Equitable canal water
allocation
Deliverable B.1
Report for project "Revitalising Irrigation in Pakistan"
University of Canterbury, Christchurch, New Zealand
in partnership with
International Water Management Institute, Lahore, Pakistan
26 June 2014
EQUITABLE CANAL WATER ALLOCATION
Table of contents
1 INTRODUCTION
3
2 MODEL DEVELOPMENT
3
2.1 EQUITY COSTS
2.2 ALLOCATION COSTS
2.3 ECWA MODEL
2.4 DETERMINING ALLOCATION COSTS
2.5 DETERMINING EQUITY COST
4
5
7
5
4
3 APPLICATION
9
3.1 MODEL SCENARIOS
3.2 RESULTS
9
10
4 CONCLUSIONS AND RECOMMENDATIONS
13
5 REFERENCES
13
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1 Introduction
In the Punjab, Pakistan, irrigation water is in short supply. Some of this is entirely intentional. The
warabandi system, originally designed during the British colonial times, was intended to operate as a
so-called protective-irrigation system, where water is applied to as large an area as possible. This
was done in order to give many farmers yield security rather than allowing optimal yields for a few.
Seckler et al. (1988) state that in the same system in India a farmer can expect to irrigate one-third of
their culturable command area (CCA) four times per season. This comes down to a “water duty” of
0.17 l s-1 ha-1 (1 ft3 per 416 acres). Bandaragoda (1996) suggests that for Pakistani Punjab the
average water duty is 0.28 l s-1 ha-1 on 100% cropping intensity. Actual water duties range from 0.200.30 l s-1 ha-1 (Bandaragoda and Rehman, 1995). Even the most generous water duty of 0.30 l s-1 ha-1
only provides 2.6 mm of irrigation water per day in an area where the evapotranspiration during the
coldest months is over 3 mm day-1 and during the hottest can reach well in excess of 9 mm day-1.
On top of the intentional deficit, there is also an actual shortage of water of water. Hussain et al.
(2011) estimates that for the year 2015, only 63% of the total irrigation water requirement can be met
from surface water resources, assuming there are no losses at all, nor any competition from other
sectors such as industry or domestic water supply. As a result, in many areas the irrigation
department does not receive enough water to supply all canals under their command with sufficient
water. Additionally many of the main canals in the Punjab are run-of-the-river systems. Discharges in
these systems fluctuate with river level (Anwar and Haq, 2013) and very low and/or very high river
levels may cause main canals to be closed all together. All these issues mean that many canals do
not always run at their design discharge level. Bhutta (1990) determined that in one study area the
canals run at less than 75% of their design discharge for 166 days of the year. In close to two thirds of
the cases this was due to low river or main canal levels, but water diversions to other parts of the
system and poor maintenance causing problems such as breaches, leakages and flooding are also at
fault.
Under those circumstances of varying and lower than expected discharges some decisions have to
be made; what discharge should each canal receive and/or should any of the canals be closed?
These decisions are made by the Irrigation Department. Current discharge amounts, canal openings
and closures appear to be unorganised and somewhat haphazard. No systematic or consistent
decision taking method has been discovered. As a result canal water allocation can be very
inequitable with some canals receiving far more water than others (even when adjusted for area). For
instance during Kharif 2011 (hot season, April-October) the 17 distributaries (sub-canals) that are
supplied by Hakra Branch Canal received on average 70% of their target allocation over the season
(PMIU, 2014). The distributary that received the most water got 76% of their target, whereas the canal
who received the least water only got 57%. It is inequities like these that create unrest between
distributaries, distrust toward the irrigation department and an unwillingness to pay for services (why
pay for something you either don’t get or cannot rely on?).
Equity is an important objective when it comes to the delivery of water. Each distributary should
receive a similar amount of water, but similarly each distributary should have an equal share of the
burden of non-delivery. Due to the chronic water shortage in the Punjab it is inevitable and
unavoidable that some distributaries do not receive water. These interruptions of service should also
be distributed in such a way that it is not the same canal that gets closed week after week.
This paper introduces an optimisation model which provides a systematic and consistent approach to
the decision making process. The model allocates the available water to the distributaries taking into
account deliveries during previous weeks. By doing this it aims to reduce inequity between the
distributaries. The results from the model will be compared to the schedules for several seasons as
reported by the irrigation department.
2 Model development
Optimisation models are built on the premise that there is a cost to be avoided i.e. minimised, or a
benefit to be maximised. When considering irrigation scheduling at farm level, maximisation of the
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benefits or profits is probably the aim. At distributary level and up it often makes more sense to
minimise the costs involved, since distributaries are not operated for profit (at least not in Pakistan).
Operating a canal has a monetary aspect, but the direct financial costs are assumed to be similar for
all distributaries and are not taken into account in this report. The indirect costs are not monetary, but
related to avoiding to undesirable situations such as canals overtopping, delivering less/more than the
target amount, etc. When considering these costs there are two aspects to consider, the equity costs
and the allocation costs. Equity costs aim to reduce the cost of giving a particular distributary more or
less water that the other distributaries. Allocation costs are meant to keep the actual delivery of water
as close to the target as possible. The concepts of equity and allocation costs are explained further
below.
2.1 Equity costs
One of the fundamental principles of the warabandi system is equity between users (Zardari and
Cordery, 2010). The system is designed such that there is a fixed amount of water available per unit
area. Due to water shortages, it is not always possible to deliver the full amount. However, even if the
actual amount of water supplied is less, the principle of equity between users is still valid.
Inequity becomes more and more apparent as a growing season progresses. If one distributary is
closed for a week, the effects are probably not too dramatic. Keeping the same distributary closed for
several weeks in a row can lead to crop failure. One of the main aims of the model is to create a
schedule that is equitable, not only over a season, but as much as possible also on a week to week
basis. After all there is no point in closing a distributary for the first three quarters of a growing season
and then trying to catch up in the last couple of weeks. By including an equity cost in the model it is
possible to improve the equity in the model. Inequity between distributaries results in a higher equity
cost, equity between distributaries results in lower equity costs. Minimising the model should therefore
produce a more equitable opening/closing schedule.
2.2 Determining equity cost
It is not enough to look at each scheduling interval individually. In a system where canal closures are
a regular occurrence, real equity can only be achieved by looking over an entire growing season.
Since all distributaries serve different sized command areas, equity is probably best measured though
cumulative depth of delivered irrigation water. The cumulative depth can be used to determine a
second penalty cost. This penalty cost, called equity cost, will ensure that those distributaries that
have received less water than others will receive priority. Anwar and Haq (2013) showed how equity
between distributaries can be measured using the Gini-index. The Gini-index will be used to test a
number of methods for determining equity costs.
The most simple way of giving priority to a particular distributary is by giving priority to those
distributaries that received no water during the previous interval, or rather penalise those that did.
This can be achieved through a 0/1 function:
eiw 
1 if irrigated during the previous interval
i  {1,..., N }
0 otherwise
(1)
where: eiw = equity cost for distributary i during interval w
Another way to determine the equity cost is to look at the difference in cumulative depth between
distributaries. It would seem logical to look at the deviation from the mean, but would result in
negative numbers, something that should be avoided in linear programming. Therefore each equity
cost is calculated based on the deviation from the maximum cumulative depth
eiw  ( Dmax w  Diw ) f
i  {1,..., N }
(2)
where: Dmax w = maximum cumulative depth of delivered irrigation water after w intervals; Diw =
cumulative depth delivered to distributary i after w intervals; and f = multiplication factor. Since
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cumulative depth can be a small number when expressed in inches (as is the case in Pakistan), ei will
also be a small number. When both allocation costs and equity costs are taken into account the equity
costs may need to be multiplied by a factor f to increase the effectiveness of the equity cost.
