CHAPTER 4 MODELING SIMULATION AND ANALYSIS OF PROJECTS USING MICROSOFT EXCEL AND SIMQUICK

Transcription

1 63 CHAPTER 4 MODELING SIMULATION AND ANALYSIS OF PROJECTS USING MICROSOFT EXCEL AND SIMQUICK 4.1 INTRODUCTION Section describes modeling and Simulation, analysis of projects using Microsoft Excel, the characteristics of the proposed Excel model for representing projects presented in section The various stages of simulation software such as project planning, project analysis are discussed. Also validation of Excel simulation software with product development project example presented in Section 4.2 and describes the application of SimQuick for modeling and simulation of project. Summary is presented in section Simulation using Microsoft Excel In this section an extended PERT simulation of the product development process is proposed. The simulation model is constructed in Microsoft Excel. The expected project completion time and percentage utilization of resources are evaluated. The assumptions of the model are Activities are performed in a particular topological order. A list of activities in a project is said to be in topological order if no activities appear in the list before all of its immediate predecessors have appeared. For the activities in Figure 4.1 the possible topological orders are a-b-c-d-e, a-b-d-c-e and a-c-b-d-e.

2 64 Figure 4.1 Sample network Task duration is random and follows triangular distribution and is shown in Figure 4.2 Three time estimates are required to compute parameters of activity duration. Optimistic time (To): It is the duration of any activity when everything goes on very well during the project. Most likely time (Tm): It is the duration of any activity when sometimes things go on very well, sometimes things go on very bad while doing the project. Pessimistic time (Tp): It is the duration of any activity when almost everything goes against our will and a lot of difficulties are faced while doing a project. Figure 4.2 Triangular distribution where, x is a Random variable; f (x) is the probability density function; 2( x To) f ( x) =, To x Tm ; ( Tp To)( Tm To) 2(Tm Tx) f (x) =, (Tp To)(Tp Tm) Tm x Tp ; f (x) = 0, Else

3 65 The availability of resources is random and assumed to follow uniform distribution and is shown in Figure 4.3. Figure 4.3 Uniform distribution The activities are scheduled as per the topological order. If an activity needs a revision due to iteration, then rescheduling of activities and resources will be done as per topological order. If more than one activity becomes eligible and they are not sharing common resources they can start simultaneously. Otherwise forthcoming activity should wait to allocated resource to become free. Interruptions can occur at any stage of PD process. It may occur due to break down of machineries, unavailability of resources, etc. The flow chart of extended PERT simulation for PD process is shown in Figure 4.4

4 66 Figure 4.4 Flowchart showing the simulation details in excel simulation

5 Steps in simulation The proposed model employs a discrete event simulation to estimate the completion time of projects. Analytical features are included so that the model can describe the complex behavior of development process. Step 1 : Enter the following Number of activities N Topological order Number of resources m required for each activity Optimistic (To), most likely (Tm) and pessimistic timings (Tp) Rework probabilities Probability range of impact for each activity Step 2 : Activity =1, find resources involved in activity 1. Early start=0 Resource ready time=0 Delay=0 Processing time=triangular (To, Tm, Tp) Early finish= Processing time Step 3 : New activity= Next activity in topological order Step 4 : Find resources involved in New Activity Early start=maximum (Resources ready time) If Delay occur Then Delay=Uniform (a, b) Else Delay=0 Processing time=triangular (To, Tm,Tp) Early finish= Early start + Processing time + Delay Step 5 : Find rework count to corresponding activity If rework exist then Step 6 Else Step 7 Step 6 : Find impact probability Rework count=rework count +1 for corresponding activity Find impact activity New activity= Impact activity

