Project Management: A case study on Environment-friendly method

implemented in dismantling of buildings

Indian Statistical Institute

SQC & OR Division, Kolkata

Indian Statistical Institute, Kolkata

Sunny Gupta Roll- QR 1101

Arpan Mukherjee Roll- QR 1102

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Project Management: A case study on Environment-friendly method

implemented in dismantling of buildings

1. Project Scheduling

In project Management scheduling involves listing down important project terminal elements with

intended start and finish dates. The important decision taken involves parameters like resource

requirements, budget, and duration.

2. Problem Statement

The problem involves a case study titled as “Environment-oriented project scheduling for the

dismantling of buildings” published in OR-Spektrum Springer-Verlag 2001. The paper presents a case

study for the environment-friendly dismantling and recycling of buildings. Based on the material

availability, techniques of dismantling and constraints on resource usefulness, a scheduling model has

been proposed in the paper to minimize the total time involved in the project. The purpose of this study

is to review the model proposed in the aforesaid paper, state about its usefulness in solving the

problem, and also propose an alternate model approach.

3. Dismantling and recycling of building materials

3.1. Dismantling

Dismantling of a building implies the gradual and systematic method of disassembling pieces of a

building, while recycling involves act of processing used or abandoned materials for use in creating new

products. Dismantling of a building represents a make-to-order production i.e. all products are

manufactured only in response to customer orders. That means no stock is built up for sales. Also the

procedure for dismantling and recycling represents the class of on-site manufacturing owing to the fact

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that all resources needed for dismantling are transferred to the site for dismantling. Thus a better

planning is required for this kind of jobs, with special care taken about the effect of the methodologies

on the environment. Due to stricter environmental regulations like the Recycling and Waste

management Act (Kreislaufwirtschafts- und Abfallgesetz (KrW-/AbfG)) in Germany or the requirements

for Integrated Pollution Prevention and Control (IPPC-Directive) of the European Union, dismantling

methods are obliged to follow the above specifications. Thus the need for environment friendly

dismantling methods and recycling of demolished items has become a subject of interest. Due to large

amount of material-flow taking place, the construction industry plays a major role in this aspect.

3.2 Problem with Dismantling and Recycling

The primary problem that arises out of dismantling of a building is that, building can be categorized as a

meta-product i.e. a collection of multiple products all with their own characteristics, combined in unique

and complex manners. The heterogeneity of composition, and as well as the multitude of the materials

form an obstacle in the usage of recycled products. A survey says that the composition of waste in the

construction sector make no distinction between waste generated from construction and that of

demolition. Besides the aforesaid problem, there are possibilities of existence of pollutants in the

demolition wastes. These pollutants could harm the environment, especially by leaching, during storage

or re-use and which impede recycling, indeed can make it impossible. The following table taken from the

paper shows us the existence of pollutants in building wastes.

Table1. Potential pollutant sources in buildings

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4. Material Flow Analysis

Due to the wide variety of materials involved in construction of a building and also the heterogeneity of

composition of the demolition products, a systematic analysis of the material flow is a pre-requisite

before techniques of demolition can be applied. A building audit is conducted, which aims at identifying

and quantifying materials in order to give decision support as to how the dismantling has to be carried

out. Based on the documents of the building (e.g. construction plans, descriptions, history) detailed data

on the composition of the building have to be collected and analyzed. Generally only a small part of the

building materials contain pollutants. Thus it is necessary to identify them before the dismantling

techniques are applied, in-order to avoid the mixing up of the toxic materials with the large number of

non-toxic materials rendering them toxic. The building audit prepares a bill of materials used in the

construction of the building, which is used to prepare the pollutant vector.

The pollution vector is represented as follows:

For each material 1 2: ( , , , , , )T

p p p ip npp v v v v v , and

For each surface 1 2: ( , , , , , )T

l l l il nll v v v v v

Let { | 1,2, , }pSP v p P denote the set of pollutant vectors for materials and

Let { | 1,2, , }lSL v l L denote the set of surfaces, based on which a sample of the pollutant matrix

is depicted below

Fig. 1. Pollutant-matrix for building materials (content in mg/kg) and surfaces (content in mg/m2) (excerpt)

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4.1. Dismantling Network

An environment-oriented network, showing the order of precedence, of different dismantling activities

is prepared. Each of the nodes represents the activities involved in the procedure. The dismantling

network for a residential building is shown below (taken from the paper).

