DESCRIPTION A Technical Report dating back to 1996. We present explicit formulas for the time of ... more DESCRIPTION A Technical Report dating back to 1996. We present explicit formulas for the time of flight and the firing angles as a function of target range, as applied to free-flight flat ballistic trajectories. These formulas depend on one empirical constant that should be determined by best fit methods to existing firing tables or results of firing tests. We further pursue a heuristic approach to find the compatible formula for the firing angle versus horizontal target range, given non-standard air pressure.
DESCRIPTION We use developments in full-information optimal stopping to decide kidney-offer admis... more DESCRIPTION We use developments in full-information optimal stopping to decide kidney-offer admissibility depending on the patient's age in treatment, on his/her estimated lifetime probabilistic profile and his/her prospects on the waiting list. We allow for a broad family of lifetime distributions – the Gamma – thus enabling flexible modeling of patients survival under dialysis. We fully automate an appropriate recursive solution in a spreadsheet application. It yields the optimal critical times for acceptance of offers of different qualities, and the ensuing expected value-to-go as a function of time. The model may serve both the organizer of a donation program for planning purposes, and the particular surgeon in making the critical decision at the proper time. It may further serve the potential individual recipient, practicing present-day patient-choice. Numerical results and their discussion are included.
DESCRIPTION A decision maker has to choose one from among a Poisson stream of i.i.d. bids, with n... more DESCRIPTION A decision maker has to choose one from among a Poisson stream of i.i.d. bids, with no recall. The stream stops at a random time with a uniform (in the �rst case) or Eralng (in the second case) distribution. We solve the problem explicitly for maximal expected gain for bids that may take on any �nite number of values. A fast procedure to solve the problem for fixed horizon is presented as well.
DESCRIPTION Two explicit approximate formulas are presented for the required sample-size in estim... more DESCRIPTION Two explicit approximate formulas are presented for the required sample-size in estimating the variance of a normal population. We study the accuracy of these formulas and find both of them very accurate.
DESCRIPTION Monotonicity and convexity properties are established. A number of new explicit resul... more DESCRIPTION Monotonicity and convexity properties are established. A number of new explicit results are presented. The usefulness of the relation En=r Sn is emphasized, where n is the number of units at hand, En is the value function, r is a discount function and Sn is the sum of threshold functions from 1 to n.
We suggest a heuristic solution procedure for Partially Observable Markov DecisionProcesses with ... more We suggest a heuristic solution procedure for Partially Observable Markov DecisionProcesses with finite action space and finite state space with infinite horizon. The algorithmis a fast, very simple general heuristic; it is applicable for multiple states (not necessarilyordered) multiple actions and various distribution functions. The quality of the algorithm ischecked in this paper against existing analytical and empirical results for two specific modelsof machine replacement. One model refers to the case of two-action and two-system stateswith uniform observations (Grosfeld-Nir [4]), and the other model refers to a case of manyordered states with binomial observations (Sinuany-Stern et al. [11]). The paper also presentsthe model realization for various probability distribution functions applied to maintenanceand quality control.
How should a firm allocate a budget among projects with different uncertain potentials and interd... more How should a firm allocate a budget among projects with different uncertain potentials and interdependent achievement levels? Parallel teams pursuing different R&D approaches towards a particular objective, whose uncertain achievement levels improve with funding, are to be allocated a fixed budget. Clearly, the optimal allocation depends on the exact objective. We consider three objectives: maximizing the probability that the most successful activity achieves some pre-specified threshold; maximizing the expected achievement of the most successful activity; and maximizing the expected number of activities reaching some threshoId(s). To model achievement levels, we use the Marshall and Olkin and a Gumbel's bivariate exponential distributions. The achievement levels in the individual activities are set to be stochastically increasing in the respective budget allocations. We analyze the models resulting from the three objectives and provide supportive numerical results. Some of the qualitative conclusions are intuitive, while others are not.
This work highlights the problem in military operations of setting safety limits for friendly for... more This work highlights the problem in military operations of setting safety limits for friendly forces, neutral forces, or civilians, to avoid sustaining unnecessary casualties both in wartime and in training. We present and investigate an analytic model which both enables the quantitative understanding of the inherent problems, and which furnishes a reasonably flexible tool in the hands of the analyst. Characteristic numerical results are displayed and analyzed: They show in particular that prevailing crude approximations are inadequate.
