93 research outputs found
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
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
Mathematical Programming and Economic Theory
The paper discusses the analogy between economic institutions and algorithms for the solution of mathematical programming problems. The simplex method for solving linear programs can be interpreted as a search for market prices that equilibrate the demand for factors of production with their supply. An interpretation in terms of the internal organization of the large firm is offered for Lenstra’s integer programming algorithm
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