The final method described here to calculate the equity cost incorporates both giving absolute priority
(through the 0/1 function) and relative priority (through the Dmax - Di function)
1 if irrigated the previous interval 
eiw  
   Dmax w  Di  f
 0 otherwise

(3)
2.3 Allocation costs
The damage done by over- and under-irrigation over several intervals is easy to understand. Underirrigation leads to drought stress and results in a reduction in yield. Over-irrigation leads to problems
such as waterlogging and salinity issues, and also results in a reduction in yield. Both should
therefore be avoided. It should be noted that in the warabandi system where protective irrigation is
practised, over-irrigation can be a good thing from an agronomic perspective. In this system underirrigation is standard and over-irrigation (up to a certain point) brings the total water allocation closer
to optimal. However, since there is a general water shortage it is likely that ”beneficial over-irrigation”
in one part of the system results in under-irrigation in other parts. Since equity is one of the guiding
principles of the warabandi system, it still should be avoided.
There usually is a range over which the effect of over and under-irrigation is not too severe, and the
model should aim to stay between those limits if a full allocation is not possible. Delivering water
outside these ranges can lead to the problems described above and should be avoided. In fact it
might be better not to deliver any water at all, rather than only a little, especially if this means another
distributary can receive the full amount. This range of possibilities means that there is not one single
value that determines the outcomes of the model. As a comparison, the maximum capacity of a
channel is determined by a single value, go over that value and the channel will overflow its
embankments, stay under the value and nothing happens. In linear programming these constraints
are called “hard constraints”, they cannot be violated under any circumstances. Constraints like the
allocation cost are “soft constraints”, they may be violated, but the more they are, the higher the cost.
In the case of the allocation costs, while delivering 100% of the target allocation would be ideal, the
actual amount can be more or less; a good example of a soft constraint.
Soft constrains can be described by a piece-wise linear function. A piece-wise linear function consists
of several straight line segments. Figure 1 shows an example of such a function. The points where
the slope of the piece-wise linear function changes are called the breakpoints. Although a piece-wise
linear function is linear in the individual segments, as a whole it is non-linear. It is still possible to use
a piece-wise linear function in a linear programme through the use of special ordered sets. The
concept of special ordered sets was first coined by Beale and Tomlin (1970), but the approach was
already described others (e.g. Beale (1968); Beale and Small (1965); and (Land and Doig, 1960).
Special ordered sets consist of a set of variables that describe the piece-wise linear function. Two
markers are introduced that change position (on the break points) depending on the segment of the
piece-wise linear function that is being considered. Any members of the set that do not lie between
the two markers are forced to become zero. The markers now function as if they were the lower and
upper bound of a normal set of variables and the linear program can now be solved.
2.4 Determining allocation costs
Including allocation costs in the model will help to reduce the chances of less than an optimal
allocation of water. Delivering the target amount should incur no cost, allocation between the limits
should result in a small cost and delivering outside the range should incur a large cost. Minimising the
model should now result in a reduction in the allocation costs. Figure 1 shows an example of the
allocation costs as a function of the amount of water delivered. In this piecewise function each line
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EQUITABLE CANAL WATER ALLOCATION
segment represents a different scenario. The figure shows 6 segments, each corresponding to the
cost of different percentage of allocated water actually delivered.
1. no or very little water supplied,
2. some, but insufficient amount of water supplied
3. sufficient water supplied, but less than optimal
4. optimal amount of water supplied
5. ample water supplied, but more than optimal
6. too much water supplied
For instance, if 100% of the allocated water has been delivered, the allocation cost is 1. This is shown
in Figure 1 as a point, numbered 4. Delivering exactly 100% of the target allocation is often not
possible. Delivering less or more than the target amount is not necessarily detrimental. There is
however a limit how much the difference can be before yield is affected. Below the lower limit the crop
will suffer from drought stress, above the upper limit waterlogging will similarly result in a yield
reduction. The exact limits depend on factors such as crop type, growth stage and acceptable yield
loss. Figure 1 show that the lower limit has been set at 80% and the upper limit at 120% (note that
these have been set arbitrarily, more research is needed to determine the appropriate limits). At those
two points the allocation cost has been set 2, a higher number indicating that water deliveries
between these limits are less desirable than 100% delivery, which was set at 1. The allocation cost
slowly increases between 100% and the limits as shown by segments 3 and 5.
In cases where not enough water can be delivered it may in fact be better to give very little or no
water at all. That way more water can be supplied to another distributary, allowing that one to reach
the lower limit. This can be achieved by giving the first segment a lower allocation cost than the
second segment. In Figure 1 10% has been chosen as the cut off. This number was chosen to
account for “leftovers”. Since it is likely that the sum of all allocations doesn’t not add up to exactly the
amount of water delivered by the branch canal, there has to be a mechanism to deal with the
remaining portion, or leftovers. By setting the lower limit at 10% small amounts of water can be let into
a channel without incurring too large a penalty. Since there is a small penalty attached to it, the model
will try to avoid creating leftovers where possible.
At the upper limit of the canal capacity, segment 6 in Figure 1, the allocation cost rapidly increases as
water delivery increases. At these levels the canal is at increasing risk of overtopping (some canals
may in fact already have overtopped, depending on the capacity). At high rates of water application
rates the high water allocation might also result in over-irrigation, waterlogging, salinity and other
related problems.
The limits and costs in Figure 1 are an example only. It is possible to change these so they better
represent the system this function is applied to. It is possible to have a different function for each
canal in the system. This makes it possible to set different levels for canals with a different capacity or
other differences such as crop type.
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Figure 1. Example of piecewise linear allocation cost function
2.5 ECWA model
For the Equitable Canal Water Allocation model (ECWA), let I = {1,…,N} be a set of distributaries to
be scheduled for opening or closing during a certain interval. The following parameters are known for
each i ∈ I: target allocation and maximum capacity. To describe the allocation cost function, let J =
{1,…,P} be a set of points that describes a piecewise linear function. The following parameters are
known for each p ∈ J: “break point” and cost. Detailed descriptions of the decision variable, objective
function and constraints follow below.
2.5.1 Decision variable
The decision to be made by the model is: how much water should be allocated to each canal?
Therefore the decision variable is Ai where Ai = allocation for distributary i.
2.5.2 Objective function
The goal of the model is to reduce the costs associated with allocating water to a distributary. This
can be achieved by using the following objective function
N
minimise
c
i 1
(4)
i
Where: ci = allocation cost of opening canal i.
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2.5.3 Hard constraints
No distributary can be allocated more water than the maximum capacity of that distributary
ai  Qmax i
i {1,..., N }
(5)
where: ai = water allocation for distributary i; and Qmax i = maximum flow capacity of distributary i.
The total allocation to all distributaries cannot be more than the total amount of water available
N
a  Q
i 1
(6)
i
where: Q = total available flow.
2.5.4 Soft constraints
Each the cost of allocating water to a canal is determined by the piecewise allocation cost function
which is described as follows

( y p1 - y p )
y



 p (x - x )
p 1 
p 1
p
P 1

x  1[ x p , x p 1 ) ( x)


(7)
where: yp = allocation cost in p; and xp = segment break p of piecewise linear cost function.
The allocation for each canal is determined by the target allocation and the cost of allocating
P
ai  y p Ai ip
i {1,..., N }
(8)
p 1
where: Ai = target allocation for distributary i; and λip = weighted variable.
The weighted variables for each distributary must add up to 1
P

ip
 1 i {1,..., N }
(9)
p 1
The allocation cost of opening each canal is determined by the weighted variables
P
ci  x pip
i {1,..., N }
(10)
p 1
No more than two of the weighted variable λ can be non-zero and must be adjacent. Therefore
{ip } is SOS2 i  N , p  P
(11)
To include the equity cost ei in the objective function, (4) should be replaced by
N
minimise(ci  ei )
(12)
i 1
To increase the importance of the equity costs (1) or (12) can be replaced by
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EQUITABLE CANAL WATER ALLOCATION
N
minimise(ci ei  ei )
(13)
i 1
The model now consists of a decision variable, ai, objective function (4) or (12) or (13) and constraints
(5)-(11) and one of (1) - (3).
3 Application
The model described previously has been applied to Hakra branch canal in the Punjab, Pakistan.
Hakra supplies 17 distributaries with a combined command area of around 200,000 hectares
(500,000 acres). Table 1 shows the number, name, target allocation and command area for these 17
distributaries. It should be noted that distributary no.15, “Flood channel” was added long after the
other distributaries. It only receives water during Kharif and even then only has junior rights.
