schlumberger optimizes receiver location-zahra mirzayeva

Technology services;

Oil-field;

Resource management;

Transaction based technology ;

Associated systems;

Semiconductor test equipment;

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Offices in over 100 countries;

Employs more than 50.000 people;

Had 8.75 billion revenues in 1999;

Leading power of electricity

gas

water meters

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Electricity can not be stored;

o Monitor the demand (carefully)o Meticulously control production

Remain competitive;

Reduce cost;

Increase efficiency; Monitor the costumers’ use of energy

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The meters

A receiver (pole)

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Poles’ height

material

Surroundings’ buildings

rural

urbanIncrease in coverage area decrease

in battery life span6

1,2,3...m meter M;

1,2,3...p pole P;

Capacity limit K;

To minimize the costo Minimum number of the poles;o Every meter is assigned to only one pole;o Do not exceed capacity limit;

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POLE Meters Covered

STEP 0 STEP 1

STEP 2 STEP 3 STEP 4 STEP 5

1 1,2,3 3 2 1* ― ― ―

2 2,3,9 3 2 1 0 0 0

3 5,6,7 3 2 1 1* ― ―

4 7,9,10 3 1 1 1* 1* ―

5 3,6,8 3 3* ― ― ― ―

6 1,4,7,9 4* ― ― ― ― ―

7 4,5,9 3 1 1 1 0 0

8 1,4,8 3 1 0 0 0 0

Greedy solution 1,3,4,5,6;

Optimal solution 2,3,4,8;

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Small problem 4208 meters 2393 poles;

Large problem 116 00 meters 20 631 poles

Geographic location of poles and meters;

The subset of poles that would cover all the meters was established manually;

The method is not reliable and scalable;

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Greedy procedure was implemented by MATLAB 171 poles;

Drawbacks of MATLAB procedure;

o Time consuming;

o High amount of data;

o Can’t address to capacity problem;

o Unable to answer what-if questions;

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Infinite capacity assumptionset covering problem;

Problem formulation;

Minimize ∑ Yj Yj 1, if pole j is selected

j=1 0,otherwise

subject to ∑ Yj ≥1 , for each i

{j I i € Cj}

The constraint ensures that every meter is covered by at least one pole;

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POLE Meters Covered

STEP 0 STEP 1

STEP 2 STEP 3 STEP 4 STEP 5

1 1,2,3 3 2 1* ― ― ―

2 2,3,9 3 2 1 0 0 0

3 5,6,7 3 2 1 1* ― ―

4 7,9,10 3 1 1 1* 1* ―

5 3,6,8 3 3* ― ― ― ―

6 1,4,7,9 4* ― ― ― ― ―

7 4,5,9 3 1 1 1 0 0

8 1,4,8 3 1 0 0 0 0

It took 2-3 days to complete MATLAB procedures;

Feasible combinations of meters and poles were sought in relying on data in MATLAB;

476 769 feasible meter-pole combination;

2393 binary variables,476 769 nonzero coefficient,4208 constraint;

In about 5 minutes CPLEX generated the result of 171 poles;

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116 600 meters,20 636 poles,1.3 million possible combination;

If meters covered by j1 is the subset of meters covered pole j2 then pole j1is excluded from the formulation;

If the set of poles covering meter i1was a subset of poles covering meter i2 meter i2 is

eliminated as it will already be covered by pole selected for i1;

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Pole(j) Meter

1 3,4

2 3,4,7

Meter(i) Pole

1 4,5

2 4,5,7

The size of formulation decreased by 50-60%;

After 3-4 hours computation time CPLEX yield the result of 1431 poles;

10-12 percent of receivers was assigned to 360 or more meters;

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Assumption so far:

“Receivers’ coverage area is infinite”

In reel problem:

“ Each receiver can cover only a finite number of meters,

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The small problem; - 4.208 meters

- 2.393 poles

- 2.393 binary variables,

- 4.208 constraints,

- 476.769 non-zero coeff.

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The large problem; - 116.600 meters

- 20.636 poles

- 144.225 binary variables,

- 6.601 constraints,

- 953.538 non-zero coeff.

“K”: # of the closest meters for each pole.

Theoretical Upper Limit for “K” : 540 meters;

Lower capacity limit is more logical;

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Each Cj the closest K;

Without capacity constraints;

Each meter to the nearest selected pole;

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Heuristic Approach Method:

# of meters in Urban Areas

> # of meters in Rural Areas

(<100)

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No capacity limit

We want to increase meter load

We want to decrease number of poles

Only %6 increase

1501

Minimize ∑ Yj

subject to ∑ Xij <= KYj, for each j

{i I i € Cj}

∑ Xij >= 1, for each i

Xij € {0 , 1}, for each i and jiçin

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Yj

1, if pole j is selected

0,otherwise

Collect the coordinates;(Geographical Info System)

Determine the distances; (MATLAB) Determine feasible combinatons; (GAMS*) Solve the combinations by IP; Assign meters to the poles with capacity restriction; Plot the results on a map. (GIS); Perform the what-if analysis;

*The General Algebraic Modeling System (GAMS) is a high-level modeling system for mathematical optimization. GAMS is designed for modeling and solving linear, nonlinear, and mixed-integer optimization problems. The system is tailored for complex, large-scale modeling applications and allows the user to build large maintainable models that can be adapted to new situations.

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Schlumberger benefited in three areas;

Save to timeo Early revenue

Save to plannero Save to labor force

Save to receivero Reliable datao Save to equipment and labor force

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Total save;

Organizational benefit;

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The integer-programming approach could be solve extensions to problem;

Different types of polesoEasy accessibility;oMultiple function use;oAssigning different weights and without a significant change;

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Different types of receivers

o N types of receiverso One type receivers on any pole

The objective here is minimize the total cost

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Thank You

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schlumberger optimizes receiver location-zahra mirzayeva

Engineering

pole meters covere d

pole o

subset of meters

closest meters

poles o

receiver pole

pole j2

meteri pole