Optimal Inventory Policies When Sales Are Discretionary

Inventory models customarily assume that demand is fully satisfied if sufficient stock is available. We analyze the form of the optimal inventory policy if the inventory manager can choose to meet a fraction of the demand. Under classical conditions we show that the optimal policy is again of the (S,s) form. The analysis makes use of a novel property of K-concave functions.Inventory theory, optimal ordering policies, (S,s) policies, K-concavity

A computer program for the generation of logic networks from task chart data

The Network Generation Program (NETGEN), which creates logic networks from task chart data is presented. NETGEN is written in CDC FORTRAN IV (Extended) and runs in a batch mode on the CDC 6000 and CYBER 170 series computers. Data is input via a two-card format and contains information regarding the specific tasks in a project. From this data, NETGEN constructs a logic network of related activities with each activity having unique predecessor and successor nodes, activity duration, descriptions, etc. NETGEN then prepares this data on two files that can be used in the Project Planning Analysis and Reporting System Batch Network Scheduling program and the EZPERT graphics program

Gravity currents in a porous medium at an inclined plane

We consider the release from a point source of relatively heavy fluid into a porous saturated medium above an impermeable slope. We consider the case where the volume of the resulting gravity current increases with time like $t^\alpha$ and show that for $\alpha<3$, at short times the current spreads axisymmetrically, with radius $r\sim t^{(\alpha+1)/4}$, while at long times it spreads predominantly downslope. In particular, for long times the downslope position of the current scales like $t$ while the current extends a distance $t^{\alpha/3}$ across the slope. For $\alpha>3$, this situation is reversed with spreading occurring predominantly downslope for short times. The governing equations admit similarity solutions whose scaling behaviour we determine, with the full similarity form being evaluated by numerical computations of the governing partial differential equation. We find that the results of these analyses are in good quantitative agreement with a series of laboratory experiments. Finally, we briefly discuss the implications of our work for the sequestration of carbon dioxide in aquifers with a sloping, impermeable cap.Comment: 10 pages, 6 figures - revised versio

Effects of Aprons on Pitfall Trap Catches of Carabid Beetles in Forests and Fields

This study compared the efficacy of three types of pitfall traps in four forest and two field habitats. Two traps had aprons and one did not. The two apron traps were the same except for a gap between the trap and the plywood-apron, allowing captures from above or below. Traps were placed in a split-plot design and had three replicates of the three trap types per habitat. The traps were emptied each week from May to September. ANOVA\u27s were performed on 12 trapped species separately over habitats, weeks, and the in- teractions between them. The nonapron trap captured over 40% more individuals than either apron trap, though apron traps tended to be more effective in fields for species found in both habitats. Habitat-trap interactions were only significant in two species. Trap-week interactions were significant in four species

Production version of the extended NASA-Langley Vortex Lattice FORTRAN computer program. Volume 1: User's guide

The latest production version, MARK IV, of the NASA-Langley vortex lattice computer program is summarized. All viable subcritical aerodynamic features of previous versions were retained. This version extends the previously documented program capabilities to four planforms, 400 panels, and enables the user to obtain vortex-flow aerodynamics on cambered planforms, flowfield properties off the configuration in attached flow, and planform longitudinal load distributions

Neighborhood complexes and generating functions for affine semigroups

Given a_1,a_2,...,a_n in Z^d, we examine the set, G, of all non-negative integer combinations of these a_i. In particular, we examine the generating function f(z)=\sum_{b\in G} z^b. We prove that one can write this generating function as a rational function using the neighborhood complex (sometimes called the complex of maximal lattice-free bodies or the Scarf complex) on a particular lattice in Z^n. In the generic case, this follows from algebraic results of D. Bayer and B. Sturmfels. Here we prove it geometrically in all cases, and we examine a generalization involving the neighborhood complex on an arbitrary lattice