Table 1. Characteristics of distributaries supplied by Hakra branch canal (PMIU, 2014)
no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Name
1L-distributary
1R-distributary
2L-distributary
2R-distributary
3L-distributary
3R-distributary
4L-distributary
4R-distributary
5R-distributary
6R-distributary
7R-distributary
8R-distributary
9-R distributary
Bakhu Shah distributary
Flood Channel distributary
Hakra Left distributary
Hakra Right distributary
total
Target Allocation
ft3 s-1
m3 s-1
83
2
19
1
19
1
22
1
10
0
353
10
9
0
226
6
36
1
546
15
273
8
24
1
211
6
6
0
73
2
23
1
510
14
2443
69
Command Area
acres
hectares
17093
6918
4965
2009
4371
1769
5306
2147
1737
703
72753
29443
1685
682
43454
17586
10550
4270
101818
41206
53855
21795
6357
2573
49195
19909
1505
609
16516
6684
5976
2418
105991
42895
503127
203615
3.1 Model scenarios
The irrigation department supplied data for Rabi 2010/11, Kharif 2011 and Kharif 2012 (PMIU, 2014).
This data shows the allocation to each distributary for each date of the growing period. Since canal
opening/closure decisions are made on a weekly basis, data was aggregated to weekly data. The
weekly data for each of these three growing seasons can be found in Appendix B. The raw data can
be found on the accompanying cd. Table 2 shows the different combinations of objective functions
and equity cost equations that were run for each season.
Table 2.Overview of model scenarios
Scenario
Objective function
A
12
B
12
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Equity cost calculated from
9
10 with f = 10
9
EQUITABLE CANAL WATER ALLOCATION
C
D
E
F
G
H
I
J
10 with f = 100
11 with f = 0.1
11 with f = 10
9
10 with f = 10
10 with f = 100
11 with f = 0.1
11 with f = 10
12
12
12
13
13
13
13
13
3.2 Results
All models were solved using Lingo 13.0 ®. Each run of the model takes less than one second on
average. Running one entire season, or 26 weeks, for each of the different scenarios can be done in
less than 4 minutes. Table 3 shows the result of one of the model runs, in this case scenario I. The
first column shows the week number, with number 1 starting on October 16, 2010. Weeks 12-14
coincided with the annual closure period. During this period Hakra branch canal runs empty so that
maintenance and cleaning of the canal can take place. When running the different scenarios it is best
to leave these weeks out completely. This prevents a ‘normal’ closure to be scheduled both directly
before the closure (in week 11) and straight afterwards (in week 15). If weeks 12-14 are left in it is
possible for a distributary to not get any water for 5 weeks in a row; leaving it out decreases the
chances of this happening. Ultimately whether this happens depends on the amount of water
available during the weeks before and after the closure period. The second column of Table 3 shows
the average discharge available during that week based on the reports from the irrigation department.
The remainder of the columns shows the discharge allocated to each distributary for each week.
Table 3 shows that most of the time distributaries receive their target amount; 69% of all deliveries are
spot on. In 21% of scheduled deliveries a distributary gets no water at all, 7% of the time a distributary
gets at least 80% of their allocation and finally 2% of the deliveries are larger than 100% (but less
than the maximum capacity of the canal). In this particular schedule, it never happens that a
distributary gets water, but less than 80% of their target amount.
Table 3. Schedule for distributaries 1-14, 16 and 17 during Rabi 2010-2011, prepared using
scenario I (in cfs)
week
1
delivery
766
1
83
2
19
3
19
4
22
2
1494
0
0
0
0
3
1432
83
19
19
22
4
1401
0
19
19
5
1590
83
19
6
1850
83
19
7
1564
83
8
1771
5
10
6
0
0 353
10
7
8
9 226
0
0
9
36
10
11
0 289
0 437
13
0
14
6
0
0 211
0
16
23
17
0
0 493
0
9 226
36 471 273
24 211
6
23
22
0 353
9 181
36
0
24 199
6
23 510
19
22
10 353
0
36 546 273
24 176
6
23
0
22
10 353
9 226
36 529
24
0
6
23 510
19
19
22
0 329
9
36
0 273
24 211
6
23 510
0
19
19
22
10
0
0 226
36 546 221
24 211
6
23 408
0
0
0
9
1868
83
19
19
28
10 353
9 226
36
10
1568
83
19
19
18
0 348
9 226
36 546
11
1185
83
19
19
0
10
0
9
0
36
15
36
0
0
0
22
8
0
0
0
0
16
1486
83
19
19
0
10
0
9 226
17
1788
83
19
19
22
0 353
9 226
18
1983
83
19
19
22
10 353
0 223
36 546
19
1954
0
19
19
22
0 353
9
20
2014
83
19
19
22
21
1869
83
19
19
22
22
1926
83
19
19
22
10
12
24
0
0 311
0
0
24 211
6
23 510
0
24 211
6
23
0 273
24 173
6
23 510
0
6
0
0
36 546 273
24 211
7
23
0
36
24 211
6
23 510
0
24 211
6
23 408
0
36 455 273
24 211
0
23 510
10 353
0 226
36 437 273
24
0
6
23 483
13 353
9 226
36 552 273
24 211
6
23
9 226
36 465 273
24 211
6
23 510
0
0
0
0
0 247
0
0
0
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23
1901
0
19
0
22
10 353
9 181
36 497
24
1894
83
19
19
22
13 353
9 271
36
25
2021
83
19
19
22
0 342
9
26
1778
83
19
19
22
10 353
36
0
0 226
0
24 211
6
23 510
0 273
24 211
6
23 532
36 546 273
24 211
6
23 408
24 211
6
23 510
0 236
The cumulative supplied depth over the entire Rabi 2010-2011 for each distributary is shown in Figure
2. It can be seen that all distributaries are close together. To determine the inequity of this delivery
schedule, each week the Gini-index was calculated. This is also shown in Figure 2. Initially the index
starts quite high, i.e. high inequity. Since it is unavoidable that some distributaries do not get any
water during that first week, it automatically means a high index. As time progresses these extremes
even out and at the end of the season ends up being much lower. For scenario I during Rabi 20102011 the Gini-index is 3.3% at the end of the season, indicating low inequity.
Figure 2. Cumulative supplied depth for scenario I, Rabi 2010-2011
3.3 Inequity
Section 3.2 shows the results of one of the scenarios. In order to determine which combination(s) of
objective function and equity cost function works best, all scenarios need to be compared. Figure 3
shows the gini-index for all scenarios plus the gini-index for the schedule as reported by the irrigation
department. It shows that the initial extremes are very common, with the irrigation department’s
schedule suffering from this more than the modelled scenarios. As expected the Gini-index evens out
fairly soon for most scenarios, with the exception of scenarios A and F. In these two scenarios the
equity cost is simply determined by giving priority to those canals that did not receive any water during
the previous week. Since depth applied is not taken into account, it is perhaps not surprising that the
“zigzagging” is more pronounced and that the final Gini-index is higher than for all other scenarios,
including that determined by the irrigation department. There is very little difference between
scenarios B-E, G-J when it comes to the Gini-index. The Gini-index for the schedule prepared by the
irrigation department lays in between scenarios A & F and the remainder of the scenarios.
RevIIP | Deliverable B.1
11
EQUITABLE CANAL WATER ALLOCATION
Appendix D shows the Gini-index for the Kharif 2011 and Kharif 2012. Although the actual numbers
are different, the trends seen in Rabi 2010-2011 are similar in both Kharif seasons, larger amount of
zigzagging for scenarios A and F with a fairly high inequity compared to the other schedules, low and
very similar numbers for scenarios B-E,G-J and the irrigation department’s schedule somewhere in
between. If the inequity of the different scenarios is so similar, is there another way to distinguish
between a good and a bad schedule?
Figure 3. Gini-index for all scenarios, Rabi 2011-2012
4 Service interruption
There are several issues when it comes to the delivery of water to the distributaries. First and
foremost there is the reliability of the delivery. Service interruptions are a serious concern for all water
users along the distributaries. The longer they last the more a crop yield is affected. As mentioned
before, even though the amount of water delivered is the same, receiving water every other week for
a season is far less damaging than receiving water for the first half of a season, followed by nothing
for the second half. Although more research in this area is required, for the moment it is assumed that
the shorter the duration of the service interruption the better.
