Abstract

Apartment Construction Industry(ACI) is an important industry area in society. Before contribute a apartment, it is necessary to contribute model of ACI to have a system to calculate the relationship between demand and order of apartment. Using Causal Loop Diagram to describe the system. Then write the difference equations and choice initial values of system variables and parameters, the mainly parameters are and . Selecting three different patterns of apartment take-up rates respectively are step increase, Random variation and sinusoidal variation. Though find the best value of parameters and to optimize the system and make the order more stabile and bullwhip effect smaller.

- Introduction

Nowadays, because of strong market demand, the construction industry grows fast. Companies should put great importance on project-management practices aid in decision making (Azevedo et al, 2013). In construction industry area, a good model to predict demand has significant influence in the running of the whole system. Using model to help Apartment Construction Industry(ACI) system running stability can make the decision more believable. This report will contribute and justify the modeling of ACI and find the best value of parameters of this model to optimize the system. The bullwhip effect and order variance will be the most important rules to measure the condition of the system.

2.Causal Loop Diagram

A causal loop diagram(CLD) are very effective tools for representing the feedback structure of systems, which can show the causal relationship of serval variables (Sterman, 2000). CLDs can be use to problems structuring and it has been common in operations management ( Perlow et al, 2002) Use the CLDs to describe the ACI system can make the system simpler and easy to understand.

In this report, the variable of is number of new apartments to be constructed during year t. is number of vacant apartments in the beginning of year t. And is number of apartments being taken up during year t. Therefore, ACL casual diagram can be built as Figure 1.1.

_{ }

Figure4.1

If considering which means estimation of apartment take-up rate made in year t-1, for year t. The ACL casual diagram will become as Figure 4.2.

Figure 4.2

3.Difference Equations

3.1 Difference Equations

The variables in this problem are:

Number of new apartments to be constructed during year t

Number of vacant apartments in the beginning of year t

Number of apartments being taken up during year t

Estimation of apartment take-up rate made in year t-1, for year t

The parameters within this system are

Target level of vacant apartments

Exponential smoothing parameter

Equals

L Delay

And the difference equations are:

Order():

Vacant():

Estimation():

3.2 Initial values

In the previous section, the difference equations have been written. To running the system, the initial values should be selected.

Below are selected initial values:

4.Simulation

To test the ACI simulation in different patterns of apartment take-up rates, we choice step increase, random variation and sinusoidal variation to describe the change of demand. And below are the process and the result of these simulation.

4.1 Step Increase

The special traits of this system is take-up rate increases from 100/year to 200/year in year 10. Using the Microsoft Excel to contribute the system (See Figure 1.1).

Figure 4.1

Calculate the bullwhip and order variance from period 5 to period 100. and respectively change from 0.1 to 1.0. The bullwhip data statistics shown in Figure 4.2 and Figure 4.3, the order variance shown in Figure 4.4.

Figure 4.2

Figure 4.3

Figure 4.4

The bullwhip is the proportion of variance of orders and variance of demand. Using this tool, we can get the rate of input and output. So the smaller bullwhip number means the better system. And the change of demand will not lead to strong fluctuate of order. And the order variance illustrates the wave of order directly, so it and be an important data to rule the stability of the system.

According the result in Figure 4.2, the bullwhip can get the smallest number which is 1.27765 when and . And Figure 4 shown in the same situation the order variance is also the smallest. So and is the best value of parameters. In this two value the stabilization of system of demand step increase is best and the bullwhip effect is the lowest.

Figure 4.3 is a line graph of the bullwhip in different and , the lines with different color mean and the number in abscissa axis mean .

When and , the line chart of demand is Figure 4.5.

Figure 4.5

4.2 Random Variation

This system is apartments/year, where RND should have a mean value of zero, and a range of about 60. To build this model, random between -30 and 30 should be created first. Than demand equal 100 plus a random. The model of the system is Figure 4.6.

Figure 4.6

Calculate the bullwhip from period 5 to period 100. and respectively change from 0.1 to 1.0. The bullwhip data statistics shown in Figure 4.6.

Figure 4.7

Because of the random are always change, every time we calculate the bullwhip the figure is different. So we test 5 times in same and and have the average.

Figure 4.7 shown when and the number of bullwhip is smallest which is 0.101898. Although demand is random, keep and can get a relatively stable order and the bullwhip effect is the smallest. When and , the order can be shown in line chart (Figure 4.8).