6 68 Go to step 4 Step 7 : If (Activity=Final activity N) Then Step 8 Else Step 3 Step 8 : Print Completion time=, Earliest finish time Step 9 : Print Each Resource usage time Step10 : STOP where Triangular (To, Tm, Tp) is a user defined function which gives value as per definition given in task duration. Uniform (a, b) is a user defined function which gives value as per definition given in delays due to interruptions Case Study A case study from an engineering industry is detailed below. This industry has a research and development (R&D) wing to deal with PD on a continuous basis. The project consists of 11 activities and the immediate predecessor relationships and duration of activities are shown in Table The model has assumed that activity duration follows triangular distribution. Table 4.1 Details of case study for excel simulation Activity To Tm Tp Resources Activity Predecessor No. (Weeks) r1 r2 r3 1 Concept Development Design Specifications Materials Methods Tooling Test Development Train 4, Prototype 4, Testing 7, Launch 9,

7 69 The network diagram is given in Figure 4.4. Figure 4.5 Project network used for excel simulation The model is simulated with uncertainty of durations, resource allocations and scheduling. The snap shot of the model in Microsoft Excel is shown in Figure 4.5.The topological order taken is It is simulated for 1000 runs Summary Modeling and simulating product development process by considering uncertainty of activity durations, iterations with learning, interruption and resource scheduling conflicts will make estimate close to reality. The statistical measure observed from simulation without considering iteration is as shown in Table 4.2. The distribution of completion time over the simulation and its corresponding probability of success are as shown in Figure 4.6 The utilization of resource over the simulation is shown in Figure 4.7.a, 4.8.b and 4.9.c. The probable completion time is in the range of weeks and corresponding probability of success is in the range of 0.55 to The associated risk is 25-45%. Since iteration is not considered this estimate is not realistic.

8 70 Figure 4.6 Snap shot of the model in microsoft excel Table 4.2 Details of statistical measures for excel simulation Median 38 Mode 35 Standard Deviation Sample Variance Kurtosis Skewness Range 74 Minimum 28 Maximum 102 Sum Count Largest(1) 102 Smallest(1) 28 Confidence Level (95.0%)

9 71 Figure 4.7 Histogram of completion time and cumulative probability of success for projects modeled in microsoft excel Figure 4.8 (a) Utilization of resource R1

10 72 Figure 4.8 (b) Utilization of resource R2 Figure 4.8(c) Utilization of resource R3 With the following additional data new model has constructed. Interruptions are assumed to distribute between 0.2 to0.8 weeks. Rework probabilities with learning for each task are as shown in Table 4.3.

11 73 Activity no Table 4.3 Rework probability with learning Rework 1 Rework 2 Rework 3 and above The statistical measure for 1000 simulation is shown in Table 4.4. The distribution of completion time and corresponding probability of success are as shown in Figure 4.8. The utilization of resourcess is shown in Figure 4.9.a, 4.9.b and 4.9.c respectively. Figure 4.9 Histogram of completion time and cumulative probability of success (with rework)

12 74 Table 4.4 Statistical measures with rework Mean Standard Error Median Mode 92 Standardd Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Largest(1) Smallest(1) Confidence Level(95.0%) Figure 4.10 (a) Utilization of resource R1 with rework

13 75 Figure 4.10 (b) Utilization of resource R2 with rework Figure 4.10 (c) Utilization of resource R3 with rework The histogram of completion time in Figure4.9 shows that the completion time is in the range of weeks. Its probability of success is The associated risk is 45-50%. When rework is taken into consideration, it is observed that the PD completion time has increased and the probability of successs has reduced. Since the constructed model is close to reality, this estimate is more realistic and reliable. In order to resource 3 capacities avoid waiting of activities for resources, resource 2 and have increased to two. Then the model is simulated for

14 times. The resultant statistical measures are shown in Table 4.5 and distribution of completion time is shown in Figure The completion time will be in the range of weeks. Its corresponding probability of success is To complete within 140 weeks, probability of success is Resultant utilization of resources are as shown in Figure 4.11.a, 4.11.b, 4.11.c. Significance of improvement by this proposed method is validated using Test of significance for difference of means of two large samples. X 1 = Mean (Statistical measures, Table 4.5) X 2 = Mean (Statistical measures, Table 4.6) n1 n2 = Sample size (No. of simulation runs =Count, Statistical measures Table 4.5) = Sample size (No. of simulation runs =Count, Statistical measures Table4. 6) s 1 = Standard deviation (Statistical measures Table4. 2) s 2 = Standard deviation (Statistical measures Table4. 2) Null hypothesis Ho: Two samples have been drawn from the same population ( X 1 = X 2 ) Table 4.5 Statistical measures with increased capacity of resources Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 1000 Largest(1) Smallest(1) Confidence Level(95.0%)

