人工知能学会研究会資料
SIG-KST-042-02(2021-11-26)

Decision support for human resource allocation in the context of a multi-projectenvironment using system dynamics modeling
Mst Taskia KHATUN a, *, Kazuo HIEKATA aa Graduate School of Frontier Sciences, The University of Tokyo, Japan

Project management in a multi-project environment(MPE) requires knowledge and experience for project managers to share humanresources across projects. Generally, project-based organizations share resources to regulate and plan the multi-project environment.
This resource allocation process can be elevated through the estimation of required resources by accessing different strategies. In thiswork, a system dynamics (SD) simulation model has been developed primarily as a project dynamic model where the resources areallocated from a shared resource pool. Three different resource allocation scenarios have been explored and computed project
performance through project behavior analysis. The obtained results show the effect of varying resource allocation scenarios on
resource utilization, overtime period, and rework. Our contribution focuses on how a resource-constrained and scheduled-constrained
project management policy can meet planned project performance while working in an MPE with a shared resource pool and knowledge
discovery of expert project managers from simulation results.
Keywords: resource allocation, shared resource pool, multi-project(MP), multi-project environment (MPE), system dynamics(SD)

1. Introduction
In a multi-project environment (MPE), usually, one project
manager leads multiple projects concurrently. Hence, asignificant challenge in an MPE concerns allocating humanresources and scheduling across projects. Resource managementand scheduling problems in MP may differ due to environmental
characteristics, project characteristics, and geographicaldistributions [1]. Furthermore, due to uncertainty, skill, andknowledge of the resources, project priority, it is often difficult
to compute accurate resource allocation to each project [2].
Hence planning proper resource allocation decisions based on
resource-constrained must be made to set resource requirements
policy by designing several scenarios and modeling them in theproblem space explicitly for quickly understanding anddescribing the problem.
Considering these situations, this study aims to develop asimulation model as a decision support system to model
resource-constrained multi-project for effective management of
human resource allocation to the projects. Furthermore, our goal
is to grant managers guidelines for efficient resource allocation
using a shared resource pool to practice based on their primaryobjective and management style.

2. Methodology
2.1 Proposed methodology

A multi-project setting can be regarded as a group of staff
being assigned to multiple tasks simultaneously, all of whichmust be completed within a certain amount of time. Thus,
project workforces are engaged in the form of time-sharing at
the individual level, allocating efforts to numerous projects tosatisfy demands for progress from various project managers atthe same time. Considering this environment, the overview ofthe proposed methodology is shown in Figure 1. The model for
effective resource allocation has been developed using system
dynamics (SD).
i. Qualitative project model+
unaccomplishedtasks+
reworkR2

required
workforces

B3+
error generation
rate+++
B1

B2-+

accomplished completion timetasks

switching
workforcesschedulepressure+

R1
overtime

productivity+

progress-++

Figure 2. CLD for tasks accomplishment process

Figure 2 depicts the qualitative project model regarding
dynamics of effective project task development and resource
allocation parameters as a causal loop diagram (CLD), a part ofSD. The reinforcing loops R1 shows the effect of schedulepressure on progress completion time, and R2 shows therelationship between project task accomplishment and therequired workforces, which causes switching workforces andaffects productivity. The balancing loop B1 depicts therelationship between schedule pressure and its effect onworkforces and project progress. Finally, the impact of schedulepressure on rework, rework with unaccomplished tasks, andcompletion time is shown in Loops B2 and B3.
ii. Project progress mechanism

Figure 1. Overview of the methodology

Figure 3 is a stock-flow diagram built on rework cycles used
as a project progress mechanism to determine each project's
progress rate. Each project consists of tasks referred to as
original work to do. After completing these tasks are referred to＊本資料の著作権は著者に帰属しますas work done. When tasks begin to develop, the error-based tasks
initially move to the stock undiscovered rework. Rework is anerror-based task that must be redeveloped to finish the project,
the stock rework to do increases the number of unaccomplishedtasks. The workforce will be allocated through a shared resource
pool. A shared resource pool and the potential interdependencies
in multi-project organizations create the need for interaction
between the project process and activities to determine how thehuman resources are to be (re)allocated and distributed.
Resource sharing from a shared resource pool has the advantage
of efficient use of the resources.
rework completion
correctly 3

rework error
rate 3
reworkdiscovery 3

rework completion
correctly 1
resource incoming

work done 1
original
progress rate 1
work to do1rework
generation 1
rework to
do 1

rework error
rate 1resourcepool

workforce

productivity

undiscovered
rework 3
workforce

3.2.1. Resource allocation
During project development, we considered the buffer size 0.
Hence a 0% buffer represented a full utilization of the resources
to complete the projects. Since the scope is the same for all
projects, for scenario 1, resources are distributed equally whenallocated to one project until it is finished.

