Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case

We analyze a finite horizon, single product, periodic review model in which pricing and production/inventory decisions are made simultaneously. Demands in different periods are random variables that are independent of each other and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. Ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered. The objective is to find an inventory policy and a pricing strategy maximizing expected profit over the finite horizon. We show that when the demand model is additive, the profit-to-go functions are k-concave and hence an (s,S,p) policy is optimal. In such a policy, the period inventory is managed based on the classical (s,S) policy and price is determined based on the inventory position at the beginning of each period. For more general demand functions, i.e., multiplicative plus additive functions, we demonstrate that the profit-to-go function is not necessarily k-concave and an (s,S,p) policy is not necessarily optimal. We introduce a new concept, the symmetric k-concave functions and apply it to provide a characterization of the optimal policy.

Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: the Infinite Horizon Case

We analyze an infinite horizon, single product, periodic review model in which pricing and production/inventory decisions are made simultaneously. Demands in different periods are identically distributed random variables that are independent of each other and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. Ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered. The objective is to maximize expected discounted, or expected average profit over the infinite planning horizon. We show that a stationary (s,S,p) policy is optimal for both the discounted and average profit models with general demand functions. In such a policy, the period inventory is managed based on the classical (s,S) policy and price is determined based on the inventory position at the beginning of each period.

Grouping For Recognition

This paper presents a new method of grouping edges in order to recognize objects. This grouping method succeeds on images of both two- and three- dimensional objects. So that the recognition system can consider first the collections of edges most likely to lead to the correct recognition of objects, we order groups of edges based on the likelihood that a single object produced them. The grouping module estimates this likelihood using the distance that separates edges and their relative orientation. This ordering greatly reduces the amount of computation required to locate objects and improves the system's robustness to error.

Trajectory Mapping ("TM''): A New Non-Metric Scaling Technique

Trajectory Mapping "TM'' is a new scaling technique designed to recover the parameterizations, axes, and paths used to traverse a feature space. Unlike Multidimensional Scaling (MDS), there is no assumption that the space is homogenous or metric. Although some metric ordering information is obtained with TM, the main output is the feature parameterizations that partition the given domain of object samples into different categories. Following an introductory example, the technique is further illustrated using first a set of colors and then a collection of textures taken from Brodatz (1966).

Generating Semantic Descriptions From Drawings of Scenes With Shadows

The research reported here concerns the principles used to automatically generate three-dimensional representations from line drawings of scenes. The computer programs involved look at scenes which consist of polyhedra and which may contain shadows and various kinds of coincidentally aligned scene features. Each generated description includes information about edge shape (convex, concave, occluding, shadow, etc.), about the type of illumination for each region (illuminated, projected shadow, or oriented away from the light source), and about the spacial orientation of regions. The methods used are based on the labeling schemes of Huffman and Clowes; this research provides a considerable extension to their work and also gives theoretical explanations to the heuristic scene analysis work of Guzman, Winston, and others.

Foundations of Actor Semantics

The actor message-passing model of concurrent computation has inspired new ideas in the areas of knowledge-based systems, programming languages and their semantics, and computer systems architecture. The model itself grew out of computer languages such as Planner, Smalltalk, and Simula, and out of the use of continuations to interpret imperative constructs within A-calculus. The mathematical content of the model has been developed by Carl Hewitt, Irene Greif, Henry Baker, and Giuseppe Attardi. This thesis extends and unifies their work through the following observations. The ordering laws postulated by Hewitt and Baker can be proved using a notion of global time. The most general ordering laws are in fact equivalent to an axiom of realizability in global time. Independence results suggest that some notion of global time is essential to any model of concurrent computation. Since nondeterministic concurrency is more fundamental than deterministic sequential computation, there may be no need to take fixed points in the underlying domain of a power domain. Power domains built from incomplete domains can solve the problem of providing a fixed point semantics for a class of nondeterministic programming languages in which a fair merge can be written. The event diagrams of Greif's behavioral semantics, augmented by Baker's pending events, form an incomplete domain. Its power domain is the semantic domain in which programs written in actor-based languages are assigned meanings. This denotational semantics is compatible with behavioral semantics. The locality laws postulated by Hewitt and Baker may be proved for the semantics of an actor-based language. Altering the semantics slightly can falsify the locality laws. The locality laws thus constrain what counts as an actor semantics.

Justified Generalization: Acquiring Procedures from Examples

This thesis describes an implemented system called NODDY for acquiring procedures from examples presented by a teacher. Acquiring procedures form examples involves several different generalization tasks. Generalization is an underconstrained task, and the main issue of machine learning is how to deal with this underconstraint. The thesis presents two principles for constraining generalization on which NODDY is based. The first principle is to exploit domain based constraints. NODDY demonstrated how such constraints can be used both to reduce the space of possible generalizations to manageable size, and how to generate negative examples out of positive examples to further constrain the generalization. The second principle is to avoid spurious generalizations by requiring justification before adopting a generalization. NODDY demonstrates several different ways of justifying a generalization and proposes a way of ordering and searching a space of candidate generalizations based on how much evidence would be required to justify each generalization. Acquiring procedures also involves three types of constructive generalizations: inferring loops (a kind of group), inferring complex relations and state variables, and inferring predicates. NODDY demonstrates three constructive generalization methods for these kinds of generalization.