Service interruptions can be broken up into two components, the quantity that is being delivered and
the frequency of that delivery. These two parameters can be easily measured and should be able to
provide an insight into how well the different models described in the previous section perform. As
described before, a minimum delivery of water is needed and anything less than this amount is
considered wasted. For the purpose of this application of Hakra branch, deliveries of less than 80% of
the target allocation fall into this category. The frequency of delivery can be measured by counting the
weeks in which no water is delivered to a particular canal. Since small gaps are inevitable and
unavoidable, it is proposed to only count service interruptions that last 2 weeks or longer.
Table 4 shows the number of service interruptions (gap count) and duration of the longest service
interruption (max gap size) for all scenarios and the schedule reported by the Irrigation Department.
Even though there was very little difference between the scenarios with regards to equity, there is a
significant difference when considering service interruptions. Table 4 for instance shows that for Rabi
2010-2011, the best performing scenario is scenario I. There are only 4 service interruptions that last
2 week or longer and the longest interruption lasts 3 weeks. As a comparison, the schedule reported
by the Irrigation Department has a total of 42 service interruptions with a maximum length of 6 weeks.
12
Deliverable B.1 | RevIIP
EQUITABLE CANAL WATER ALLOCATION
The results for Kharif 2011 and Kharif 2012 show a similar pattern. The complete tables for those two
seasons can be found in Appendix E.
Table 4. Gap count and maximum gap size for all scenarios, Rabi 2010-2011
A
B
C
D
E
F
G
H
I
Gap count
6
26
26
10
6
6
26
26
4
Max gap size
3
4
4
3
3
3
4
4
3
J IrrDept
6
42
3
6
5 Conclusions and recommendations
The work done for in this study has shown that it is possible to use linear programming to determine
the opening/closing schedules for a water short irrigation system. The method developed minimises
inequity and limits service interruptions where possible. This has the potential to provide a much more
dependable service to water users who are facing an uncertain cropping season due to water
shortages. Water that is allocated in a fair and equitable way can reduce the potential for social unrest
and may encourage water users to pay for the services provided.
There are still some shortcomings to the models that were developed. Although there seems to be a
difference between the 2 objective functions provided, three cropping seasons is not enough data to
provide a definite conclusion as to which one results in a better schedule. Similarly, no sensitivity
analysis was done of the multiplication factor which determines the equity cost. While it appears there
are differences when using different values, it is not clear which would result in a better schedule.
At the moment the model works on the principle that all water entering a branch canal must be
completely allocated to the distributaries. This can result in small amounts of water being let in to a
distributary. It might be possible to prevent this wastage by taking in less water, allowing the water to
be reused downstream. This however is probably only ever acceptable to users within the branch
canal command area if users receive some form of compensation, whether it is monetary or in the
form of extra water during a subsequent interval.
Canals within the same system may have different rights to water. For instance in Hakra Branch
Canal the Flood Channel only has junior rights. In this study the Flood Channel was left out all
together during Rabi and was assumed to have full rights during Kharif. Some adjustment to the
model is necessary to fully capture the complexity of the junior rights and senior rights.
For future work it would be good to use the schedules obtained with the method described in this
report in a crop growth model. This will help to confirm which model gives the best results. Based on
crop modelling results it might be possible to determine which of the service interruption parameters
has a larger influence on yield.
6 References
Anwar AA and Haq ZU, (2013). “An old-new measure of canal water inequity”. Water International,
38(5), 536-551.
Bandaragoda DJ (1996). “Institutional conditions for effective water delivery and irrigation scheduling
in large gravity systems: evidence from Pakistan”. In: Irrigation Scheduling: from Theory to Practice Proceedings, proceedings of the ICID/FAO Workshop on Irrigation scheduling, Rome, 12-13
September 1995, FAO Water Report 8.
Bandaragoda DJ and Rehman SU (1995). Warabandi in Pakistan’s canal irrigation systems: widening
gap between theory and practice. IIMI Country paper Pakistan No. 7, International Irrigation (now
Water) Management Institute, Sri Lanka, 89pp.
RevIIP | Deliverable B.1
13
EQUITABLE CANAL WATER ALLOCATION
Beale EML (1968). Mathematical programming in practice. Pitmans, London.
Beale EML and Small RE (1965). “Mixed integer programming by a branch and bound technique”. in:
Kalenich WA, ed., Proceedings of the IFIP Congress 1965, Spartan Press, Washington, 2, 450-451
Beale EML and Tomlin JA (1970). “Special facilities in a general mathematical programming system
for nonconvex problems using ordered sets of variables”, in: Lawrence J, ed., Proceedings of the fifth
international conference on operational research, Tavistock Publications, London, 447–454.
Bhutta MN, (1990). Effect of varying discharges on the equity of water distribution in the irrigation
system. Ph.D. dissertation, Centre of Excellence in Water Resources Engineering, Universwity of
Engineering and Technology, Lahore, Pakistan.
Hussain I, Hussain Z, Sial MH, Akram W and Farhan MF (2011). “Water balance, supply and demand
and irrigation efficiency of Indus Basin”. Pakistan Economic and Social Review, 49(1), 13-38.
Land AH and Doig AG (1960). “An automatic method for solving discrete programming problems”.
Econometria, 28, 497-520.
PMIU, 2014. Database of the Programme Monitoring and Implementation Unit for Canal Operations
and Discharge Data in Irrigation Department, www.irrigation.punjab.gov.pk, accessed 2013 and 2014.
Seckler D, Sampath RK, Raheja SK (1998). “An index for measuring the performance of irrigation
management systems with an application”. Water Resources Bulletin, 24(4), 855-860.
Zardari NU and Cordery I (2010). Éstimating the effectiveness of a rotational irrigation delivery
system: a case study from Pakistan.” Irrigation and Dainage 59, 277-290.
14
Deliverable B.1 | RevIIP
EQUITABLE CANAL WATER ALLOCATION
Appendix A: Lingo code ECWA model
RevIIP | Deliverable B.1
15
!**********************************************************************************************************;
!**
**;
!**
Equitable Canal Water Allocation model
**;
!**
**;
!**
model developed by Tonny de Vries for IWMI-Pakistan
**;
!**
**;
!**
RevIIP project, 2014
**;
!**
**;
!**********************************************************************************************************;
model:
sets:
canal: demand, allocation, cost, maxQ, PreviousAllocation, PenaltyCost;
point/1..7/: costX, allocationY;
link(canal, point): weight;
endsets
data:
availability, demand, maxQ, PreviousAllocation, PenaltyCost =
@OLE('C:\Users\ttd13\Documents\RevIIP\ECWA\RevIIP.ECWA.Hakra.WeeklyModel.Rabi2010_11.xl
sm', 'Availability', 'Demand', 'MaxQ', PreviousAllocation, PenaltyCost);
@OLE('C:\Users\ttd13\Documents\RevIIP\ECWA\RevIIP.ECWA.Hakra.WeeklyModel.Rabi2010_11.xl
sm', 'allocation') = @writefor( canal(i): allocation(i));
costX =
allocationY =
enddata
5,
0.00,
10,
0.10,
10,
0.79,
2,
0.80,
1,
1.00,
2,
1.20,
10;
1.50;
@for( canal(i): allocation(i) <= maxQ(i));
@sum(canal(i): allocation(i)) = availability;
@for( canal(i): @gin(allocation(i)));
@for( canal(i): cost(i) = @sum( point(p): costX(p) * weight(i,p)));
@for( canal(i): allocation(i) = @sum( point(p): allocationY(p) * demand(i) * weight(i,p)));
@for(canal(i): @sum( point(p): weight(i,p)) = 1);
@for( link(i,p): @sos2('SOS_2' + canal(i), weight(i,p)));
min = @sum( canal(i): cost(i)*penaltycost(i) +10*penaltycost(i));
end
go
quit
!NOTE: the name and path of the document will have to be changed when run from any other location
than the one mentioned above (shown above under “data”).
