem is to schedule the jobs so as to minimize the makespan. This problem is NP-hard in the strong sense for a general number of machines. We focus in particular on the two-machine case that is also NP-hard at least in the ordinary sense. We prove some properties that identify a speci c class of optimal schedules, and then use these properties in designing an approximation algorithm and a branchand-bound type optimization algorithm. The approximation algorithm, of which we present three versions, has a worst-case performance guarantee of 3=2 along with an excellent empirical performance. The optimization algorithm solves large instances quickly. Finally, we identify a few well solvable special cases and present a pseudopolynomial algorithm for the case in which the rst and the last operations of any job (on the primary machine) are identical.

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