Figure 4.8

4.3 Sinusoidal Variation

The demand in this system is take-up rate change as sinusoidal variation. And the sine wave has a period of 5 years, 10 years and 50 years.

4.3.1 5 years

Using the Microsoft Excel to contribute the system (Figure 4.9)

Figure 4.9

Calculate the bullwhip and order variance from period 5 to period 500. and respectively change from 0.1 to 1.0. The bullwhip data statistics shown in Figure 4.10 and Figure 4.11, the order variance shown in Figure 4.12.

Figure 4.10

Figure 4.11

Figure 4.12

From the result in Figure 4.10, the bullwhip can get the smallest number which is 0.142 when and . And Figure 4.12 shown when and the order variance is also the smallest. Therefore, when apartment take-up rate is , and is the best value of parameters, and the stabilization of system of demand step increase is best and the bullwhip effect is the lowest.

Figure 4.11 is a line graph of the bullwhip in different and , the lines with difference color mean and the number in abscissa axis mean . In general, when increase from 0.1 to 1.0, the figures of bullwhip are also increase. And has same situation in this model.

When and in this model, the order line chart is Figure 4.13

Figure 4.13

4.3.2 10 years

Using the Microsoft Excel to contribute the system (Figure 4.14)

Figure 4.14

Calculate the bullwhip and order variance from period 5 to period 500. and respectively change from 0.1 to 1.0. The bullwhip data statistics shown in Figure 4.15 and Figure 4.16, the order variance shown in Figure 4.17.

Figure 4.15

Figure 4.16

Figure 4.17

From the result in Figure 4.15, the bullwhip can get the smallest number which is 0.4897 when and . And Figure 4.17 shown when and the order variance is also the smallest (98.66). Therefore, when apartment take-up rate is where the sine wave has a period of 10 years, and is the best value of parameters. At this point, the stabilization of system of demand step increase is best and the bullwhip effect is the lowest.

Figure 4.16 is a line graph of the bullwhip in different and , the lines with different color mean and the number in abscissa axis mean . There are some fluctuate when is increase from 0.1 to 1. Although the lowest point is still , but there is a wave trough when .

When and in this model, the order line chart is Figure 4.18

Figure 4.18

4.3.3 Years 50

Using the Microsoft Excel to contribute the system (Figure 4.19)

Figure 4.19

Calculate the bullwhip and order variance from period 5 to period 500. and respectively change from 0.1 to 1.0. The bullwhip data statistics shown in Figure 4.20 and Figure 4.21, the order variance shown in Figure 4.22.

Figure 4.20

Figure 4.21

Figure 4.22

From the result in Figure 4.20, the bullwhip can get the smallest number which is 1.018 when and . And Figure 4.22 shown when and the order variance is also the smallest which is 205.2. Therefore, when apartment take-up rate is where the sine wave has a period of 50 years, and is the best value of parameters, and the stabilization of system of demand step increase is best and the bullwhip effect is the lowest.

Figure 4.21 is a line graph of the bullwhip in different and , the lines with different color mean and the number in abscissa axis mean . In general, when increase from 0.1 to 1.0, the figures of bullwhip are decline. And has same situation in this model. However, this rule is not complete apply to this model so we can find and rather than

and is the best value.

When and in this model, the order line chart is Figure 4.23

Figure 4.23

- Conclusion

Though the step of causal loop diagrams, write difference equation and simulation, the best value of and have been found. When demand change as step increase, and is the best value of parameters. And and are the best value of change as random variation and sinusoidal variation where the sine wave has a period of 5 years or 10 years. Finally, when the sinusoidal period become 50 years, the best value is and .

There are two limitations when making the report because of the limited of time. First, this report only covers these three situation. Some situation such as the demand is normal distribution was not test. Second, only using bullwhip and order variance to measure the system is not enough comprehensive.

Reference

Azevedo, R et al. 2013. Performance Measurement to Aid Decision Making in the Budgeting Process for Apartment-Building Construction: Case Study Using MCDA-C. *Journal of Construction Engineering & Management. *1 February 2013. pp226-236.

Perlow, L et al. 2002. The speed trap: Exploring the relationship between decision making and temporal context. *Academy of Management Journal* 45(5). pp931–955.

Sterman J. 2000. *Business Dynamics: Systems Thinking and Modeling for a Complex World*. McGraw Hill: Boston, MA.