We propose an aparametric approximation technique to estimate the point of intersection of a pair... more We propose an aparametric approximation technique to estimate the point of intersection of a pair of antagonistic curves, when it is assumed that the input information for both curves consists of several, possibly noisy candidate curves from dierent sources. The problem of determining an intersection point is inherent in the study of many equilibrium phenomena in the natural and behavioral sciences. Our technique is iterative and is based on an ad hoc line-to-point transformation and on common regression analysis. The article oers the rationale behind our approach, an analytical investigation of its applicability, and a thorough numerical study of the accuracy of the technique for one speci®c demand-and-supply case. Further applications, which extend from the model of two antagonistic curves, are also discussed. Ó
International Journal of Production Economics, 2003
In pull production management systems such as JIT, deliveries must be made on an as-needed basis ... more In pull production management systems such as JIT, deliveries must be made on an as-needed basis only, and production begins only when requested. It is supposed to match customer demand, i.e., producing only enough to replenish what the customer has used or sold. In this work, we argue that there should be a certain degree of independence between successive links of the supply chain, to allow flexibility in production management in individual links. We attempt to identify the degree of independence and level of flexibility in terms of lot sizing and delivery scheduling in a single-vendor-single-buyer system. Toward this aim, appropriate two-sided vendor-buyer inventoryproduction models are formulated, some interesting conclusions from their analysis are drawn, and a numerical study, which compares relevant policies, is discussed. It shows that imposing a lot-for-lot production on the JIT supplier is strikingly un-economical. On the other hand, delivery on demand can be met without intervening in the supplier's operations, and where deviation from the optimal of the resulting joint total costs is tolerable. r (I. David). 0925-5273/02/$ -see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 -5 2 7 3 ( 0 2 ) 0 0 2 7 4 -8
Journal of Optimization Theory and Applications, 2000
The optimal expenditure pattern for a double-path engineering project, i.e., a project composed o... more The optimal expenditure pattern for a double-path engineering project, i.e., a project composed of a nonroutine risky R&D path and a routine nonrisky preparatory path, manufacturing related or marketing related, is studied via the calculus of variations to derive a set of twin second-order nonlinear differential equations whose solution yields the optimal joint expenditure. Assuming independence between the risky and
The basic Lucas model for risky R&D projects is revisited. New solutions for optimal expenditures... more The basic Lucas model for risky R&D projects is revisited. New solutions for optimal expenditures are explored by exploiting the merits of the theory of differential equations. After applying the calculus of variations, a nonlinear differential equation is presented whose solution provides the optimal control for a constant conditionalcompletion density function and different time-dependent return models. New, exact, and approximate solutions are presented and discussed. It is found, for the class of risky R&D projects under study, that the behavior over time of the optimal expenditure is functionally similar to that of the expected return.
ABSTRACT The problem of determining the timing of risky R&D tasks (activities) and non-ro... more ABSTRACT The problem of determining the timing of risky R&D tasks (activities) and non-routine tasks is analysed through a simple non-linear mathematical programming model. The model ignores issues related to the flow of information gathered at each time point as a function of the amount of resources invested to this time point (see Lucas 1971, Management Science , 17 , 679-697, including his followers, and the literature on managerial economics for alternative approaches). The typical non-convex or non-concave structure of the objective function, which maximizes the expected discounted net value of the project, implies the possibility of multiple local optimal solutions. Forpracticalpurposes,theglobalsolution canbeidentified either by employing global optimization methods satisfying the K - T necessary conditions, i.e. Z (the gradient function of the objective function) 0, or by enumerating the objective value function for, at most, four basic solutions. An illustrative example indicates that solutions establishing overlapping and non-overlapping tasks can be candidates for optimality.
Probability in the Engineering and Informational Sciences, 2011
In this paper we propose a prototype model for the problem of managing waiting lists for organ tr... more In this paper we propose a prototype model for the problem of managing waiting lists for organ transplantations. Our model captures the double-queue nature of the problem: there is a queue of patients, but also a queue of organs. Both may suffer from "impatience": the health of a patient may deteriorate, and organs cannot be preserved longer than a certain amount of time. Using advanced tools from queueing theory, we derive explicit results for key performance criteria: the rate of unsatisfied demands and of organ outdatings, the steady-state distribution of the number of organs on the shelf, the waiting time of a patient, and the long-run fraction of time during which the shelf is empty of organs.
