Jason D. Papastavrou

The Dynamic and Stochastic Knapsack Problem

The Dynamic and Stochastic Knapsack Problem (DSKP) is defined as follows. Items arrive according to a Poisson process in time. Each item has a demand (size) for a limited resource (the knapsack) and an associated reward. The resource requirements and rewards are jointly distributed according to a known probability distribution and become known at the time of the items arrival. Items can be either accepted or rejected. If an item is accepted, the items reward is received; and if an item is rejected, a penalty is paid. The problem can be stopped at any time, at which time a terminal value is received, which may depend on the amount of resource remaining. Given the waiting cost and the time horizon of the problem, the objective is to determine the optim al policy that maximizes the expected value (rewards minus costs) accumulated. Assuming that all items have equal sizes but random rewards, optimal solutions are derived for a variety of cost structures and time horizons, and recursive algorithms for computing them are developed. Optimal closed-form solutions are obtained for special cases. The DSKP has applications in freight transportation, in scheduling of batch processors, in selling of assets, and in selection of investment projects.>

The Dynamic and Stochastic Knapsack Problem with Random Sized Items

A resource allocation problem, called the dynamic and stochastic knapsack problem (DSKP), is studied. A known quantity of resource is available, and demands for the resource arrive randomly over time. Each demand requires an amount of resource and has an associated reward. The resource requirements and rewards are unknown before arrival and become known at the time of the demands arrival. Demands can be either accepted or rejected. If a demand is accepted, the associated reward is received; if a demand is rejected, a penalty is incurred. The problem can be stopped at any time, at which time a terminal value is received that depends on the quantity of resource remaining. A holding cost that depends on the amount of resource allocated is incurred until the process is stopped. The objective is to determine an optimal policy for accepting demands and for stopping that maximizes the expected value (rewards minus costs) accumulated. The DSKP is analyzed for both the infinite horizon and the finite horizon cases. It is shown that the DSKP has an optimal policy that consists of an easily computed threshold acceptance rule and an optimal stopping rule. A number of monotonicity and convexity properties are studied. This problem is motivated by the issues facing a manager of an LTL transportation operation regarding the acceptance of loads and the dispatching of a vehicle. It also has applications in many other areas, such as the scheduling of batch processors, the selling of assets, the selection of investment projects, and yield management.

A stochastic and dynamic model for the single-vehicle pick-up and delivery problem

In this paper a stochastic and dynamic model for the Pick-up and Delivery Problem is developed and analyzed. Demands for service arrive according to a Poisson process in time. The pick-up locations of the demands are independent and uniformly distributed over a service region. A single vehicle must transport the demands from the pick-up to the delivery location. Once a demand has been picked up it can only be dropped off at its desired delivery location. The delivery locations are independent and uniformly distributed over the region, and they are independent of the pick-up locations. The objective is to minimize the expected time in the system for the demands. Unit-capacity vehicle and multiple-capacity vehicle variations are considered. For each variation, bounds on the performance of the routing policies are derived for light and heavy traffic. The policies are analyzed using both analytical methods and simulation.

A stochastic and dynamic routing policy using branching processes with state dependent immigration

Abstract A stochastic and dynamic vehicle routing problem called the Dynamic Traveling Repairman Problem (DTRP) was introduced by Bertsimas and van Ryzin. Several routing policies were analyzed in light traffic and in heavy traffic conditions. But, the good light traffic policies become very quickly unstable with increasing traffic intensity, and the good heavy traffic policies are inefficient in light traffic conditions. In this paper, a new routing policy is defined and analyzed, using results from branching processes with state dependent immigration. This policy not only performs optimally in light traffic, but also performs very well in heavy traffic. This is important to the designer of a service system because the traffic conditions may be variable and/or be unpredictable, and having to switch routing policies could prove to be costly and difficult to implement.

Models of the warning process: important implications towards effectiveness

This paper presents a model-guided evaluation of research findings pertaining to warning signs and labels. Several results of significance are noted. First, the observed noticing, reading, and behavioral influence of warnings varied greatly between studies. Analyzing behavior from the perspective of information processing at different levels of performance provides a way of clarifying these mixed research results. Second, this analysis raises the question of how to best accommodate people at varying levels of performance. This seems to be one of the most difficult problems in warning design, in that the most effective warnings at each level are fundamentally different. Third, this analysis points out directions for future research. In particular, there is a strong need to focus future research on skill and rule-based behavior for a wide ranging set of products and use environments.

