Strategic commitment to price to stimulate downstream innovation in a supply chain

It is generally in a firm’s interest for its supply chain partners to invest in innovations. To the extent that these innovations either reduce the partners’ variable costs or stimulate demand for the end product, they will tend to lead to higher levels of output for all of the firms in the chain. However, in response to the innovations of its partners, a firm may have an incentive to opportunistically increase its own prices. The possibility of such opportunistic behavior creates a hold-up problem that leads supply chain partners to underinvest in innovation. Clearly, this hold-up problem could be eliminated by a pre-commitment to price. However, by making an advance commitment to price, a firm sacrifices an important means of responding to demand uncertainty. In this paper we examine the trade-off that is faced when a firm’s channel partner has opportunities to invest in either cost reduction or quality improvement, i.e. demand enhancement. Should it commit to a price in order to encourage innovation, or should it remain flexible in order to respond to demand uncertainty. We discuss several simple wholesale pricing mechanisms with respect to this trade-off.     

An Application of Branch and Cut to Open Pit Mine Scheduling

The economic viability of the modern day mine is highly dependent upon careful planning and management. Declining trends in average ore grades, increasing mining costs and environmental considerations will ensure that this situation will remain in the foreseeable future. The operation and management of a large open pit mine having a life of several years is an enormous and complex task. Though a number of optimization techniques have been successfully applied to resolve some important problems, the problem of determining an optimal production schedule over the life of the deposit is still very much unresolved. In this paper we will critically examine the techniques that are being used in the mining industry for production scheduling indicating their limitations. In addition, we present a mixed integer linear programming model for the scheduling problems along with a Branch and Cut solution strategy. Computational results for practical sized problems are discussed.     

Algorithm for Optimal Triangulations in Scattered Data Representation and Implementation

Scattered data collected at sample points may be used to determine simple functions to best fit the data. An ideal choice for these simple functions is bivariate splines. Triangulation of the sample points creates partitions over which the bivariate splines may be defined. But the optimality of the approximation is dependent on the choice of triangulation. An algorithm, referred to as an Edge Swapping Algorithm, has been developed to transform an arbitrary triangulation of the sample points into an optimal triangulation for representation of the scattered data. A Matlab package has been completed that implements this algorithm for any triangulation on a given set of sample points.     

Homomorphic Feller Cocycles on a C*-Algebra

When a Fock-adapted Feller cocycle on a C*-algebra is regular,completely positive and contractive, it possesses a stochasticgenerator that is necessarily completely bounded. Necessaryand sufficient conditions are given, in the form of a sequenceof identities, for a completely bounded map to generate a weaklymultiplicative cocycle. These are derived from a product formulafor iterated quantum stochastic integrals. Under two alternativeassumptions, one of which covers all previously considered cases,the first identity in the sequence is shown to imply the rest.     

The alternating semigroups: Generators and congruences

The idea of an even permutation has recently been generalized, via path notation, to one-one partial transformations (charts) in the symmetric inverse semigroupsC _n. The even charts form the alternating semigroupA _n ^c ⊂C _n . Generators ofA _n ^c are identified: It then follows that forn≥5,A _n ^c is the collection of restrictions of the even permutations (of rankn). Like theC _n case, the congruences ofA _n ^c form a chain. Part of this research was supported by a Mary Washington College faculty development grant.     

(2 + 1) Resonance enhanced multiphoton ionization of hydrogen chloride in a pulsed supersonic jet: Vacuum wavenumbers of rotational lines with detailed band analysis for excited electronic states of HCl

A comprehensive study of the excited electronic states of HCl is reported. Using resonance enhanced multiphoton ionization ((2 + 1) REMPI) and time-of-flight mass spectrometry (TOFMS) over 120 band systems are analyzed. Supersonic jet techniques are used to prepare rotationally cold species for laser spectroscopy in the 77 000 to 96 000 cm⁻¹ region. At least 50 new electronic states are characterized as well as several features only tentatively assigned previously. A long vibrational progression consisting of 29 vibrational levels of the deeply bound V¹Σ⁺(0⁺) valence/ion-pair state is studied. We also extend the identification and analysis to high vibrational levels of low-lying Rydberg states. The assignments of [²Π_i] Rydberg state complexes are evaluated in terms of spin-orbit coupling and united-atom calculations. In several band systems, the spectra exhibit anomalous rotational line intensities and broadened linewidths which are consistent with predissociation. Multiphoton ionization with mass spectrometry permits the investigation of isotope effects as well as the appearance of fragment species associated with repulsive potential curves.     

The explicit construction of irreducible polynomials over finite fields

For a finite field GF(q) of odd prime power order q, and n 1, we construct explicitly a sequence of monic irreducible reciprocal polynomials of degree n2 ^m (m = 1, 2, 3, ...) over GF(q). It is the analog for fields of odd order of constructions of Wiedemann and of Meyn over GF(2). We also deduce iterated presentations of GF (q ⁿ 2).     

Local minima for indefinite quadratic knapsack problems

We consider the complexity of finding a local minimum for the nonconvex Quadratic Knapsack Problem. Global minimization for this example of quadratic programming is NP-hard. Moré and Vavasis have investigated the complexity of local minimization for the strictly concave case of QKP; here we extend their algorithm to the general indefinite case. Our main result is an algorithm that computes a local minimum in O(n(logn)²) steps. Our approach involves eliminating all but one of the convex variables through parametrization, yielding a nondifferentiable problem. We use a technique from computational geometry to address the nondifferentiable problem.Supported in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research, Department of Energy, under contract W-31-109-Eng-38, in part by a Fannie and John Hertz Foundation graduate fellowship, and in part by Department of Energy grant DE-FG02-86ER25013.A000.