Fig.2. Dismantling network for a residential building

4.2. Different Dismantling Techniques

The model to be prepared is a scheduling model which aims at optimizing the time required for the total

project to be finished. For this purpose it is essential to define the time required for each of the

dismantling techniques, once the above said network is prepared. Each of the activities in the above

network can be processed in different ways. An example of different processing which can be applied to

the disassembling of outer walls has been shown below

These different activities have their different time of processing (in hr. /m3). Out of these alternatives

only one can be applied for the particular activity maintaining certain environmental constraints or

other specifications if required. Thus for a particular activity j , different modes of activities are denoted

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by m , where {1,2, , }jm M and for two activities a andb , aM is not necessarily equal to

bM .The

duration of performing activity j in mode m is denoted by jmd

Now, for a particular mode of activity, there are two types of resources associated with it which are

renewable resources (machines, workers, etc.), which gets replenished after each activity is

accomplished and non-renewable resources (financial budget etc.) which are fixed for a particular

project and is supposed to get exhausted by its end.

5. Model Formulation

Based on the discussions in the earlier sections the model that can be prepared out of the given topic

needs the consideration of following variables

5.1. Objective Function and Constraints

jmnq : Capacity of non-renewable resource n , consumed by dismantling activity j performed in mode m

jmrq : Capacity of renewable resource r , consumed by dismantling activity j performed in mode m for

each period the activity is in process

rtQ : Capacity of renewable resource r , r R , available in period t , and

nQ : Total capacity of non-renewable resource n , n N .

To reduce the number of variables further, the earliest and the latest finishing times and j jEF LF for

each activities are calculated using the critical path analysis. Thus the model can be formulated as

Minimize, 1

( ) .J J

J

M LF

Jmt

m t EF

x t x

for the unique sink J .

Here, t denotes the period in which the activity J is performed in mode m and Jmtx is a binary variable

which denotes whether the action is taken or not. Thus 0,1Jmtx , and hence

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1

1j j

j

M LF

jmt

m t EF

x

1,2, ,j J (1)

Furthermore let us consider jP as the set of activities already completed before the thj activity has

started. Hence,

1 1

. ( ).j ji i

i j

M LFM LF

imt jm jmt

m t EF m t EF

t x t d x

2, , , jj J i P (2)

Imposing the limitations on the availability of resources, following two more constraints can be

formulated

1

1 1

.j jmM t dJ

jmr jm rt

j m t

q x Q

, 1,2, ,r R t T (3)

1 1

.j j

j

M LFJ

jmn jm n

j m EF

q x Q

n N (4)

The above mentioned model is a Binary-Linear Programming problem, i.e. the decision variables

0,1Jmtx are binary. The model belongs to the class of combinatorial optimization problems and is

one of the Multi-Mode Resource-Constrained Project Scheduling Problems (MRCPSP). The reason for

incorporating the term Multi-Mode is because of the involvement of different mode of processing for a

particular activity which makes the solution space large. The complexity of this problem is NP-complete

(where NP stands for Nondeterministic Polynomial), where the time required to solve the problem using

any currently known algorithm increases very quickly as the size of the problem grows. The algorithm

proposed to solve this problem is “branch and bound algorithm”.

5.2. Branch and Bound Algorithm

Solving NP-complete discrete optimization problems to optimality is often an immense job requiring

very efficient algorithms, and the B&B paradigm is one of the main tools in construction of these. A B&B

algorithm searches the complete space of solutions for a given problem for the best solution. However,

explicit enumeration is normally impossible due to the exponentially increasing number of potential

solutions. The use of bounds for the function to be optimized combined with the value of the current

best solution enables the algorithm to search parts of the solution space only implicitly.

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The B&B follows a search tree, where previous decision influences the next decision in following the

route for optimal solution to a problem. The decision of the initial problem formulates the next route

which is also called the sub-problem, and the procedure follows recursively.

Fig 3: Illustration of the search space of B&B.

The search terminates when there are no unexplored parts of the solution space left, and the optimal

solution is then the one recorded as "current best".

5.3. Sample Format of Data

Table 2. Data of the case study

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5.4. Prototype Model

To illustrate the efficiency of the model described above, we have developed a prototype model with 3

nodes, A- Dismantling of windows, B- Dismantling of pipes and C- Dismantling of walls. Each of the

nodes has two modes of operation. The table, showing the durations of the activities is given below.

Activity Mode Duration (hrs.)

A 1 2

2 5

B 1 3

2 4

C 1 7

2 6

Thus the different values of the finishing time for the unique sink C are:

Mode 1 Mode 2

12 11

13 12

15 14

16 15

Hence the objective is to minimize

Where, 11 12 13 14 21 22 23 24 1C C C C C C C Cx x x x x x x x and the variables are binary.

The second set of constraints pertains to the precedence relations

For the 2nd activity,

11 21 11 12 21 222 5 2 5 2 5A A B B B Bx x x x x x .

This signifies that when activity A, operating at mode 1 ends at t=2hrs activity B starts at t=2 for two

different modes, which are represented by variables 11Bx and 21Bx . Similar explanation holds for activity

A operating in mode 2.

