Renewal Theory Class Notes for ISEN 618
October 2, 2007
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Introduction and Preliminaries
The physical basis on which renewal theory rests is very simple. Suppose we observe a particular (randomly occuring) phenomenon, e.g., the times at which a d

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Preface to Dynamic Programming The approach taken herein for the development of materials on dynamic programming as a problem solving tool is based on the concept that computer solution algorithms are of great educational value for learning and solving ce

1 MOR/DP: A Computer System For Dynamic Programming The last example illustrates a considerable computational effort can be required to numerically solve discrete dynamic programming problems. To facilitate such solutions, we have developed a microcompute

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Changing Production Levels Consider a production planning problem where demands in each period do not have to be met and excess production can not be carried over into the next period. This problem is one of changing the production levels over a plannin

1
A Simple Mathematical Programming Problem Consider a single constraint separable optimization problem of the form:
max z = gi ( xi )
i =1 n
n
st
h (x ) b
i =1 i i
xi 0 and integers for all i . This problem can be solved by dynamic programming even when

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Nonserial Problem Consider the nonlinear integer programming problem
2 2 2 max z = 3 x1 + 6 x2 + ( 4 x3 + 2 x 4 )( x5 + 3 x6 )
st
2 x1 + 4 x2 + 4 x3 + 2 x4 + x5 + 5 x6 20 xi 0, and integer for all i.
This problem does not have the characteristics need t

Production Planning with Stochastic Demands In many production planning or inventory reordering problems, the demands are not known exactly. Forecasts based on historical demands are frequently used to estimate these values. In most situations, these are

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Expected Returns for Stochastic Versus Deterministic Policies An interesting aspect of stochastic problems as they are handled by dynamic programming has to do with the expected return for the optimal policy. The solution policies that result from a sto

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Reliability Problem Consider a prototype reliability problem where n components in series define the reliability of a system. It is possible to install multiple units of a given component which results in a corresponding increase in that component's rel

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Sequencing Problems Consider the problem of sequencing a set of n jobs on a single machine with all of the jobs initially available for processing. The objective is to sequence the jobs on the machine so as to minimize an additive function of the comple

DP Topics Outline Reference Texts for Dynamic Programming: Nemhauser (out of print): Introduction to Dynamic Programming Denardo: Dynamic Programming: Models and Applications Dreyfus and Law: The Art of Dynamic Programming Computer Software Support for DP

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Developing an MOR/ML Dynamic Programming Program
At this point, we have modeled a variety of dynamic programming models and solved
them both by hand and by use of the MOR/DP support package. It is now time to
consider the details of the computational me

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