On-line control model for network construction projects

An activity-on-arc network project of the PERT type with random activity durations is considered. For each activity, its accomplishment is measured in percentages of the total project. When operated, each activity utilizes resources of a pregiven capacity and no resource reallocation is undertaken in the course of the project's realization. Each activity can be operated at several possible speeds that are subject to random disturbances and correspond to one and the same resource capacity; that is, these speeds depend only on the degree of intensity of the project's realization. For example, in construction projects partial accomplishments are usually measured in percentages of the total project, while different speeds correspond to different hours a day per worker. The number of possible speeds is common to all activities. For each activity, speeds are sorted in ascending order of their average values—namely speeds are indexed. It is assumed that at any moment t>0 activities, in operation at that moment, have to apply speeds of one and the same index that actually determines the project's speed. The progress of the project can be evaluated only via inspection at control points that have to be determined. The project's due date and the chance constraint to meet the deadline are pregiven. An on-line control model is suggested that, at each control point, faces a stochastic optimization problem. Two conflicting objectives are imbedded in the model:(1) to minimize the number of control points, and(2) to minimize the average index of the project's speeds which can be changed only at a control point.At each routine control point, decision-making centers on determining the next control point and the new index of the speeds (for all activities to be operated) up to that point. The model's performance is verified via simulation.The developed on-line control algorithm can be used for various PERT network projects which can be realized with different speeds, including construction projects and R&D projects.     

On the optimal management of project risk

The uncertainty of project networks has been mainly considered as the randomness of duration of the activities. However, another major problem for project managers is the uncertainty due to the randomness of the amount of resources required by each activity which can be expressed by the randomness of its cost. Such randomness can seriously affect the discounted cost of the project and it may be strongly correlated with the duration of the activity.In this paper, a model considering the randomness of both the cost and the duration of each activity is introduced and the problem of project scheduling is studied in terms of the project's discounted cost and of the risk of not meeting its completion time. The adoption of the earliest (latest) starting time for each activity decreases (increases) the risk of delays but increases (decreases) the discounted cost of the project. Therefore, an optimal compromise has to be achieved. This problem of optimization is studied in terms of the probability of the duration and of the discounted cost of the project falling outside the acceptable domain (Risk function) using the concept of float factor as major decision variable. This last concept is proposed to help the manager to synthetize the large number of the decision variables representing each schedule for the studied project. Numerical results are also presented for a specific project network.     

Weather Risk in Offshore Projects

Risk analysis tools have been used to help manage various projects. This paper describes a case study in which an extension to the stochastic project network model was developed for a risk analysis of an oil platform installation, quantifying the possible impact of the weather on the project's schedule. Examination of the weather data suggested the use of a Markov weather model combined with a separate residence time distribution for key states. The weather model was incorporated into the stochastic project network allowing the interactions of the various project uncertainties to be examined. While the weather introduced a significant additional risk to the project, analysis of management's options indicated that much of the risk might be avoided. In particular, the analysis quantified the benefits of scheduling the project start to take advantage of the seasonal variations and hiring heavy duty equipment to operate in more arduous conditions.     

Estimating NPV variability for deterministic models

For decision makers the variability in the net present value (NPV) of an investment project is an indication of the project's risk. Risk analysis is one way to estimate this variability. However, risk analysis requires knowledge about the joint-distribution function of the inputs. Modeling this is often very difficult if not impossible for large long-term investment projects, such as energy infrastructures. In practice, the analysis of the variability is then usually restricted to deterministic sensitivity analysis, such as `one-factor-at-a-time' and scenario analysis. These deterministic analyses, however, do not account for the total variability in the NPV. This paper shows that the use of experimental design (taken from statistical theory) in combination with regression (meta) modeling is a better approach.. 1782 1150 V 3     

Mathematica™ in context

Aspects of the problem of teaching introductory undergraduate mathematics are considered in the context of both an increased participation rate in higher education as well as increasingly sophisticated computational technology. In particular, some of the changes in student and governmental expectations of course outcomes are canvassed, and an ongoing project initiated as a response both to these changes and to the availability of modern computational algebra systems that have sophisticated user interfaces is described. The project's aim is to develop students' mathematical understanding by undertaking practical laboratory work focused on applications that are perceived by students to be relevant to their social context and employment aspirations.     