DESCRIPTION A Technical Report dating back to 1996. We present explicit formulas for the time of ... more DESCRIPTION A Technical Report dating back to 1996. We present explicit formulas for the time of flight and the firing angles as a function of target range, as applied to free-flight flat ballistic trajectories. These formulas depend on one empirical constant that should be determined by best fit methods to existing firing tables or results of firing tests. We further pursue a heuristic approach to find the compatible formula for the firing angle versus horizontal target range, given non-standard air pressure.
DESCRIPTION We use developments in full-information optimal stopping to decide kidney-offer admis... more DESCRIPTION We use developments in full-information optimal stopping to decide kidney-offer admissibility depending on the patient's age in treatment, on his/her estimated lifetime probabilistic profile and his/her prospects on the waiting list. We allow for a broad family of lifetime distributions – the Gamma – thus enabling flexible modeling of patients survival under dialysis. We fully automate an appropriate recursive solution in a spreadsheet application. It yields the optimal critical times for acceptance of offers of different qualities, and the ensuing expected value-to-go as a function of time. The model may serve both the organizer of a donation program for planning purposes, and the particular surgeon in making the critical decision at the proper time. It may further serve the potential individual recipient, practicing present-day patient-choice. Numerical results and their discussion are included.
DESCRIPTION A decision maker has to choose one from among a Poisson stream of i.i.d. bids, with n... more DESCRIPTION A decision maker has to choose one from among a Poisson stream of i.i.d. bids, with no recall. The stream stops at a random time with a uniform (in the �rst case) or Eralng (in the second case) distribution. We solve the problem explicitly for maximal expected gain for bids that may take on any �nite number of values. A fast procedure to solve the problem for fixed horizon is presented as well.
DESCRIPTION Two explicit approximate formulas are presented for the required sample-size in estim... more DESCRIPTION Two explicit approximate formulas are presented for the required sample-size in estimating the variance of a normal population. We study the accuracy of these formulas and find both of them very accurate.
DESCRIPTION Monotonicity and convexity properties are established. A number of new explicit resul... more DESCRIPTION Monotonicity and convexity properties are established. A number of new explicit results are presented. The usefulness of the relation En=r Sn is emphasized, where n is the number of units at hand, En is the value function, r is a discount function and Sn is the sum of threshold functions from 1 to n.
We suggest a heuristic solution procedure for Partially Observable Markov DecisionProcesses with ... more We suggest a heuristic solution procedure for Partially Observable Markov DecisionProcesses with finite action space and finite state space with infinite horizon. The algorithmis a fast, very simple general heuristic; it is applicable for multiple states (not necessarilyordered) multiple actions and various distribution functions. The quality of the algorithm ischecked in this paper against existing analytical and empirical results for two specific modelsof machine replacement. One model refers to the case of two-action and two-system stateswith uniform observations (Grosfeld-Nir [4]), and the other model refers to a case of manyordered states with binomial observations (Sinuany-Stern et al. [11]). The paper also presentsthe model realization for various probability distribution functions applied to maintenanceand quality control.
How should a firm allocate a budget among projects with different uncertain potentials and interd... more How should a firm allocate a budget among projects with different uncertain potentials and interdependent achievement levels? Parallel teams pursuing different R&D approaches towards a particular objective, whose uncertain achievement levels improve with funding, are to be allocated a fixed budget. Clearly, the optimal allocation depends on the exact objective. We consider three objectives: maximizing the probability that the most successful activity achieves some pre-specified threshold; maximizing the expected achievement of the most successful activity; and maximizing the expected number of activities reaching some threshoId(s). To model achievement levels, we use the Marshall and Olkin and a Gumbel's bivariate exponential distributions. The achievement levels in the individual activities are set to be stochastically increasing in the respective budget allocations. We analyze the models resulting from the three objectives and provide supportive numerical results. Some of the qualitative conclusions are intuitive, while others are not.
This work highlights the problem in military operations of setting safety limits for friendly for... more This work highlights the problem in military operations of setting safety limits for friendly forces, neutral forces, or civilians, to avoid sustaining unnecessary casualties both in wartime and in training. We present and investigate an analytic model which both enables the quantitative understanding of the inherent problems, and which furnishes a reasonably flexible tool in the hands of the analyst. Characteristic numerical results are displayed and analyzed: They show in particular that prevailing crude approximations are inadequate.