EQUITABLE CANAL WATER ALLOCATION
Appendix B: Reported schedules Hakra Branch
Rabi 2010-2011
Kharif 2011
Kharif 2012
RevIIP | Deliverable B.1
17
RevIIP | Deliverable B.1
Table 5. Rabi 2010-2011, weekly discharge (cfs) for Hakra Branch Canal as reported by the Irrigation Department
Distributary
number
16-10-2010
23-10-2010
30-10-2010
06-11-2010
13-11-2010
20-11-2010
27-11-2010
04-12-2010
11-12-2010
18-12-2010
25-12-2010
01-01-2011
08-01-2011
15-01-2011
22-01-2011
29-01-2011
05-02-2011
12-02-2011
19-02-2011
26-02-2011
05-03-2011
12-03-2011
19-03-2011
26-03-2011
02-04-2011
09-04-2011
1
0
80
65
53
93
93
80
80
93
93
27
0
0
0
0
74
0
74
86
86
49
35
86
86
84
47
2
0
18
14
11
17
19
16
17
19
3
11
0
0
0
0
12
20
18
17
20
17
16
17
20
16
16
3
3
17
17
11
20
20
14
20
20
20
6
0
0
0
0
6
20
20
20
15
15
20
20
20
20
17
4
0
19
19
13
22
22
18
18
22
3
13
0
0
0
0
4
22
22
19
22
22
22
22
22
22
21
5
5
5
9
10
10
10
5
10
10
10
4
0
0
0
0
10
0
9
10
6
3
3
10
9
8
3
6
0
339
113
226
242
274
339
253
401
56
268
0
0
0
36
320
370
327
177
259
352
368
297
88
333
324
7
3
2
6
6
4
9
6
9
9
9
4
0
0
0
0
6
0
8
9
9
5
5
9
9
9
5
8
0
211
70
141
142
71
213
0
249
249
71
0
0
0
0
103
0
213
249
211
132
83
248
233
216
112
9
10
31
31
21
36
36
26
36
36
36
10
0
0
0
0
10
36
36
36
32
33
36
36
21
36
31
10
0
490
218
343
421
298
511
158
600
295
127
0
0
0
0
0
577
599
588
397
282
588
574
546
278
444
*Note: Distributary 15 did not receive any water during Rabi 2010-2011 and is therefore not included.
11
80
180
254
184
277
280
80
280
136
7
181
0
0
0
0
273
273
270
103
234
266
244
212
19
273
273
12
7
9
23
18
25
25
18
25
25
25
11
0
0
0
0
18
0
21
24
24
14
8
25
25
25
13
13
51
0
154
102
90
233
148
238
238
221
46
0
0
0
0
170
0
168
226
238
136
79
241
241
223
105
14
0
9
9
6
10
10
8
8
10
1
6
0
0
0
0
6
10
7
5
6
6
6
6
6
6
5
16
19
3
16
10
7
16
10
23
0
20
13
0
0
0
0
16
23
7
16
23
23
15
3
23
23
23
17
588
81
414
246
174
434
72
596
0
520
387
0
0
0
0
458
437
184
369
432
514
398
95
526
449
339
TOTAL
766
1494
1432
1401
1590
1850
1564
1771
1868
1568
1185
0
0
0
36
1486
1788
1983
1954
2014
1869
1926
1901
1894
2021
1778
13
Table 6. Kharif 2011, weekly discharge (cfs) for Hakra Branch Canal as reported by the Irrigation Department
Distributary
number
16-04-2011
23-04-2011
30-04-2011
07-05-2011
14-05-2011
21-05-2011
28-05-2011
04-06-2011
11-06-2011
18-06-2011
25-06-2011
02-07-2011
09-07-2011
16-07-2011
23-07-2011
30-07-2011
06-08-2011
13-08-2011
20-08-2011
27-08-2011
03-09-2011
10-09-2011
17-09-2011
24-09-2011
01-10-2011
08-10-2011
1
77
83
83
71
12
83
90
90
26
64
90
90
75
0
90
90
87
79
74
29
0
0
0
66
85
77
2
16
20
20
20
17
20
20
20
20
18
16
6
19
20
20
6
15
20
20
8
0
0
0
13
12
10
3
20
20
11
8
20
20
20
3
14
20
20
13
3
20
20
3
0
14
20
10
0
0
3
12
11
5
4
22
22
22
22
19
22
22
22
22
22
19
6
19
19
22
8
18
21
22
10
0
0
3
14
14
11
5
6
4
9
10
9
0
10
10
10
6
3
8
9
9
0
0
7
10
7
0
0
0
0
5
6
10
6
308
194
184
358
359
353
44
312
400
403
230
108
402
364
310
241
265
349
344
117
0
0
57
200
123
175
7
9
9
9
6
1
9
9
9
3
5
9
9
8
0
9
1
8
4
3
6
0
0
5
8
9
9
8
190
233
212
133
32
226
248
242
69
171
249
251
209
0
246
252
203
152
97
68
0
0
0
170
205
212
9
36
36
21
10
36
36
36
5
26
36
36
26
6
36
36
5
0
25
35
17
0
0
2
29
24
10
10
482
534
285
160
586
546
556
77
402
563
567
416
95
614
621
89
0
343
583
397
35
48
275
570
486
85
11
252
117
117
259
295
273
0
245
294
283
136
84
294
295
309
46
212
306
310
153
12
0
132
273
67
149
12
20
25
25
18
4
25
25
25
7
14
25
25
22
0
26
4
19
11
9
19
0
0
8
26
26
26
13
205
236
227
148
27
212
227
223
62
122
233
242
202
0
256
37
176
105
83
184
0
0
39
218
258
224
14
6
6
6
6
5
6
6
6
6
6
5
5
6
6
6
2
4
6
6
2
0
0
0
0
2
3
15
50
74
74
53
2
74
63
68
18
31
74
74
62
0
71
11
52
32
25
63
8
0
8
63
67
51
16
13
13
23
23
20
0
23
23
23
10
10
23
23
23
3
15
23
23
19
20
8
0
3
13
16
23
17 TOTAL
171
1883
264
1890
512
1840
521
1826
435
1879
10
1915
539
1938
534
1914
507
1909
191
1965
203
1925
526
1912
464
1918
552
1958
14
2059
209
1019
515
1604
537
2037
388
2045
134
1237
85
148
129
177
250
785
128
1808
363
1774
592
1672
Table 7. Kharif 2012, weekly discharge (cfs) for Hakra Branch Canal as reported by the Irrigation Department
Distributary
number
31-03-2012
07-04-2012
14-04-2012
21-04-2012
28-04-2012
05-05-2012
12-05-2012
19-05-2012
26-05-2012
02-06-2012
09-06-2012
16-06-2012
23-06-2012
30-06-2012
07-07-2012
14-07-2012
21-07-2012
28-07-2012
04-08-2012
11-08-2012
18-08-2012
25-08-2012
01-09-2012
08-09-2012
15-09-2012
22-09-2012
1
45
90
53
21
81
37
12
46
53
19
87
26
90
90
26
75
90
64
7
90
89
26
62
34
47
37
2
20
18
14
7
15
14
9
12
0
9
17
8
19
19
19
19
19
19
19
19
19
19
16
5
1
19
3
10
9
18
17
19
6
11
11
0
20
18
6
20
6
11
20
14
3
20
20
5
14
20
8
4
20
4
22
22
17
7
16
16
13
16
0
14
18
10
22
22
22
22
22
22
22
22
22
22
22
6
8
22
5
5
2
5
3
1
4
7
7
0
9
0
10
10
3
6
9
8
1
10
10
1
7
7
1
1
8
6
185
93
268
121
15
300
141
183
0
84
353
0
397
126
297
379
265
102
415
415
99
295
410
146
163
383
7
5
5
9
8
8
9
4
4
5
1
9
0
7
3
5
9
6
1
9
9
3
6
8
2
2
9
8
260
249
179
40
238
74
0
139
167
59
230
53
260
262
109
204
262
187
27
262
262
72
172
99
107