A note on an iterative forward/backward scheduling technique with reference to a procedure by Li and Willis

In this note we propose an iterative scheduling technique which consists of consecutive forward/backward scheduling passes aimed at reducing the project duration by smoothing out the project's resource profile. The idea of iterative scheduling is initiated by Li and Willis in their related paper. The only common point between their scheduling technique and the one proposed here is the iterative feature. The two techniques differ both in algorithmic aspects and in the way activities are selected for scheduling at a decision point. In the technique proposed here activities are evaluated by well-reputed dispatching rules and a conflict based decision-making process called Local Constraint Based Analysis (LCBA). The results on benchmark problems from the literature demonstrate that LCBA specifically exploits the flexible activity time windows provided by the iterative scheduling technique.     

A zero-one model for project portfolio selection and scheduling

A zero-one integer linear programming model is proposed for selecting and scheduling an optimal project portfolio, based on the organisation's objectives and constraints such as resource limitations and interdependence among projects. The model handles some of the issues that frequently arise in real world applications but are not addressed by previously suggested models, such as situations in which the amount of available and consumed resources varies in different periods. It also allows for interactive adjustment following the optimisation process, to provide decision makers a method for controlling portfolio selection, based on criteria that may be difficult to elicit directly. It is critical for such a system to provide fast evaluation of alternatives the decision makers may want to examine, and this requirement is addressed. The proposed model not only suggests projects that should be incorporated in the optimal portfolio, but it also determines the starting period for each project. Scheduling considerations can have a major impact on the combination of projects that can be incorporated in the portfolio, and may allow the addition of certain projects to the portfolio that could not have been selected otherwise. An example problem is described and solved with the proposed model, and some areas for future research are discussed.     

Myopic control of stochastic inventories with intermittent updates: continuous <Emphasis Type="Italic">versus</Emphasis> periodic replenishment

A manufacturer who is responsible for supplying a retailer with a single product is considered. The retailer sells the product in response to stochastic demand and provides the manufacturer with periodic updates about his inventories. Replenishing the retailer's inventory under two myopic base-stock policies is addressed. These policies, referred to as vendor managed inventory, represent a relatively new approach to allocating responsibility in the replenishment process. Specifically, the manufacturer, who is responsible for the retailer's inventories, can replenish them either continuously at any point in time or periodically, at one point in time for each period. The myopic replenishment policies that are considered are of a base-stock type. It is shown that the selected policies become optimal as the number of review periods tends to infinity. Furthermore, the two replenishment alternatives are compared in terms of both base-stock levels and expected costs, including those for inventory holding/shortage and transportation costs. Although continuous rather than periodic replenishment is evidently more expensive in terms of transportation costs, it is shown that even when the transportation cost constitutes more than 55% of the total average cost, it may still be preferable to replenish continuously rather than periodically.     

Tracking Demands in Optimal Control of Managerial Systems with Continuously-Divisible, Doubly Constrained Resources

The paper addresses problems of allocating continuously divisible resources among multiple production activities. The resources are allowed to be doubly constrained, so that both usage at every point of time and cumulative consumption over a planning horizon are limited as it is often the case in project and production scheduling. The objective is to track changing in time demands for the activities as closely as possible. We propose a general continuous-time model that states the problem in a form of the optimal control problem with non-linear speed-resource usage functions. With the aid of the maximum principle, properties of the solutions are derived to characterize optimal resource usage policies. On the basis of this analytical investigation, numerical scheduling methods are suggested and computationally studied. This revised version was published online in July 2006 with corrections to the Cover Date.     

