LBS Journal of Management & Research
Year : 2004, Volume : 2, Issue : 1
First page : ( 73) Last page : ( 81)
Print ISSN : 0972-5814.

Construction planning through goal programming: A case study

Sharma J.K.*, Reader, Das Binay Bhanu**, Director

* Faculty of Management Studies, University of Delhi, Delhi-110 007

** Krishna Institute of Management and Technology, Ghaziabad

Goal programming is a powerful OR technique and has gained wide application in every field of activities. Through this technique the different goals can be prioritised and utilisation of various resources with the given constraints can be evaluated to achieve the overall objective of the organisation. This case study demonstrates the application of GP in construction industries.

Top

Introduction

Top

Aims

Top

Goals of the Management

Top

Sources of Data

Parameters of the Case Study

1. Land Availability: Total land available is 35 hectares out of which 20 hectares can be built inclusive of service blocks and others during first phase of construction. Balance land is to be used for future expansion.

2. Description of units: The types of building and the estimated cost under the current cost-index along with the number of units envisaged at final development stage are as under:

   Buildings/Utility Estimated Cost (in lakhs) Number of units limited to • Office-blocks 20 4 • Stores-blocks 20 4 • General development 60 2 • Type I Quarters (lower income group, each block having six dwelling units per store 10 40 blocks (240 D.U.) • Type II Quarters (higher income group, each block having six dwelling units per store 10 30 block (180 D.U.)

3. Escalation: The excepted escalations in cost are indicated irrespective of the type of building by relative cost-indices: First year: 1.0; Second year: 1.1; Third year: 1.2; Forth year: 1.3.

4. Land requirements: Requirements of land for each type of building including access, service etc. under existing planning regulations have been approximated as under:

   Type of building Land requirements* for each category per unit (in ha) For one storeyed For single storeyed For three storeyed • Office blocks 1.0 0.70 0.55 • Stores-blocks 1.1 0.80 0.65 • Type I Quarters 0.30 0.20 0.12 • Type II Quarters 0.40 0.30 0.22 *Land requirements are shown in terms of total number of blocks. Explanation is: For type 1 Quarters, the alternatives can be 240 ground floor dwelling units all as single storeys; or 120 ground floor dwelling units (each with an upper storey d.u.) for two storeyed construction; or 80 ground floor d.u. (each with 2 upper storey d.us.) for three storeyed construction.

5. Funds allocation: The rough estimate based on current cost-index factors for all the building requirements can be tabulated as under. The cost are the same irrespective of the number of storeys adopted.

   Type of Building/Utility Total Cost (in Lakhs) • Office building 80 • Stores blocks 80 • Area development cost 120 • Type I Quarters 400 • Type II Quarters 300

6. Budget for construction: The total project is divided into 2 phases:

   Phase I - extended over 3 years, the budget will be sanctioned from the beginning of the project.

   Phase II - extended over 3 years but effective since one year later (2,3,4) so the funds will be sanctioned one year later than for phase I. The sanction would imply a distribution of budgetary allocation in the production of 20%, 50% and 30% in each phase. It is clear that the cost of approx. Rs. 490 lakhs per phase is reflected accordingly as Rs. 98, 245 and 147 lakhs in the successive years.

   Year Lower Limit Upper Limit (In lakhs of rupees, marginally rounded up) 1 98 98 2 345 365 3 395 420 4 150 167

Goal Programming Mode

The following variables, constants and priority factors are taken into consideration and to be defined.

Variables

Constants

Objective function

Where:

Priority of Goals Defined

1. 1. The total allotted 20 hectares of land should not be exceeded,

   2. Expenditure in each year shall strictly be limited to the upper limit.

2. 1. The year-by-year expenditure should not be far different from lower limit,

   2. General development (Phase I - Bulk water supply, distribution and electricity supply; Phase II. Construction of roads, drains, culverts, horticulture and land-scaping) should be accomplished as pertinent to the ultimate development.

3. 1. Type I quarters should be equitably taken up in both phases i.e., 20 blocks in each phase with each block consisting of 6 d.us.