61
9
18
15
32
28
36
10
21
21
0
36
34
10
36
10
21
36
26
5
36
36
8
26
36
15
7
36
10
598
534
449
394
554
247
348
329
0
535
243
1413
91
468
650
401
177
635
647
25
519
510
421
148
454
515
11
150
90
291
179
78
214
300
209
0
234
0
292
300
86
171
302
284
43
300
300
43
214
300
141
65
291
12
13
11
25
25
4
16
25
11
0
19
0
26
11
26
26
11
7
26
22
7
26
26
17
7
13
18
13
235
258
209
135
217
74
144
148
0
168
0
235
35
178
251
102
74
258
210
34
243
254
111
59
142
171
14
8
7
5
3
5
3
2
3
0
3
5
3
6
6
6
6
6
6
6
6
6
6
5
0
0
6
15
0
0
17
32
61
53
70
63
17
43
74
18
63
23
48
81
61
0
79
86
12
59
87
43
10
85
16
23
20
9
10
16
13
13
13
0
16
0
23
3
23
23
16
23
20
3
23
23
23
23
11
9
16
17 TOTAL
311
1908
535
1958
324
1924
139
1169
347
1711
600
1690
297
1417
272
1487
157
399
79
1348
644
1732
0
2133
551
1921
564
1915
236
1927
284
1976
620
1964
485
1877
0
1832
599
1963
518
1898
271
1850
377
2094
309
1034
258
1291
183
1880
EQUITABLE CANAL WATER ALLOCATION
Appendix C. Schedules for Rabbi 2010-2011
Note: schedules for Kharif 2011 and Kharif 2012 can be found on the accompanying cd
21
Deliverable B.1 | RevIIP
Table 8. Scenario A, Rabi 2010-2011
week. delivery
1
766
2
1494
3
1432
4
1401
5
1590
6
1850
7
1564
8
1771
9
1868
10
1568
11
1185
15
36
16
1486
17
1788
18
1983
19
1954
20
2014
21
1869
22
1926
23
1901
24
1894
25
2021
26
1778
1
2
3
4
5
6
7
8
9
10
11
12
13
14
16
17
83
0
83
0
83
0
83
8
83
0
83
0
83
0
83
8
83
0
83
0
83
60
83
19
2
19
1
19
15
19
15
19
0
19
0
19
2
19
15
19
2
19
0
19
1
19
19
2
19
1
19
16
0
19
2
19
1
17
16
2
19
0
19
16
1
19
1
19
0
22
3
22
0
22
0
22
2
22
0
22
0
22
3
22
2
22
17
22
0
22
2
22
10
1
10
1
10
1
10
12
1
10
1
10
1
10
12
13
0
10
1
10
1
10
0
0
439
0
353
0
353
424
427
440
438
278
0
0
353
441
441
439
439
36
353
0
353
423
9
1
9
0
9
1
9
11
1
9
0
9
0
9
0
9
1
9
0
9
0
9
1
226
271
22
226
0
226
0
226
226
0
226
0
226
281
226
258
0
226
226
0
226
0
226
36
4
36
0
36
43
0
36
4
36
3
0
36
0
36
3
36
28
36
0
36
3
36
0
682
165
546
345
546
0
546
23
546
0
0
546
29
546
482
431
546
618
657
683
683
31
289
27
273
0
273
5
273
27
273
0
273
0
273
328
328
0
273
326
328
0
273
0
273
24
3
24
2
24
3
24
18
24
0
24
0
24
3
24
2
24
28
2
24
2
24
3
0
4
211
0
211
0
211
14
211
0
211
0
211
254
0
211
0
211
21
211
0
211
0
6
1
6
0
6
1
6
0
6
0
6
0
6
1
6
0
6
6
0
6
0
6
1
23
3
23
0
23
3
23
2
23
0
23
0
23
3
23
0
23
3
23
0
23
2
23
0
51
510
271
510
637
460
408
510
510
15
0
0
510
198
510
638
2
510
612
525
638
637
10
11
12
13
14
16
17
0 289
24
0
6
23
0
3
3
51
Table 9. Scenario B, Rabi 2010-2011
week delivery
1
2
3
4
5
6
7
8
9
19
19
22
10
0
9 226
36
1
766
83
2
1494
0
2
2
3
1 439
1 271
4
1
3
1432
0
19
19
22
0 353
9 200
36
0
0
24 211
6
23 510
4
1401
83
19
19
22
10
9 156
36
0 273
24 211
6
23 510
5
1590
83
19
19
22
10 345
9
0
36
0 273
24 211
6
23 510
6
1850
83
19
19
22
10 283
9
0
36 437 260
24 211
6
23 408
7
1564
83
19
19
22
10 292
0
0
36 546 273
24 211
6
23
0
8
1771
83
19
19
22
10 283
0 226
36 546 263
24 211
6
23
0
9
1868
83
19
19
22
0
0
9 226
36 546 219
24 211
6
23 425
10
1568
83
19
19
22
0
0
9 226
36 437
0
24 211
6
23 453
11
1185
0
19
0
22
0 325
9
0
36
0
0
24 211
6
23 510
0
0
0
4 682
27
15
36
0
19
1
0
0
0
0
0
0
6
16
1486
83
19
19
22
10 353
0 226
36
0 257
24
0
6
23 408
17
1788
83
19
19
22
10 353
9 226
36
0 273
24 211
0
23 480
18
1983
83
19
19
22
10 353
9 226
36 540
0
24 211
0
23 408
19
1954
83
19
19
22
0 353
9 195
36 546
0
24 211
6
23 408
20
2014
83
19
19
22
0 335
9
0
36 546 273
24 211
6
23 408
21
1869
0
19
19
0
10 294
0
0
36 546 273
24 211
6
23 408
22
1926
0
19
19
22
10
0
1 226
36 546 273
24 211
6
23 510
23
1901
83
0
0
22
10
0
9 226
36 546 273
24 211
6
23 432
24
1894
83
19
24
22
10 353
9 226
36 575 273
24 211
6
23
25
2021
83
19
19
22
0 353
9 226
36 520 273
24
0
6
23 408
26
1778
83
19
19
22
0 353
9 226
36
24 211
6
23 474
10
0
0 273
0
0
0
Table 10. Scenario C, Rabi 2010-2011
week delivery
1
2
3
4
5
6
7
8
9
19
19
22
10
0
9 226
36
10
11
12
13
14
16
17
0 289
24
0
6
23
0
3
3
51
1
766
83
2
1494
0
2
2
3
1 439
1 271
4
1
3
1432
0
19
19
22
0 353
9 200
36
0
0
24 211
6
23 510
4
1401
83
19
19
22
10
9 156
36
0 273
24 211
6
23 510
5
1590
83
19
19
22
10 345
9
0
36
0 273
24 211
6
23 510
6
1850
83
19
19
22
10 283
9
0
36 437 260
24 211
6
23 408
7
1564
83
19
19
22
10 292
0
0
36 546 273
24 211
6
23
0
8
1771
83
19
19
22
10 283
0 226
36 546 263
24 211
6
23
0
9
1868
83
19
19
22
0
0
9 226
36 546 219
24 211
6
23 425
10
1568
83
19
19
22
0
0
9 226
36 437
0
24 211
6
23 453
11
1185
0
19
0
22
9
0
36
0
0
24 211
6
23 510
15
36
0
19
1
0
0
0
0
0
0
0
0
6
16
1486
83
19
19
22
10 353
0 226
36
0 257
24
0
6
23 408
17
1788
83
19
19
22
10 353
9 226
36
0 273
24 211
0
23 480
18
1983
83
19
19
22
10 353
9 226
36 540
0
24 211
0
23 408
19
1954
83
19
19
22
0 353
9 195
36 546
0
24 211
6
23 408
20
2014
83
19
19
22
0 335
9
0
36 546 273
24 211
6
23 408
21
1869
0
19
19
0
10 294
0
0
36 546 273
24 211
6
23 408
22
1926
0
19
19
22
10
0
1 226
36 546 273
24 211
6
23 510
23
1901
83
0
0
22
10
0
9 226
36 546 273
24 211
6
23 432
24
1894
83
19
24
22
10 353
9 226
36 575 273
24 211
6
23
25
2021
83
19
19
22
0 353
9 226
36 520 273
24
0
6