A generalized activity network model

In recent years activity networks for projects with both random and deterministic alternative outcomes in key nodes have been considered. The developed control algorithm chooses an optimal outcome direction at every deterministic alternative node which is reached in the course of the project's realization. At each routine decision-making node, the algorithm singles out all the subnetworks (the so-called joint variants) which correspond to all possible outcomes from that node. Decision-making results in determining the optimal joint variant and following the optimal direction up to the next decision-making node. However, such models cover a limited class of alternative networks, namely, only fully-divisible networks which can be subdivided into nonintersecting fragments. In this paper, a more generalized activity network is considered. The model can be applied to a broader spectrum of R&D projects and can be used for all types of alternative networks, for example, for non-divisible networks comprising nodes with simultaneously ‘must follow’, random ‘exclusive OR’ and deterministic ‘exclusive or’ emitters. The branching activities of the third type refer to decision-making outcomes; choosing the optimal outcome is the sole prerogative of the project's management. Such a model is a more universal activity network; we will call it GAAN—Generalized Alternative Activity Network. The problem is to determine the joint variant optimizing the mean value of the objective function subject to restricted mean values of several other criteria. We will prove that such a problem is a NP-complete one. Thus, in general, the exact solution of the problem may be obtained only by looking through all the joint variants on the basis of their proper enumeration. To enumerate the joint variants we will use the lexicographical method in combination with some techniques of discrete optimization. A numerical example will be presented. Various application areas are considered.     

Introducing system dynamics to the BBC World Service: an insider perspective

The paper relates the story of the encounter between system dynamics modelling and the BBC World Service told from the perspective of a manager who was also championing the approach inside the World Service. The outcome provides interesting lessons and useful ideas on the contribution to organisational change that can and cannot be expected from a system dynamics project. The paper opens with a review of the published literature on the impact of system dynamics within organisations. The BBC World Service organisation and culture are then briefly described, with particular reference to potential fits and misfits with the system dynamics approach. The process of building a World Service model is described, both in terms of historical and technical stages. The project's impact on the organisation is reported, whether the impact arose by design or default. This appraisal covers the model building process, the analysis of simulations and finally the development of a microworld or gaming simulator. The paper concludes with comments on the merits of system dynamics to an organisation like the BBC World Service, pinning down the tangible and less tangible benefits delivered, and making suggestions to encourage acceptability of the approach.     

A partial cooperation model for non-unique linear two-level decision problems

This paper examines a linear static Stackelberg game where the follower's optimal reaction is not unique. Traditionally, the problem has been approached using either an optimistic or a pessimistic framework, respectively, representing the two extreme situations of full cooperation and zero cooperation from the follower. However, partial cooperation from the follower is a viable option. For partial cooperation, the leader's optimal strategy may be neither optimistic nor pessimistic. Introducing a cooperation index to describe the degree of follower cooperation, we first formulate a partial cooperation model for the leader. The two-level problem is then reformulated into a single-level model. It is shown that the optimistic and pessimistic situations are special cases of the general model, and that the leader's optimal choice may be an intermediate solution.     

System catastrophe: A distributive model for collective phenomenon

The phenomenon of system catastrophe often occurs in a system with a network structure. A system's resources can be utilized in two different modes: efficiently or inefficiently. When actions with inefficient mode pose no threat to other users or, in other words, when they employ resources that would otherwise be idle, they do not waste the system's resources at all. But when critical levels of inefficient uses of system's resources are reached, there is a sudden decrease in the capacity of the system due to the multiplication effects of inefficient factors. This collective inefficiency results in everyone getting worse in average. The common theme behind the catastrophe phenomenon demonstrates a possible explanation for the famous question about the choice between market and hierarchy. That is, when all firms pursue their own individual interests, resulting in a collective breakdown, they turn to consolidated ways of carrying out transactions.     

Student Outcomes in a Local Systemic Change Project

The Local Systemic Change initiative of the National Science Foundation supports projects focusing primarily on teacher enhancement through extensive professional development and the use of standards‐based curriculum materials. The underlying rationale is that the effective use of such materials will ultimately result in enhanced student learning. However, the research base regarding the impact of these efforts on student learning is rather lean. This paper describes the results of a curriculum‐aligned assessment comprising selected items from the Third International Mathematics and Science Study. The assessment was administered to fifth graders involved in a Local Systemic Change project to address the following questions: How does the performance of students involved in the project compare nationally and internationally? and Does length of involvement in the project make a difference in student performance? Additional evidence to relate student outcomes to the project's systemic change efforts are provided.     