15 77 Alternate hypothesis H1: ( X 1 X 2 ) The Test statistics is z = X 1 X s1 s2 + n1 n2 The value of z is calculated as The critical value of z corresponding to 5% level of significance is 1.64 for one tailed test and 1.96 for two tailed test. The corresponding value for 1% level of significance is 2.33 and Since the value of z is greater than the standardd value (critical value) for both the cases, the difference is highly significant. Hence, the null hypothesis is rejected. Therefore we can conclude that significant difference is attained by increasing the resource capacity. Figure 4.11 Histogram of completion time and cumulative probability of success (with increased capacity of resources)

16 78 Figure 4.12(a) Utilization of resource R1 with increased resource capacity Figure 4.12(b) Utilization of resource R2 with increased resource capacity

17 79 Figure 4.12(c) Utilization of resource R3 with increased resource capacity 4.2 SIMULATION USING SIMQUICK This section describes the application of SimQuick for modeling and simulation of project. The completion time of the project is estimated for unconstrained and constrained resource environments. Assumptions of the model are Activities are performed in a particular topological order Task duration of each activity is random The basic steps involved in this methodology are 1. Conceptually build a model of the process using the building blocks of SimQuick. 2. Enter this conceptual model into SimQuick 3. Test process improvement ideas with the model Building blocks and control panel in SimQuick: The five building blocks used in SimQuick simulation are Entrance, Exit, Workstation, Buffers and Decision points. The output results can obtain in View Results. The control panel of the SimQuick window is shown in Figure Each

18 80 button transfers control to a work sheet containing the SimQuick tables through which one specifies a simulation. Figure 4.13 Simquick control panel Entrance: Arrival of entity is defined by Entrance block. This is where objects enter the process. Inputs to this block are Time between arrivals and Objects per arrival. Time between arrivals is defined by appropriate probability distribution. Objects per arrival define number of entities entering the system. Objects leaving this block are guided by the Output destination Workstation: Processing of entity is defined by workstation. Input to this block is the Working time of the workstation, which is defined by the appropriate distribution. Objects leaving this block are guided by the Output destination. Resourcee involved in that process can also defined by Resource Name and Resourcess needed.

19 81 Buffers: This is where objects can be stored. Buffer can represent a location in a where house or factory where inventory can be stored, or a place where people can stand on line at a post office, etc. It is used as storage counting block. Input to this block is how many objects it can hold. It counts number of objects entering buffer. Thus it is defined to determine average entities leaving system. For our project purpose Capacity value assigned is one. Simulation control: It is used to define time units per simulation and number of simulations Case Study A typical case study from an engineering industry is presented. The list of various activities, immediate predecessor relationship, activity durations and the resource required (man power) to complete the activity are detailed in Table 4.6. The activities in the project are considered as the jobs and resources are considered as workstations in the process. The details of the model parameters are shown in Table 4.7.

20 82 Activity A Description of activity Concept development Table 4.6 Project details under study Immediate predecessors Expected duration Resource (days) required T o T m T p _ B Concept testing A C System level design B D Detailed design C E Implement modifications C F Product drawing E G Conceptual mapping. C H Stage drawing F I Trial planning D J Get customer feed back H,I K Tool plan manufacturing C L Pre- launch plan K M Training L N Build prototype M,J O Product trail N P Capability studies O Q Debug faults P R Certify the product Q S Initial production run P T Prepare for advertisement S U Roll out final product-launch T,R,G