23 408
26
1778
83
19
19
22
0 353
9 226
36
24 211
6
23 474
0
0 325
10
0
4 682
27
0 273
0
0
0
Table 11. Scenario D, Rabi 2010-2011
week delivery
1
2
3
4
5
6
7
8
9
10
0
9 226
36
1 439
1 271
1
766
83
19
19
22
2
1494
0
2
2
3
3
1432
83
19
19
22
10
4
1401
83
19
19
22
10 353
5
1590
83
19
19
22
0 340
6
1850
83
19
19
22
7
1564 104
19
19
22
8
1771
0
19
19
9
1868
83
19
19
10
1568
1
18
11
1185
83
19
0
10
11
12
13
14
16
0 289
24
0
6
23
0
3
4
1
3
51
24 211
6
23 510
24 211
6
23
24
0
6
23 510
4 682
9 187
36
9
36 546
40
27
0 273
0
0
9 226
36
10 341
0
36 546
0
24 211
6
23 510
10
0
9 226
36
0 273
24 211
6
23 582
22
10 353
9 220
36 546 273
24 211
6
23
22
7 353
9
36 546
0
24 211
6
23 510
19
22
10 283
0 273
24 210
6
23 408
0
0
0
0
0
0
21
0
6
0 510
0
0
0
0
9 226
36
0 273
17
0 546
0
0
0
0
15
36
0
0
17
0
10
0
9
0
0
0
0
16
1486
83
19
17
22
0
0
0 226
36 546 273
24 211
6
23
0
17
1788
83
19
19
22
10 353
9 190
36
0 273
24 211
6
23 510
18
1983
83
19
19
22
0 304
9
36 546 273
24 211
6
23 408
19
1954
83
19
19
22
10 328
0 226
36 437
0
24 211
6
23 510
20
2014
0
19
19
22
0 301
9 226
36 437 273
24 211
6
23 408
21
1869
83
19
24
22
10 353
10 265
36
0 273
24 211
6
23 510
22
1926
83
19
0
22
10 283
0
36 546 255
24 211
6
23 408
23
1901
83
19
19
22
13 423
9 226
36
0 277
24 211
6
23 510
24
1894
83
19
19
22
13 384
9 226
36 546 273
24 211
6
23
25
2021
83
19
19
22
13
0
9 226
36 547 273
24 211
6
23 510
26
1778
83
19
19
22
0 353
9 226
36
24 211
6
23 474
0
0
0
0 273
0
Table 12. Scenario E, Rabi 2010-2011
week delivery
1
2
3
4
5
6
7
8
9
83
19
19
22
10
0
9 226
36
1 439
1 271
1
766
2
1494
0
2
2
3
3
1432
83
19
19
22
10
4
1401
83
19
19
22
10 353
5
1590
0
19
19
22
0 283
6
1850
83
19
19
22
7
1564
83
19
19
22
8
1771
83
19
19
9
1868
83
19
19
10
1568
0
19
11
1185
83
15
36
0
16
1486
17
1788
18
19
0
10
11
12
13
14
16
17
0 289
24
0
6
23
0
3
3
51
4 682
4
1
24 211
6
23 510
0
24 211
6
23
0 273
24 211
6
23 484
9 187
36
9
36 546
40
27
0 273
0
9 181
36
10 341
0
36 546
0
24 211
6
23 510
13
0
9 226
36
0 273
24 211
6
23 600
22
0 353
9 181
36 546 239
24 211
6
23
22
10 353
6
36 546
0
24 211
6
23 510
19
22
0 283
19
19
22
10
19
2
0
0
83
19
19
22
10
83
19
19
22
1983
83
19
19
22
0 353
1954
83
19
19
22
10
20
2014
83
19
0
22
21
1869
99
19
19
22
22
1926
0
19
19
23
1901
83
19
19
24
1894
83
19
19
22
0 324
25
2021
70
19
19
22
10 353
26
1778
0
19
19
22
11 353
9 226
0
0
0
9 226
36
0 273
24 211
6
23 417
0
0
0
36 501 273
24 169
0
9
0
0
0
11 226
36
10 353
0 226
9 226
36 442
0 226
10 353
9
13 353
9 226
22
0 353
9 226
22
10 353
0 181
9
0
6
23
0
0
6
0
0
0 273
24 211
6
23 523
36 537 219
24 211
6
23
0
24 211
6
23 510
36 492 273
24 211
6
23 510
36 437 273
24 209
6
23 510
36
24 237
6
23 510
36 546 235
24
0
6
23 408
36 437
0
24 211
6
23 477
0
36 437 273
24 211
6
23 408
0 226
36 436 273
24
0
0
23 510
36 546 273
24 211
6
23
0
17
0
0
0
0 273
0
0
Table 13. Scenario F, Rabi 2010-2011
week delivery
1
2
3
4
5
6
7
8
9
10
0
9 226
36
1 439
1 271
1
766
83
19
19
22
2
1494
0
2
2
3
3
1432
83
19
19
22
4
1401
0
1
1
0
5
1590
83
19
19
22
6
1850
0
15
16
0
1 353
7
1564
83
19
0
22
10 424
8
1771
8
15
19
2
12 427
11 226
9
1868
83
19
2
22
1 440
1 226
10
1568
0
0
19
0
10 438
11
1185
83
19
1
22
1 278
10
0
1 353
10
0
9
22
0 226
9
0
1 226
9
9
0
0
0 226
15
36
0
0
17
0
10
0
9
16
1486
83
19
16
22
1
0
0 226
17
1788
0
2
2
3
10 353
9 281
18
1983
83
19
19
22
12 441
0 226
19
1954
8
15
0
2
13 441
9 258
20
2014
83
19
19
22
0 439
21
1869
0
2
16
17
10 439
22
1926
83
19
1
22
23
1901
0
0
19
0
24
1894
83
19
1
22
25
2021
60
1
19
2
10 353
26
1778
83
19
0
22
0 423
1
36
10 353
1
0
0
10
11
12
13
14
16
0 289
24
0
6
23
0
3
4
1
3
51
24 211
4 682
27
36 165 273
0 546
0
36 345 273
43 546
0
36 546
4
5
0 273
27
23 273
36 546
0
3
0 273
0
0
0
36 546 273
0
29 328
36 546 328
0 271
24 211
6
23 510
0
1
3 637
24 211
3
6
23 460
18
14
0
2 408
24 211
6
23 510
0
0
24 211
0
6
0
0 510
23
15
0
0
0
0
24 211
6
23
0
3 254
1
3 510
0
6
23 198
2 211
24
0
0 510
36 431 273
24
0
6
23 638
9 226
28 546 326
28 211
6
0 226
36 618 328
9
0
0 226
9
0
1 226
0 657
0
23 510
0
0
1
3 482
6
0
2
0
36 683 273
3 683
36
0
31 273
2
3
2
21
0
23 510
24 211
6
0 612
0
0
23 525
24 211
6
2 638
1
23 637
2
3
0
Table 14. Scenario G, Rabi 2010-2011
week delivery
1
2
3
4
5
6
7
8
9
19
19
22
10
0
9 226
36
10
11
12
13
14
16
17
0 289
24
0
6
23
0
3
3
51
1
766
83
2
1494
0
2
2
3
1 439
1 271
4
1
3
1432
0
19
19
22
0 353
9 200
36
0
0
24 211
6
23 510
4
1401
83
19
19
22
10
9 156
36
0 273
24 211
6
23 510
5
1590
83
19
19
22
10 345
9
0
36
0 273
24 211
6
23 510
6
1850
83
19
19
22
10 283
9
0
36 437 260
24 211
6
23 408
7
1564
83
19
19
22
10 292
0
0
36 546 273
24 211
6
23
0
8
1771
83
19
19
22
10 283
0 226
36 546 263
24 211
6
23
0
9
1868
83
19
19
22
0
0
9 226
36 546 219
24 211
6
23 425
10
1568
83
19
19
22
0
0
9 226
36 437
0
24 211
6
23 453
11
1185
0
19
0
22
9
0
36
0
0
24 211
6
23 510
15
36
0
19
1
0
0
0
0
0
0
0
0
6
16
1486
83
19
19
22
10 353
0 226
36
0 257
24
0
6
23 408
17
1788
83
19
19
22
10 353
9 226
36
0 273
24 211
0
23 480
18
1983
83
19
19
22
10 353
9 226
36 540
0
24 211
0
23 408
19
1954
83
19
19
22
0 353
9 195