For the 3rd activity similar constraints will be applicable,

11 21 11 12 13 14 21 22 23 242 5 5 6 8 9 5 6 8 9A A C C C C C C C Cx x x x x x x x x x

11 12 13 14 21 22 23 2412 13 15 16 11 12 14 15C C C C C C C Cx x x x x x x x

A B C

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11 12 21 21 11 12 13 14 21 22 23 245 6 8 9 5 6 8 9 5 6 8 9B B B B C C C C C C C Cx x x x x x x x x x x x

One can note that, since the network is a straight one, thus the coefficients of the decision variables

equals on both the sides.

For the sake of simplicity, without considering the constraints for resources one can clearly see the

minimum value of the objective to be 11hrs and, 21 1Cx . This satisfies the precedence relations as

21 1Ax and 11 1Bx , with rest of the binary variables equals 0.

6. Alternate Approach for Modeling

In the above model, the total time for finishing the project was targeted as the objective for

minimization. However as we know that for any improved methodology to be applied, or if the a project

is targeted to be finished at an earlier time, then improved technique or more labor has to be invested

on that activity, and hence the cost for that activity increases. Again, better method of activity

performance ensures proper separation of hazardous material and recyclable material from the

dismantled building. Hence from their selling, some surplus budget can be gained.

The previous model had fixed the total financial budget, taking it as one of the non-renewable resource.

Here we take the decision variable as the cost involved in each of the activities and hence try to

minimize the total budget involved in the project.

For this we assign a cost value to each of the modes of activities to be performed, naming it jmC , which

refers to the cost involved with activity j being performed in mode m minus the profit obtained for

performing the task. Our task is modified to the minimization of the pooled financial expenditure

involved in the project, considering an upper limit for the total time permissible in the project.

Thus the model equation becomes,

Minimize1 1

( )jMJ

jm jm

j m

x x C

,

Where j denotes the set of activities to be performed and m denotes the different modes of processing

that can be performed for a particular activity. Like the previous model, jmx , a binary decision variable

which is 1 if the certain mode of processing is applied on the activity and 0 if it’s not. Thus, 0,1jmx ,

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1

1jM

jm

m

x

for a particular activity and like the previous one, this is also a Binary-Linear Programming

problem.

Since, we have put a limitation on the overall time available for the project. Thus,

1 1

jMJ

jm jm

j m

x d T

, whereT is the total available time for the project. (5)

Unlike the previous model, here we do not perform the critical path analysis for the network but assume

that the value ofT will be specified by the project owner.

In the alternate model, we exclude total financial budget from the category of non-renewable resources.

However the constraints pertaining to the availability of renewable and non-renewable resources are

consistent with the previous approach. Assuming that the consumptions of resources for different

modes of activities are different, thus constraint in-equations are,

1 1

.jMJ

jmr jm rm

j m

q x Q

(6)

Where, rmQ : Capacity of renewable resource r , r R , available for the mode m

And, 1 1

.jMJ

jmn jm n

j m

q x Q

(7)

7. Alternate Bi-objective Formulation

The model can also be formulated as a bi-objective problem where we simultaneously have to minimize

both the time required and the cost involved in the process. As seen earlier, both the financial budget

and the time involved can be taken as function of the modes of activities involved in the project. It is

also assumed that to reduce the time allotted for an activity, amount of resource in the form of

technology, fuel, manpower etc. to be invested, increases, and thus it increases the cost of performing

the activity. Thus the cost involved and the durations, forms conflicting functions i.e. minimizing one of

them will maximize the other. Similar to the first model, we consider the variable JmtC as the cost of

performing activity j in mode m by time t incorporating the profit associated with performing of the

task.

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Thus, the objective functions can be written as

Minimize, 1

1

( ) .J J

J

M LF

Jmt

m t EF

x t x

for each activity J .

And, 2

1

( ) .J J

J

M LF

Jmt Jmt

m t EF

x C x

The constraints involving the resource limitations and the precedence relations will be similar to that of

the first model.

8. Comparison of the Models

All the three models belong to the class of Binary-Linear Programming Program, where the

decision variable remains almost same.

For the first model, we need the critical path analysis for having different finishing times for

different modes, pertaining to the critical path. For the second model we lift up the restriction.

Again the bi-objective model requires the critical path analysis to be performed.

The Alternate Model also takes care of the usefulness of the different dismantling activities in

raising the financial budget, and hence stringent rules in maintaining the budget is not required.

The network precedence constraint is not needed in the alternate model, as we are more

concerned with the cost involved in an activity. Analysis can separately be performed for the

different paths, and then the optimal and as well as the modes of operation can then be

selected.

References

“Environment-oriented project scheduling for the dismantling of buildings” by Frank Schultmann and

Otto Rentz. OR-Spektrum 2001.