21 83 Table 4.7 Details of model parameters for the project under study for simulation using simquick Control name Activity name Input parameters Output destinations Resource Units needed Workstation A Working time = Nor(12,2) B, Output Objects =1 6 Workstation B Working time = Nor(15.33) C, Output Objects =1 8 D, Output Objects =1 Workstation Working time = Nor(3,1) E, Output Objects =1 G, Output Objects =1 2 K, Output Objects =1 Workstation D Working time = Nor(6,2) I, Output Objects =1 3 Workstation E Working time = Nor(12,2) F, Output Objects =1 6 Workstation G Working time = Nor(15.67,5.13) U, Output Objects =1 9 Workstation F Working time = Nor(24,3.6) H, Output Objects =1 10 Workstation H Working time = Uni (5,7) J, Output Objects =1 3 Workstation I Working time = Nor(11,3.6) J, Output Objects =1 6 Workstation J Working time = Nor(17,3) N, Output Objects =1 9 Workstation K Working time = Nor(2,1) L, Output Objects =1 1 Workstation L Working time = Nor(15,5) M, Output Objects= 1 8 Workstation M Working time = Nor(5,2) N, Output Objects =1 3 Workstation N Working time = Nor(15,2) O, Output Objects =1 8 Workstation O Working time = Nor(3,1) P, Output Objects =1 2 Workstation P Working time = Nor(10,3.61) Q, Output Objects =1 S, Output Objects =1 5 Workstation Q Working time = Constant(2) R, Output Objects =1 2 Workstation R Working time = Nor(2,2) U, Output Objects =1 1 Workstation S Working time = Nor(10,3) T, Output Objects =1 5 Workstation T Working time = Nor(7,2) U, Output Objects =1 4 Workstation U Working time = Nor(8,4) End, Output objects=1 4 Buffer Start Capacity =1;Initial objects=1 A, Output Objects =1 - Buffer End Capacity =1;Initial objects=0 - -

22 84 With these model parameters, the process is simulated for 200 runs. A typical spreadsheet simulation input is shown in Figure The process simulation is done for unlimited resource environment and constrained resource environment Model View (Note: Cannot edit model here) Simulation controls: Time units per simulation 500 Number of simulations 200 Work Stations: 1 Name a Working time Nor(12,2) Output # of output Resource Resource destination(s) objects name(s) # units needed B 1 za 6 2 Name b Working time Nor(15.33,1.53) Output # of output Resource Resource destination(s) objects name(s) # units needed C 1 za 8 Figure 4.14 Typical spread sheet simulation input for project In the constrained resource environment, the man power availability is considered and is assumed that maximum available man power is 15. The completion time of the project is calculated for both cases and histograms of completion time are plotted. By setting the model parameters, the process is

23 85 simulated for 200 runs. Time units per simulation are taken as 500.Mean inventory at the end is the fraction of time during the simulation that the project is completed. Project duration (PD completion time) = (1-mean inventory at the end)*(simulation duration) In the case of unlimited resource environment, mean inventory at the end = ; project completion time= ( )*500= days. In the case of limited resources, Mean inventory at the end = project completion time = ( )*500=183.2 days. By this method completion time of the project is calculated and is tabulated in Table 4.8 and 4.9 respectively. Table 4.8 Project completion time under unlimited resources

24 86 Table 4.9 Project completion time under constrained resources Summary The project is modeled and simulated using SimQuick. The completion time of the Project is computed in the unlimited and constrained resource environments separately. The histogram of completion time is plotted in Figure 4.14 and 4.15 respectively.

