Raymond G. Vickson

A survey of the maximum principles for optimal control problems with state constraints

This paper gives a survey of the various forms of Pontryagins maximum principle for optimal control problems with state variable inequality constraints. The relations between the different sets of optimality conditions arising in these forms are shown. Furthermore, the application of these maximum principle conditions is demonstrated by solving some illustrative examples.

Two Single Machine Sequencing Problems Involving Controllable Job Processing Times

Abstract This paper presents simple methods for solving two single machine sequencing problems when job processing times are themselves decision variables having their own associated linearly varying costs. These are the problems of minimizing the total processing cost plus either the average flow cost or the maximum tardiness cost. The paper treats only problems with zero ready times and no precedence constraints.

Periodic Review Production Models With Variable Yield And Uncertain Demand

Abstract A periodic-review production model with variable yield (uncertain supply) and uncertain demand is formulated and investigated. First, we provide a complete analysis of the final (single) period problem. The order point turns out to be unaffected by the yield distribution, but the expected yield corresponding to optimal lot size generally does not equal the difference between the order point and initial stock. We then explore properties of the two-period problem, the solution of which is generally non-myopic. Finally, the solution structure of the n-period problem is reported.

Stochastic optimization models in finance

Mathematical Tools: Expected Utility Theory Convexity and the Kuhn-Tucker Conditions Dynamic Programming Qualitative Economic Results: Stochastic Dominance Measures of Risk Aversion Separation Theorems Static Portfolio Selection Models: Mean-Variance and Safety First Approaches and Their Extensions Existence and Diversification of Optimal Portfolio Policies: Effects of Taxes on Risk Taking Dynamic Models Reducible to Static Models: Models That Have a Single Decision Point Risk Aversion over Time Implies Static Risk Aversion Myopic Portfolio Policies Dynamic Models: Two-Period Consumption Models and Portfolio Revision Models of Optimal Capital Accumulation and Portfolio Selection Models of Option Strategy The Capital Growth Criterion and Continuous-Time Models.

Optimal lot streaming for multiple products in a two-machine flow shop

This paper treats the optimal lot streaming problem for multiple products in a two-machine flow shop with job setup times and sublot transfer times. If production lots are not preempted, an independent transfer lot sizing problem is obtained for each job; this problem is the same for any regular measure of performance. For continuous transfer lot sizes a closed-form optimal solution is obtained, while for integer valued lot sizes a fast polynomial algorithm is developed. The makespan minimization problem with lot streams is reduced to an equivalent two-machine makespan problem without lot streams or setup/transfer times but with modified processing times, and can thus be solved by Johnsons algorithm. The procedures are illustrated in an example.

Optimal two-threshold policies in an M/G/1 queue with two vacation types

This paper treats two-threshold policies for an M/G/1 queue with two types of generally distributed random vacations: type 1 (long) and type 2 (short) vacations. Upon returning from a vacation, the server observes the queue length. If this is less than the lower threshold, the server takes a type 1 vacation; if it is between the two thresholds, the server takes a type 2 vacation; and if it is at or above the upper threshold, the server resumes serving the queue exhaustively. There is a shutdown cost for starting a series of vacations, a linear customer waiting cost, and type-dependent vacation reward rates. Renewal theory or the PASTA property is used to develop expressions for the average queue length and the average system cost for generally distributed vacations. A search procedure, which is provably finite for exponentially distributed vacations, is developed for determining the optimal threshold values.

OPTIMAL STORAGE LOCATIONS IN A CAROUSEL STORAGE AND RETRIEVAL SYSTEM.

Abstract This paper examines the problem of optimal product location in a single bi-directional carousel storage and retrieval system. For items with independent demands, it establishes the long-run average optimality of a simple demand rate ranking and partitioning scheme which has previously been suggested in the literature through heuristic reasoning and simulation studies.

BATCHING AND SEQUENCING OF COMPONENTS AT A SINGLE FACILITY

We formulate and solve a single-machine scheduling problem where each job requires a component unique to that job and one which is common to all jobs. We develop an optimal dynamic programming algorithm for this problem which minimizes total job flow time. In addition we show that scheduling jobs rather than components efficiently is desirable and may lead to improved coordination between production and assembly.

A two-carousel storage location problem

We describe a problem of storing products in carousels that are grouped in pods of two. Each pod is served by one operator. The aim is to minimize the long-run average rotational time per retrieval operation. We formulate the problem as a new type of nonlinear partitioning problem and discuss several heuristic solution procedures.

The Optimal Service Policies In An M/G/1 Queueing System With Multiple Vacation Types

Abstract In this paper, we consider a single server queueing system with Poisson arrivals and multiple vacation types, in which the server can choose one of several types of vacations to take when he finishes serving all customers in the system. Upon completion of a vacation, the server checks the number of customers waiting in the system. If the number of customers is greater than a critical threshold, the server will resume serving the queue exhaustively; otherwise, he will take another vacation. A variety of vacation types are available and the choice is at the discretion of the server. The cost structure consists of a constant waiting cost rate, fixed costs for starting up service, and reward rates for taking vacations. It is shown that this infinite buffer queueing system can be formulated as a finite state Semi-Markov decision process (SMDP). With this finite state model, we can determine the optimal service policy to minimize the long-term average cost of this vacation system. Some practical stochastic production and inventory control systems can be effectively studied using this SMDP model.