Retailer’s inventory policies for a one time only manufacturer trade deal of uncertain duration

This paper models a retailer’s response to temporary manufacturer’s trade deals characterized by a time interval of random length, but with the ending date known before its occurrence. Uncertainty is handled through a reordering point, which serves as a trigger mechanism for a new special order and is activated at the discount termination date. The model generates ordering policies, applicable to any probability distribution and is shown to yield well-known deterministic optimal policies as a limiting case.     

COEXISTENCE OR EXCLUSION IN A COMPETITIVE COMMON-POOL FISHERY: A REVISIONIST VIEW

ABSTRACT. One of the earliest applications of game theory to renewable resource modeling was Colin Clark's analysis, in 1980, of the competitive exploitation of a common-pool resource. His model described the dynamics of a single Gordon-Schaeffer fish stock, being harvested non-cooperatively by two or more independently managed fleets. He showed that aggressive harvesting by all fleets (a Nash equilibrium) would lead to stock drawdown to a level which would successively eliminate all of the less efficient harvesters. Furthermore, when the fleets were closely matched, the survivor(s) of this aggressive competition would be forced, by the threat of competitors' reentry, to hold the stock in its severely degraded state, and hence to harvest at only marginal profitability. This outcome has often been compared to the open access “tragedy of the commons.” and to the outcome of the well-known “prisoners' dilemma” game. In this article I will argue that, for closely matched fleets, a more likely outcome is that the fleets will tacitly agree, without overt communication, to focus simultaneously on a specific set of coordinated policies which will permit their continuing coexistence and profitable operation. This policy profile also forms a Nash equilibrium, one which is secured by the mutual ability of the fleets to quickly recognize and credibly punish any unilateral deviations from the anticipated actions. Thus the dynamic harvesting game more nearly resembles the repeated prisoners' dilemma than it does the classical single stage version.     

Bayesian model averaging for multivariate extremes

The main framework of multivariate extreme value theory is well-known in terms of probability, but inference and model choice remain an active research field. Theoretically, an angular measure on the positive quadrant of the unit sphere can describe the dependence among very high values, but no parametric form can entirely capture it. The practitioner often makes an assertive choice and arbitrarily fits a specific parametric angular measure on the data. Another statistician could come up with another model and a completely different estimate. This leads to the problem of how to merge the two different fitted angular measures. One natural way around this issue is to weigh them according to the marginal model likelihoods. This strategy, the so-called Bayesian Model Averaging (BMA), has been extensively studied in various context, but (to our knowledge) it has never been adapted to angular measures. The main goal of this article is to determine if the BMA approach can offer an added value when analyzing extreme values.     

A calibrated model of local food system of Hawaii: What are the economic implications of the state's food goals and policies?

We develop a fully calibrated positive mathematical programming model for Hawaii's local food systems—which captures the production and the consumer sides of the market. Then we use the model to assess two proposed policies—a general excise tax (GET) exemption on locally produced foods, and an investment in agricultural infrastructure. For the GET exemption case, our results indicate an economic gain of $118 per $100 cost. On the other hand, an investment in 1,200 acres of land injected to support local production may generate an economic gain of up to $357 per $100 annual cost of the investment. However, these estimates should be considered preliminary, and thus viewed with caution. Although the model is used to capture Hawaii's local food systems, we believe that our model is generalizable and can be adopted by other economies to assess their respective food localization policies. Recommendations for Resource Managers

• Local food policies need to be based on quantitative terms instead of mere armchair speculation because often their potential outcomes may vary significantly.

• The current modeling framework demonstrates the potential of using positive mathematical programming (PMP) in capturing the intricacies of local food systems. However, this exploratory exercise should be viewed as preliminary in nature and the ensuing results were taken with caution because many important factors such as labor availability may have been left out.

• Thus, further model refinements are necessary to better capture the complexities of local food systems such as farm heterogeneity, availability of farm labor, water availability, and interisland transportation of farm products in the case of Hawaii.