36 546
0
24 211
6
23 408
20
2014
83
19
19
22
0 335
9
0
36 546 273
24 211
6
23 408
21
1869
0
19
19
0
10 294
0
0
36 546 273
24 211
6
23 408
22
1926
0
19
19
22
10
0
1 226
36 546 273
24 211
6
23 510
23
1901
83
0
0
22
10
0
9 226
36 546 273
24 211
6
23 432
24
1894
83
19
24
22
10 353
9 226
36 575 273
24 211
6
23
25
2021
83
19
19
22
0 353
9 226
36 520 273
24
0
6
23 408
26
1778
83
19
19
22
0 353
9 226
36
24 211
6
23 474
0
0 325
10
0
4 682
27
0 273
0
0
0
Table 15. Scenario H, Rabi 2010-2011
week delivery
1
2
3
4
5
6
7
8
9
19
19
22
10
0
9 226
36
10
11
12
13
14
16
17
0 289
24
0
6
23
0
3
3
51
1
766
83
2
1494
0
2
2
3
1 439
1 271
4
1
3
1432
0
19
19
22
0 353
9 200
36
0
0
24 211
6
23 510
4
1401
83
19
19
22
10
9 156
36
0 273
24 211
6
23 510
5
1590
83
19
19
22
10 345
9
0
36
0 273
24 211
6
23 510
6
1850
83
19
19
22
10 283
9
0
36 437 260
24 211
6
23 408
7
1564
83
19
19
22
10 292
0
0
36 546 273
24 211
6
23
0
8
1771
83
19
19
22
10 283
0 226
36 546 263
24 211
6
23
0
9
1868
83
19
19
22
0
0
9 226
36 546 219
24 211
6
23 425
10
1568
83
19
19
22
0
0
9 226
36 437
0
24 211
6
23 453
11
1185
0
19
0
22
0 325
9
0
36
0
0
24 211
6
23 510
15
36
0
19
1
0
0
0
0
0
0
0
0
6
16
1486
83
19
19
22
10 353
0 226
36
0 257
24
0
6
23 408
17
1788
83
19
19
22
10 353
9 226
36
0 273
24 211
0
23 480
18
1983
83
19
19
22
10 353
9 226
36 540
0
24 211
0
23 408
19
1954
83
19
19
22
0 353
9 195
36 546
0
24 211
6
23 408
20
2014
83
19
19
22
0 335
9
0
36 546 273
24 211
6
23 408
21
1869
0
19
19
0
10 294
0
0
36 546 273
24 211
6
23 408
22
1926
0
19
19
22
10
0
1 226
36 546 273
24 211
6
23 510
23
1901
83
0
0
22
10
0
9 226
36 546 273
24 211
6
23 432
24
1894
83
19
24
22
10 353
9 226
36 575 273
24 211
6
23
25
2021
83
19
19
22
0 353
9 226
36 520 273
24
0
6
23 408
26
1778
83
19
19
22
0 353
9 226
36
24 211
6
23 474
10
0
0
4 682
27
0 273
0
0
0
Table 16. Scenario I, Rabi 2010-2011
week delivery
1
2
3
4
5
6
7
8
9
83
19
19
22
10
0
9 226
36
1
766
2
1494
0
0
0
0
3
1432
83
19
19
22
4
1401
0
19
19
5
1590
83
19
19
6
1850
83
19
7
1564
83
19
8
1771
0
19
19
22
10
0
9
1868
83
19
19
28
10 353
10
1568
83
19
19
18
0 348
11
1185
83
19
19
0
10
15
36
0
0
0
22
8
16
1486
83
19
19
0
10
17
1788
83
19
19
22
18
1983
83
19
19
22
10 353
19
1954
0
19
19
22
0 353
20
2014
83
19
19
22
21
1869
83
19
19
22
22
1926
83
19
19
22
23
1901
0
19
0
22
24
1894
83
19
19
22
13 353
25
2021
83
19
19
22
0 342
26
1778
83
19
19
22
10 353
0 353
0
11
12
13
14
16
17
0 289
24
0
6
23
0
0
0 211
0
0
9 226
36 471 273
24 211
6
23
22
0 353
9 181
36
0
24 199
6
23 510
22
10 353
0
36 546 273
24 176
6
23
0
22
10 353
9 226
36 529
24
19
22
0 329
9
36
10
0
10
0
0 437
0
0
0
0
6
23 510
0 273
24 211
6
23 510
0 226
36 546 221
24 211
6
23 408
9 226
36
24 211
6
23 510
9 226
36 546
0
24 211
6
23
0
9
0
36
0 273
24 173
6
23 510
0
0
0
0
0
9 226
0 353
9 226
0 223
36 546
9
0
10 353
0 226
13 353
9 226
0
10 353
0
0
0
0 493
0 311
0
6
0
0
36 546 273
24 211
7
23
0
36
24 211
6
23 510
0
24 211
6
23 408
36 455 273
24 211
0
23 510
36 437 273
24
0
6
23 483
36 552 273
24 211
6
23
9 226
36 465 273
24 211
6
23 510
9 181
36 497
0
24 211
6
23 510
9 271
36
0 273
24 211
6
23 532
9
36 546 273
24 211
6
23 408
36
24 211
6
23 510
0
0 226
0
0
0 247
0 236
0
0
0
Table 17. Scenario J, Rabi 2010-2011
week delivery
1
2
3
4
5
6
7
8
9
83
19
19
22
10
0
9 226
36
1 439
1 271
10
11
12
13
14
16
17
0 289
24
0
6
23
0
3
3
51
1
766
2
1494
0
2
2
3
3
1432
83
19
19
22
10
4
1401
83
19
19
22
10 353
5
1590
0
19
19
22
0 283
6
1850
83
19
19
22
7
1564
83
19
19
22
8
1771
83
19
19
9
1868
83
19
19
10
1568
0
19
19
22
9 226
36
11
1185
83
19
19
22
10
0
0
0
15
36
0
19
2
0
0
0
9
0
0
16
1486
83
19
19
22
10
0
11 226
36
17
1788
83
19
19
22
10 353
0 226
18
1983
83
19
19
22
0 353
9 226
36 442
19
1954
83
19
19
22
10
0 226
20
2014
83
19
0
22
10 353
9
21
1869
99
19
19
22
13 353
9 226
22
1926
0
19
19
22
0 353
9 226
23
1901
83
19
19
22
10 353
0 181
24
1894
83
19
19
22
0 324
9
25
2021
0
19
0
0
10 283
26
1778
83
19
19
22
10 353
0 226
0
4 682
4
1
24 211
6
23 510
0
24 211
6
23
0 273
24 211
6
23 484
9 187
36
9
36 546
40
27
0 273
0
9 181
36
10 341
0
36 546
0
24 211
6
23 510
13
0
9 226
36
0 273
24 211
6
23 600
22
0 353
9 181
36 546 239
24 211
6
23
22
10 353
6
36 546
0
24 211
6
23 510
0 273
24 211
6
23 417
36 501 273
24 169
6
23
0
0
6
0
0
0 273
24 211
6
23 523
36 537 219
24 211
6
23
0
24 211
6
23 510
36 492 273
24 211
6
23 510
36 437 273
24 209
6
23 510
36
24 237
6
23 510
36 546 235
24
0
6
23 408
36 437
0
24 211
6
23 477
0
36 437 273
24 211
6
23 408
9 186
36 437 273
24 211
0
23 510
36
24 211
6
23 473
0 283
0
0
0
0
0
0
0 273
0 273
0
0
0
Appendix D. Gini-index
Figure 4. Gini-index for all scenarios, Kharif 2011
Figure 5. Gini-index for all scenarios, Kharif 2012
Appendix E. Service interruptions
Table 18. Service interruptions for Hakra Branch canal, Kharif 2011
A
B
C
D
E
F
G
H
I
J IrrDept
GapCount
4
27
27
2
6
4
27
27
2
6
60
MaxGapSize
3
4
4
2
3
3
4
4
2
3
9
Table 19. Service interruptions for Hakra Branch canal, Kharif 2012
A
B
C
D
E
F
G
H
I
J IrrDept
GapCount
7
26
26
6
8
7
26
26
6
8
60
MaxGapSize
4
6
6
4
5
4
6
6
4
5
8