group members amarasena r.g.c. (061004d) de mel w.r. (061013e) dolapihilla i.n.k. (061017u)...
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GROUP MEMBERSAMARASENA R.G.C. (061004D)DE MEL W.R. (061013E)DOLAPIHILLA I.N.K. (061017U)KUMARAJITH R.M.E. (061031G)
Dynamic Programming
Dynamic Programming is an algorithm design method
that can be used when the solution to a problem may
be viewed as the result of a sequence of decisions.
Typical steps of Dynamic Programming Characterize the structure of an optimal solution.
Recursively define the value of an optimal
solution.
Compute the value of an optimal solution in a
bottom-up fashion.
Compute an optimal solution from
computed/stored information.
Application areas
Airline
Hotel
Apparel
Manufacturing
Healthcare
Broadcast
Energy
Rail
Tour operators
Cargo
Restaurants
Golf
Car rental
Applications
Network Problems
Man power scheduling
Inventory management
Resource allocation Problems
Optimal Stopping Problems
Applications cont.
Bioinformatics –
computerized analysis of biological data
the use of computers to extract and analyze
biological data, especially in studying the
nucleotide sequences of DNA and other nucleic
acids
Computer science: theory, graphics, AI, systems.
Network Problem
Many applications of dynamic programming
reduce to finding the shortest (or longest) path
that joins two points in a given network.
For larger networks dynamic programming is
much more efficient for determining a shortest
path than the explicit enumeration of all paths.
Inventory Problems Dynamic programming can be used to
solve an inventory problem with the following characteristics:1. Time is broken up into periods, the
present period being period 1, the next period 2, and the final period T. At the beginning of period 1, the demand during each period is known.
2. At the beginning of each period, the firm must determine how many units should be produced. Production capacity during each period is limited.
3. Each period’s demand must be met on time from inventory or current production. During any period in which production takes place, a fixed cost of production as well as a variable per-unit cost is incurred.
4. The firm has limited storage capacity. This is reflected by a limit on end-of-period inventory. A per-unit holding cost is incurred on each period’s ending inventory.
5. The firms goal is to minimize the total cost of meeting on time the demands for periods 1,2, …., T.
Resource Allocation Problems
Resource-allocation problems, in which limited
resources must be allocated among several activities,
are often solved by dynamic programming.
To use dynamic programming to do resource
allocation, three assumptions must be made:
The amount of a resource assigned to an activity
may be any non negative number.
The benefit obtained from each activity is
proportional to the amount of the resource
assigned to the activity.
The benefit obtained from more than one activity is
the sum of the benefits obtained from the
individual activities.
Optimal Stopping Problems
A special class of problems involving a
discrete choice are those in which there is a
single decision to put an end to an ongoing
problem.
A student must decide when to give up trying to
solve a homework problem.
A firm must decide when to exit an industry.
A firm decides when to stop working on the
development of a product and to launch it
Applications in detail
Managing warehouse space
Several items
Total volume
Value of unit volume
Maximize revenue?
Replacing machines
To calculate the maximum time for using a machine.
Machine price
Operating and maintaining cost
Selling price
Applications cont.
Number of teams can be allocated to different
areas in such a way that the total effectiveness
is high
Number of days can be allocated for specific
tasks.
Dynamic Programming in High Density Barcodes
Symbol Technology has developed a new design for barcodes, that has a capacity of several hundred bytes.
Dynamic programming in Civil engineering
The application of dynamic programming to slope stability analysis
- Stresses acting can be analysed
Dynamic programming in the fields of structural engineering and water resources engineering.
Used in continuous beamsgeometric layout of trusswater allocationcapacity expansionreservoir operation
Limitations
Cost
Time
Thus dynamic programming can only be efficient
when there are not too many partial results to
compute!