   2. Similarly, 15 blocks (each block consisting of 6 d.us.) of Type II Quarters should be constructed in each phase.

4. Construction of stores-blocks should be distributed as 2 units in each phase.

5. Construction of office-blocks should be distributed as 2 units in each phase.

Constraints

1. 1. Construction Programme Phase I

      x₁₁ + d⁻₁₁ – d⁺₁₁ = 2

      x₂₁ + d⁻₂₁ – d⁺₂₁ = 2

      x₃₁ + d⁻₃₁ – d⁺₃₁ = 1

      x₄₁ + d⁻₄₁ – d⁺₄₁ = 20

      x₅₁ + d⁻₅₁ – d⁺₅₁ = 15

   2. Construction Programme Phase – II

      x₁₂ + d⁻₁₂ – d⁺₁₂ = 2

      x₂₂ + d⁻₂₂ – d⁺₂₂ = 2

      x₃₂ + d⁻₃₂ – d⁺₃₂ = 1

      x₄₂ + d⁻₄₂ – d⁺₄₂ = 20

      x₅₂ + d⁻₅₂ – d⁺₅₂ = 15

2. Land Requirements Constraints

   1.0x₁₁ + 1.0x₁₂ – x_L-1 + d⁻_L-1 – d⁺_L-1 = 0

   1.1x₂₁ + 1.1x₂₂ – x_L-2 + d⁻_L-2 – d⁺_L-2 = 0

   0.3x₄₁ + 0.3x₄₂ – x_L-4 + d⁻_L-4 – d⁺_L-4 = 0

   0.4x₅₁ + 0.4x₅₂ – x_L-5 + d⁻_L-5 – d⁺_L-5 = 0

   x_L-1 + x_L-2 + x_L-3 + x_L-4 + x_L-5 + d⁻_L – d⁺_L = 0

3. Requirements of funds:

   0.2*1.0 (20.0x₁₁ + 20.0x₂₁ + 60.0x₃₁ + 10.0x₄₁+ 10.0x₅₁) + d⁻_t-11 – d⁺_t-11 = 98.00

   (First year)

4. 1. 0.5*1.1 (20.0x₁₁ + 20.0x₂₁ + 60.0x₃₁ +10.0x₄₁ + 10.0x₅₁)+ 0.2*1.1 (20.0x₁₂ +20.0x₂₂ + 60.0x₃₂ + 10.0x₄₂ + 10.0x₅₂)+ d⁻_t-12 – d⁺_t-12 = 345.00

      (Second year)

   2. (b) 0.5*1.1 (20.0x₁₁ + 20.0x₂₁ + 60.0x₃₁ +10.0x₄₁ + 10.0x₅₁) + 0.2*1.1 (20.0x₁₂ +20.0x₂₂ + 60.0x₃₂ + 10.0x₄₂ + 10.0x₅₂) +d⁻_t-u2 – d⁺_t-u2 = 365.00

      (Second year)

5. 1. 0.3*1.2 (20.0x₁₁ + 20.0x₂₁ + 60.0x₃₁ +10.0x₄₁ + 10.0x₅₁) + 0.5*1.2 (20.0x₁₂ +20.0x₂₂ + 60.0x₃₂ + 10.0x₄₂ + 10.0x₅₂) +d⁻_t-12 – d⁺_t-13 = 395.00

      (Third year)

   2. 0.3*1.2 (20.0x₁₁ + 20.0x₂₁ + 60.0x₃₁ +10.0x₄₁ + 10.0x₅₁) + 0.5*1.2 (20.0x₁₂ +20.0x₂₂ + 60.0x₃₂ + 10.0x₄₂ + 10.0x₅₂) +d⁻_t-u3 – d⁺_t-u3 = 420.00

      (Third year)

6. 1. 0.3*1.3 (20.0x₁₂ + 20.0x₂₂ + 60.0x₃₂ +10.0x₄₂ + 10.0x₅₂) + d⁻_t-14 – d⁺_t-14 = 150.00

      (Fourth year)

   2. 0.3*1.3 (20.0x₁₂ + 20.0x₂₂ + 60.0x₃₂ +10.0x₄₂ + 10.0x₅₂) + d⁻_t-44 – d⁺_t-44 = 167.00

      (Fourth year)

Results and Analysis

The analysis of the data has been done by using QSB₊ package to arrive at the best decision.

From the results of first run it is clear that the first priority goal has been fully achieved as far as requirement of land and upper limit of expenditure are concerned.

Second priority goal has been achieved but at the cost of construction programme, it is possible to execute the general development work of both the phases.

Third priority goal has been fully achieved as there will be shortage of 1 block of type I and 15 block of type II quarters in phase II construction programme.

The forth and fifth priority goals have been fully achieved.

As the residential programme of the organisation can not be executed fully, a second attempt can be made with 2-storeyed construction with some change in priorities.

To overcome the shortage in type - II quarters, change in policy is made to go for 2-storeyed construction for office blocks and stores retaining, however, single-storeyed construction for residences. The priorities are as below:

From the results of this run, it is clear that the first priority goal is fully achieved. But second priority goal has not been achieved as only 7 blocks of type I and one of the 15 blocks of type II quarters can be constructed in Phase II.

Priority goals 3, 4 and 5 are fully met. As for second run we assumed single-storeyed construction of quarters, the Phase II could not be achieved within the financial construction.

Now we assume the double-storeyed construction for residences also.

From the above results, it is clear that the second priority goal of construction in Phase II is again not achieved fully as type II quarters can not be taken up all. Goal 1 is fully achieved.

Priority goals 3 and 4 are achieved in years 1 and 2. Whereas the expenditure level is much below the lower limits prescribed for the 3^rd and 4^th years. Priority goal 5 has also not been achieved, as 1.50 hectares of extra land will be required.

Assume 3-storeyed construction for both type I and type II quarters while the office blocks, stores blocks construction will be 2-storeyed. The results of this change without changing the priorities among the goals are listed below:

Moving from single storeyed to two storeyed construction only for office and stores blocks, number of quarters to be constructed has increased within all the parameters but the required number of quarters has not been possible.

Admitting two storeyed construction for residences also the third run improves over the second as for as type I quarters are concerned but it still falls short of criteria for type II quarters.

Finally, during forth run by allowing residential construction of three storeyed, all the goals could be achieved and moreover, it leaves more space unutilised for future expansion.

Hence a satisfactory solution could be attempted through iterative goal settings.

Top

Conclusions

Top

Tables