This paper presents a goal programming approach to the problem of scheduling aggregate production and work force. The approach is illustrated via two case applications. Numeric results are derived and compared to those of two other approaches. The results suggest that goal programming may be an effective approach for solving certain types of planning models.
One hundred years ago, Konovalov developed and tested the rule that at a congruent transformation the phase boundary reaches an extremum. An important equation for the slopes of phase boundaries, derived by Gibbs five years earlier, provides the underlying theoretical basis for the rule, which is still commonly ignored. Applications of the GibbsKonovalov equation to congruent transformations, retrograde solubility, phase boundary inflections, and solid-liquid equilibrium are discussed.Basic thermodynamic principles, such as the phase rule, put constraints on the possible configurations of phase diagrams. One thermodynamic rule developed and tested experimentally by Konovalov 1 one hundred years ago fixed the slopes of coexistence curves of vaporliquid equilibria of binary solutions. Gibbs gave a more general expression for the slopes of phase boundaries five years earlier. 2 The specialized form of the GibbsKonovalov equation that we will use appears in a textbook by Schottky, Ulich and Wagner2 This equation is generally applicable and does not depend on any assumptions such as special solution models. It is discussed here to show that a variety of phase diagram features are accounted for by a single equation and to point out its applications, which are often overlooked in research papers, data compilations and textbooks. Because the Gibbs-Konovalov equation is a general thermodynamic relationship, a significant consideration in evaluating phase diagrams is the adherence of phase boundary slopes and curvatures to this thermodynamic requirement.
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