Distributed detection by a large team of sensors in tandem

The problem of decentralized binary hypothesis testing by a team consisting of N decision makers (DMs) in tandem is considered. Each DM receives an observation and transmits a binary message to its successor; the last DM has to decide which hypothesis is true. Necessary and sufficient conditions are derived for the probability of error to asymptotically (as N to infinity ) go to zero. The result is generalized for multiple hypothesis and multiple messages. An easily implementable suboptimal decision scheme is also considered; necessary and sufficient conditions for the probability of error to asymptotically go to zero are derived for this case as well. The tradeoff between the complexity of the decision rules and their performance is examined, and numerical results are presented.<<ETX>>

An experimental comparison of conservative versus optimal collision avoidance warning system thresholds

In the distributed signal detection theoretic (DSDT) model, the human operator and the warning mechanism are independent decision makers who work together as a team. The DSDT demonstrates that the optimal warning threshold, in general, differs from the signal detection theoretic (SDT) threshold, which assumes a single decision maker. This prediction was tested in an experiment where drivers received monetary rewards for making safe passing decisions on a driving simulator. The experiment focused on evaluating the quality of the decision making of the drivers, and not on perceptual issues. A collision avoidance system provided a warning when the probability of an inadequate overtaking gap exceeded a threshold. Three thresholds were tested. The control threshold resulted in no detections or false alarms. The DSDT threshold resulted in some misses but no false alarms. The SDT threshold resulted in no misses but frequent false alarms. As predicted, (1) drivers performed the best when the warning system used the DSDT threshold, and (2) use of the SDT threshold improved performance over the control threshold, even though four of the 10 drivers occasionally ignored the warning and made risky passing attempts in the SDT conditions, possibly because of earlier false alarms. These findings support the conclusion that the DSDT model is a useful, quantitative tool that should be used by warning designers.

Improving the effectiveness of warnings by increasing the appropriateness of their information content: some hypotheses about human compliance

Abstract The ways that warnings are administered vary greatly. A warning may come as a message broadcast on the radio about severe weather, as a flashing light in the cockpit of an airplane, or as an audible smoke alarm. Typically, warnings provide an auditory or visual signal to assist in the detection of an anticipated stimulus. However, warnings tend to operate in an all or none mode: either the warning is present, or it is not. Consequently, the information they provide is limited. If warnings are provided too often, their information content becomes even lower and frequent false alarms render them ineffective because of the “cry-wolf” effect. On the other hand, if warnings are not administered frequently enough, they result in too many potentially costly misses. In this conceptual paper, it is argued that the effectiveness of warnings might be significantly improved if warnings are made more “intelligent” by providing information about the likelihood of the occurrence of the stimulus. Several representative cases are discussed and analyzed in order to demonstrate the advantages of the proposed methods.

DECISION INTEGRATION FUNDAMENTALS IN DISTRIBUTED MANUFACTURING TOPOLOGIES

Advances in control, communications, computer science and engineering have made it possible to design and implement large scale systems, where the decision making, control and information processing are distributed. This research effort attempts to establish the theoretical foundation of operational decision integration for such systems. Decision integration is a method to improve the quality of decision making. The basic elements of the integration process are defined. A simple distributed hypothesis testing model is employed to demonstrate that properly designed integration always improves the quality of the decisions. The problem of organizing decision making agents into architectures of integration (parallel versus hierarchical) is addressed. Several elementary decision architectures for small organizations are analyzed, and their performance is compared. The results are also extended for the case of flexible architectures with adaptive topology. The implications of integration are discussed with resp...

Acceptance and Dispatching Policies for a Distribution Problem

A dynamic and stochastic distribution problem with a number of terminals and a fleet of vehicles is analyzed. Customers request the transportation of batches of loads between different origins and destinations. A request can be accepted or rejected; if the request is accepted, a reward is received. Holding costs for vehicles and loads at terminals as well as transportation costs are included in the model. The objective is to determine a policy for accepting transportation requests and for dispatching vehicles that maximizes the expected value (rewards minus costs) of operating the distribution system. A Markov decision process model is developed, optimal policies are characterized, and algorithms that exploit the structure of the problem are developed.