A branch and bound algorithm for solving a class of nonlinear integer programming problems

This article presents a branch and bound method for solving the problem of minimizing a separable concave function over a convex polyhedral set where the variables are restricted to be integer valued. Computational results are reported.     

Rescheduling to minimize makespan on a changing number of identical processors

We consider the problem of rescheduling n jobs to minimize the makespan on m parallel identical processors when m changes value. We show this problem to be NP-hard in general. Call a list schedule totally optimal if it is optimal for all m = 1, …,n. When n is less than 6, there always exists a totally optimal schedule, but for n ≥ 6 this can fail. We show that an exact solution is less robust than the largest processing time first (LPT) heuristic and discuss implications for polynomial approximation schemes and hierarchical planning models.     

Optimal refueling sequence for a mixed fleet with limited refuelings

Consider a fleet of vehicles comprised of K₁ identical tankers and K₂ identical nontankers (small aircraft). Tankers are capable of refueling other tankers as well as nontankers. The problem is to find that refueling sequence of the tankers that maximizes the range simultaneously attainable by all K₂ nontankers. A recent paper established that the “unit refueling sequence,” comprised of one tanker refueling at each of K₁ refueling operations, is optimal. The same paper also proffered the following conjecture for the case that the number of refueling operations is constrained to be less than the number of tankers: A nonincreasing refueling sequence is optimal. This article proves the conjecture.     

Bounding methods for facilities location algorithms

Single- and multi-facility location problems are often solved with iterative computational procedures. Although these procedures have proven to converage, in practice it is desirable to be able to compute a lower bound on the objective function at each iteration. This enables the user to stop the iterative process when the objective function is within a prespecified tolerance of the optimum value. In this article we generalize a new bounding method to include multi-facility problems with l_p distances. A proof is given that for Euclidean distance problems the new bounding procedure is superior to two other known methods. Numerical results are given for the three methods.     

Test for the extreme value and weibull distributions based on normalized spacings

Discussed in this article are tests for the extreme-value distribution, or, equivalently, for the two-parameter Weibull distribution when parameters are unknown and the sample may be censored. The three tests investigated are based on the median, the mean, and the Anderson-Darling A² statistic calculated from a set zⁱ of values derived from the spacings of the sample. The median and the mean have previously been discussed by Mann, Scheuer, and Fertig [10] and by Tiku and Singh [14]. Asymptotic distributions and points are given for the test statistics, based on recently developed theory, and power studies are conducted to compare them with each other and with two other statistics suitable for the test. Of the normalized spacings tests, A² is recommended overall; the mean also gives good power in many situations, but can be nonconsistent.