Minsum Criteria Research Articles

Batch scheduling of nonidentical job sizes with minsum criteria

This paper concerns the problem of scheduling jobs with unit processing time and nonidentical sizes on single or parallel identical batch machines. The objective is to minimize the total completion time of all jobs. We show that the worst-case ratio of the algorithm based on the bin-packing algorithm First Fit Increasing lies in the interval \(\left[ \frac{109}{82}, \frac{2+\sqrt{2}}{2}\right] \approx [1.3293, 1.7071]\) for the single machine case, and is no more than \(\frac{6+\sqrt{2}}{4}\approx 1.8536\) for the parallel machines case.

Path Planning of an AGV in the Presence of Two Elliptical Forbidden Regions

The paper presents the methodology to obtain the path planning of an AGV in the presence of elliptical forbidden regions. The algorithms to compute the shortest unconstrained Euclidean distances are presented. In case of the elliptical forbidden regions Further Reduced Search Area (FRSA) Technique is used. This approach overcomes the inadequacies of earlier techniques and can yield solutions to problems involving elliptical forbidden regions. The MATLAB programming is graphic interactive and enables the user to continuously monitor the state and progress of computation. Min-sum criteria have been used to find optimum location of a new facility through revised Hook and Jeeves search method.

Parallel machines scheduling with machine maintenance for minsum criteria

This paper considers a parallel-machine scheduling problem with machine maintenance. There are unavailable periods on each of the first k machines, and the remaining m − k machines are always available, where 1 ⩽ k ⩽ m is an integer. The objective is to minimize the total completion time of all jobs. We show the classical SPT algorithm has a worst-case ratio of at most 1 + m - 1 m - k when k < m. If there is exactly one unavailable period on each of the first k machines, and the unavailable periods do not overlap, the worst-case ratio of SPT is at most 2 + k - 1 m - 1 , and no polynomial time approximation algorithm with worst-case ratio less than m m - 1 can exist when k = m unless P = NP.

Improved bounds for scheduling conflicting jobs with minsum criteria

We consider a general class of scheduling problems where a set of conflicting jobs needs to be scheduled (preemptively or nonpreemptively) on a set of machines so as to minimize the weighted sum of completion times. The conflicts among jobs are formed as an arbitrary conflict graph. Building on the framework of Queyranne and Sviridenko [2002b], we present a general technique for reducing the weighted sum of completion-times problem to the classical makespan minimization problem. Using this technique, we improve the best-known results for scheduling conflicting jobs with the min-sum objective, on several fundamental classes of graphs, including line graphs, ( k + 1)-claw-free graphs, and perfect graphs. In particular, we obtain the first constant-factor approximation ratio for nonpreemptive scheduling on interval graphs. We also improve the results of Kim [2003] for scheduling jobs on line graphs and for resource-constrained scheduling.

POLYLINE FITTING OF PLANAR POINTS UNDER MIN-SUM CRITERIA

Fitting a curve of a certain type to a given set of points in the plane is a basic problem in statistics and has numerous applications. We consider fitting a polyline with k joints under the min-sum criteria with respect to L1- and L2-metrics, which are more appropriate measures than uniform and Hausdorff metrics in statistical context. We present efficient algorithms for the 1-joint versions of the problem and fully polynomial-time approximation schemes for the general k-joint versions.

Non-Approximability Results for Scheduling Problems with Minsum Criteria

We provide several non-approximability results for deterministic scheduling problems whose objective is to minimize the total job completion time. Unless 𝒫 =𝒩𝒫, none of the problems under consideration can be approximated in polynomial time within arbitrarily good precision. Most of our results are derived by APX-hardness proofs. We show that, whereas scheduling on unrelated machines with unit weights is polynomially solvable, the problem becomes APX-hard if release dates or weights are added. We further show APX-hardness for scheduling in flow shops, job shops, and open shops. We also investigate the problems of scheduling on parallel machines with precedence constraints and unit processing times, and two variants of the latter problem with unit communication delays; for these problems we provide lower bounds on the worst-case behavior of any polynomial-time approximation algorithm through the gap-reduction technique.

On locating a single path-like facility in a general graph

The problem of locating a path-like facility of fixed length in a tree can be solved in polynomial time. However, this problem is NP-complete even on very sparse graphs such as outerplanar graphs. We show that if the length of the facility to be located is small then the corresponding path location problem can be solved efficiently. We suggest O (n 4 log n) and O (n 4 ) algorithms to solve the problem of locating small paths with minmax and minsum criteria on a general graph. We also give a method to solve small path location problems with a general nonlinear objective function. If the path-like facility to be located is known to be contained in some path with at most r nodes then we show that, for fixed r, the path location problem is solvable in polynomial time.

Scheduling identical jobs on uniform parallel machines

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, maximum 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+1) time dynamic programming algorithm for minimizing total completion time.