25 87 Based on simulation the histogram of project completion time under unlimited resource environment is shown in Figure The project gets good chance of completion within 166 days. But in reality the resources are limited. For simulating the real time behavior, the available man power is limited to 15 and the simulation results are presented in Figure The completion time of the project in this case is 188 days. Figure 4.15 Frequency histogram of project completion time with unlimited resources Figure 4.16 Frequency histogram of project completion time under constrained resources

26 COST MANAGEMENT IN PROJECTS USING SIMULATION To reduce a project completion time, additional resources for activities along the critical path of the project network is used and the technique is called crashing. The computer simulation model is developed using spread sheet to determine the order in which activities should be crashed as well as the optimal crashing strategy for a project network. The objective is to obtain the optimal crashing configuration to minimize the total project cost.the procedure is as follows. Prepare a simulation model of the project network Identify the potential/ feasibility of crashing each activity in the network and the related costs. Utilize a spread sheet simulation optimization tool to determine the optimal project crashing configuration. The simulation model is used to determine the project duration and the additional project cost (crash + penalty costs). The crashing procedure is illustrated by using the case example reported in the literature (Haga 1998). The project network is shown in Figure 4.16 The activity details of the network along with the precedence relationships are listed in Table 4.9 The activities on this critical path each have a potential of crashing up to 3 time units. The respective parameters of the activity time distributions and unit crashing costs are listed in Table The target completion time of the project is 180. The equation defining the penalty cost for late completion is 0, if T 180 p = 10( T 180), if T 180 where T is the resulting completion time of the project The projects without crashing and optimal crashing configuration were simulated 1000 times to generate the distribution of completion time as

27 89 in Figure and the cumulative distribution of the total project cost as in Figure 4.18 Table 4.11 tabulated the average, standard deviation of the project duration and project cost. Figure 4.17 Manufacturing project network example under study for crashing Table 4.10 Input details for manufacturing project network under study Activity Predecessor Activity Predecessors , , , , , , , , , ,22, , , , ,31, , , , ,35

28 90 16% 14% Probability 12% 10% 8% 6% Original Optimal 4% 2% 0% Duration Figure 4.18 Probability of project completion time Table 4.11 Time estimates and crashing cost for the project activities Activity To Tm Tp Crash cost T 0 -Optimistic time T m- Most likely time T p- Pessimistic time

29 91 Cum m ulative% 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Original Optimal Cost Figure 4.19 Cumulative distribution of the project cost Table 4.12 Comparison between project duration and cost without crashing and with crashing Project duration Project Cost Average Std.Dev. Average Std. Dev. Original Optimal Cost management of projects by Net Present Value (NPV): The expected return on capital for project is the cost of capital. The values of the future net incomes discounted by the cost of the capital are project net present value. The financial success of projects can be efficiently analyzed with simulation. The use of spread sheet simulation for estimating net present value of the project is illustrated. Case example: A car manufacturing company is developing a new model of compact car; this car is assumed to generate sales for the next five years. It has gathered information about the following quantities through focus

30 92 groups with the marketing and engineering departments. Fixed cost of the car is assumed to be rupees 1.4 crore.the fixed cost is incurred at the beginning of year 1, before any sales are recorded. Margin per car is the unit selling price minus the variable cost of producing car. The manufacturer assumes that in year 1, the margin will decrease by 4%.The demand for the sales of the car are the uncertain quantity. The car manufacturer assumes sales-number of car sold in the first year is triangularly distributed with parameters for rupees100000, , and Every year after that, the company assumes sales will decrease by some percentage where this percentage is triangularly distributed with parameters 5%, 8% and 10%.The company also assumes the percentage decreases in successive years are independent of one another. Depreciation and taxes of the company depreciates its development cost on a straight line basis over the lifetime of the car. The corporate tax rate is 40%. Discount rate Figs are cost of capital at 15%. The spread sheet model is developed as shown in Figure 3.11 and by simulation NPV of the project is estimated. 4.4 SUMMARY This chapter presents modeling and simulation of projects using Excel has presented a generic model to estimate completion time and associated probability of success by capturing characteristics of projects such as iterations, uncertainties of durations, delays, complex resource allocation and scheduling. The simulation is performed with and without considering rework probability. Expected Project completion time and resource utilization are evaluated. Using SimQuick simulation software, the Product development project is simulated with unlimited resource environment and constrained resource environment. Simulation can successfully utilized for finding net present value of the projects.