We propose an aparametric approximation technique to estimate the point of intersection of a pair... more We propose an aparametric approximation technique to estimate the point of intersection of a pair of antagonistic curves, when it is assumed that the input information for both curves consists of several, possibly noisy candidate curves from dierent sources. The problem of determining an intersection point is inherent in the study of many equilibrium phenomena in the natural and behavioral sciences. Our technique is iterative and is based on an ad hoc line-to-point transformation and on common regression analysis. The article oers the rationale behind our approach, an analytical investigation of its applicability, and a thorough numerical study of the accuracy of the technique for one speci®c demand-and-supply case. Further applications, which extend from the model of two antagonistic curves, are also discussed. Ó
International Journal of Production Economics, 2003
In pull production management systems such as JIT, deliveries must be made on an as-needed basis ... more In pull production management systems such as JIT, deliveries must be made on an as-needed basis only, and production begins only when requested. It is supposed to match customer demand, i.e., producing only enough to replenish what the customer has used or sold. In this work, we argue that there should be a certain degree of independence between successive links of the supply chain, to allow flexibility in production management in individual links. We attempt to identify the degree of independence and level of flexibility in terms of lot sizing and delivery scheduling in a single-vendor-single-buyer system. Toward this aim, appropriate two-sided vendor-buyer inventoryproduction models are formulated, some interesting conclusions from their analysis are drawn, and a numerical study, which compares relevant policies, is discussed. It shows that imposing a lot-for-lot production on the JIT supplier is strikingly un-economical. On the other hand, delivery on demand can be met without intervening in the supplier's operations, and where deviation from the optimal of the resulting joint total costs is tolerable. r (I. David). 0925-5273/02/$ -see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 -5 2 7 3 ( 0 2 ) 0 0 2 7 4 -8
Journal of Optimization Theory and Applications, 2000
The optimal expenditure pattern for a double-path engineering project, i.e., a project composed o... more The optimal expenditure pattern for a double-path engineering project, i.e., a project composed of a nonroutine risky R&D path and a routine nonrisky preparatory path, manufacturing related or marketing related, is studied via the calculus of variations to derive a set of twin second-order nonlinear differential equations whose solution yields the optimal joint expenditure. Assuming independence between the risky and
The basic Lucas model for risky R&D projects is revisited. New solutions for optimal expenditures... more The basic Lucas model for risky R&D projects is revisited. New solutions for optimal expenditures are explored by exploiting the merits of the theory of differential equations. After applying the calculus of variations, a nonlinear differential equation is presented whose solution provides the optimal control for a constant conditionalcompletion density function and different time-dependent return models. New, exact, and approximate solutions are presented and discussed. It is found, for the class of risky R&D projects under study, that the behavior over time of the optimal expenditure is functionally similar to that of the expected return.
ABSTRACT The problem of determining the timing of risky R&D tasks (activities) and non-ro... more ABSTRACT The problem of determining the timing of risky R&D tasks (activities) and non-routine tasks is analysed through a simple non-linear mathematical programming model. The model ignores issues related to the flow of information gathered at each time point as a function of the amount of resources invested to this time point (see Lucas 1971, Management Science , 17 , 679-697, including his followers, and the literature on managerial economics for alternative approaches). The typical non-convex or non-concave structure of the objective function, which maximizes the expected discounted net value of the project, implies the possibility of multiple local optimal solutions. Forpracticalpurposes,theglobalsolution canbeidentified either by employing global optimization methods satisfying the K - T necessary conditions, i.e. Z (the gradient function of the objective function) 0, or by enumerating the objective value function for, at most, four basic solutions. An illustrative example indicates that solutions establishing overlapping and non-overlapping tasks can be candidates for optimality.
Probability in the Engineering and Informational Sciences, 2011
In this paper we propose a prototype model for the problem of managing waiting lists for organ tr... more In this paper we propose a prototype model for the problem of managing waiting lists for organ transplantations. Our model captures the double-queue nature of the problem: there is a queue of patients, but also a queue of organs. Both may suffer from "impatience": the health of a patient may deteriorate, and organs cannot be preserved longer than a certain amount of time. Using advanced tools from queueing theory, we derive explicit results for key performance criteria: the rate of unsatisfied demands and of organ outdatings, the steady-state distribution of the number of organs on the shelf, the waiting time of a patient, and the long-run fraction of time during which the shelf is empty of organs.
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Papers by Israel David