For scenarios 1 and2, since resources are dedicated to the projects, the staff'sproductivity remains the same.
On the other hand, in scenario 3, there is a delay between theswitching from one project to another, productivity is affected
work done 2

original
progress rate 2
work to do2
reworkgeneration 2
rework error
rate 2
reworkdiscovery 2

3.2 Result analysis

projects and thus affect resource utilization. Due to resource

rework completion
correctly 2

rework to
do 2

Resources will be sharedwiththeprojects
whenever a new project
arrives

project arrives, resources are switched and shared among theproductivity

reworkdiscovery 1

resource

project's start time based on project arrival. Hence, when a newresource
outgoing

workforce

undiscoveredrework 1

Sharedscheme

all projects start concurrently. In scenario 2, all resources arework done 3

original
progress rate 3
work to do3
reworkgeneration 3
rework todo 3

Scenario3

adversely. The resource utilization has been obtained while
analyzing the project completion for each project, as shown inundiscovered
rework 2

Figure 4. The impact of resource switching on productivity isshown in figure 5.
productivity

Figure 3. Project progress mechanism

task/person/day.04.03

3. Case study
In MPE, several projects need to be executed either
simultaneously or singularly, depending on project status anddelivery time. Projects in an MPE usually execute
simultaneously. This situation often causes schedule pressure if
there is a resource-constrained problem [3]. In this study, threedifferent projects with the same scope have been considered.
Through the simulation result, the resource utilization for eachproject, the effect of the overtime period, and rework have beendiscussed, which will help to knowledge discovery of expert
project managers.
3.1 Resource allocation scenarios.02.01
04080

Relaxed resource
dedication scheme

320360to resource switching400

3.2.2. Rework behavior
Resource capacity and allocation process, shifting resourcesfrom one project to another, affect project behavior. During thesimulation, resource switching due to new project arrival,productivity, and progress are responsible for rework production.
Figure 6 shows the rework behavior of the projects for eachscenario.

•Scenario
2280

Figure 5. Productivity affects due

Table 1 Scenario list for simulation

Description
Dedicated resources will
be assigned to eachproject, and projects will
start concurrently
Resources
thatarefinished on one project
are allocated to newprojects. The project will
start one after another200 240
Time (Day)scenario•Scenario type
Resource
dedication scheme

160

Figure 4. Resource utilization of each

Since we considered a shared resource pool, hence based on
projects’ deadlines and resource requirements, three different
scenarios have been evaluated in this study for project behavior
check, as shown in table 1.
No.
Scenario1120

overall productivity•

Peak is affected by
the number projects
developed at atime.
1 project low peak,
3 projects high peak
Resource switchingcauses ups anddown to the peakvalue

Figure 6. Rework behavior of all scenarios

For scenario 1, when projects start simultaneously, rework foreach project also happens accordingly. Because three projects
are being developed simultaneously, the amount of rework is
substantial in this situation. In scenario 2, since projects arecompleted one after another, the amount of rework has been
depicted separately. Rework generation is affected by the
number of resources and the project duration. Switchingresources depending on new project arrival affects productivity
and progress, resulting in delayed rework production in projects
evolving under scenario 3. However, because there is aconcurrency between projects, the quantity of rework becomessignificant. Therefore, the project manager can depict theimpression of a resource sharing scheme on rework in an MPE
through the rework behavior.
3.3.3. Overtime impact
While working in a resource-constrained and scheduleconstrained environment and resources are allocated from ashared resource pool, overtime is obvious to meet the project
deadline. During our analysis, overtime has been computed
based on the gap between the expected completion time and thedeadline. Since rework increases unaccomplished tasks, it also
causes overtime to meet the deadline. The working hour isrepresented by AFMDP (Actual Fraction of Man-Day in aproject). When the workforces work with nominal working
hours, the value of AFMDP is 1. However, working overtime
increases the value of AFMDP is > 1. Figure 7 shows theovertime impact for each scenario.

Figure 7. Overtime impact to all scenarios

The overtime behavior for each scenario happens as follows
Scenario 1•
Overtime happens later due to longer duration•Since rework goes to peak slowly, it requires highovertime later
Scenario 2•Overtime happens earlier as projects are happening assingle•
Requires low overtime as resources are high and happen
for a long time
Scenario 3•
Overtime happens moderately as resources are averagedue to resource switching•
Since rework
goes to peak, moderately overtime
finished earlier•
Resources switching causes starting overtime earlier thanscenario 1
The obtained results show the effect of the allocation strategies
on resource utilization, rework, and overtime. In an MPE setting,the generated resource allocation results serve as a usefulparadigm for assessing the interplay among project performancevariables and the effects of managerial decisions for resource
allocation.

4. Discussion
The proposed SD project dynamic model exhibits an approachof resource allocation from a shared resource pool, affecting theMPE’s potential to accomplish planned project milestones. Thisoutcome is beneficial when working in resource-constrainedMPEs. Projects are intended to be executed on time with this
fixed capacity, relying on the workforce to work overtime. As

explained through the scenarios, the arrival of new projects
causes resource switching and affects project performance
behavior. Furthermore, the presence of rework causes the same
effect. Hence, when the resource capacity is fixed, and a sharedresource pool is used to allocate each project, our proposed
method gives a proposition of using a resource allocation
scheme and an excellent way to handle project performance.
i.
Dedicated resources are assigned to every single
project in the multiple-single project setting. Throughthis scheme, the resource allocation problem issettled at the beginning of the projects. As a result, thecomplexity of controlling the portfolio of projects inexecution is comparable with controlling a single
project.
ii.
Using a relaxed resource dedication scheme, a project
can obtain full staffing in the early stages to meet thedue date more quickly. But in this case, the focus is asa single project environment mainly focused on theindividual project’s performance characteristics.
iii.
For a shared resource scheme, a shared resource poolis used for resource switching by all projects in theportfolio. Thus, it has the advantage of efficient use ofresources. However, switching resources from one
project to another causes a delay and conflict if there
is a lack of resources.
The resource allocation in a multi-project setting is complex.
Hence our proposed method acts as a decision support system
for resource allocation strategies which gives an explicit
impression on project performance behavior, including theuncertainty of rework generation. Moreover, project managers
can trace the issue of needing and sharing the resources from ashared resource pool, resource availability, and interdependency
between projects and operations to be a complication in an MPE.

5. Conclusion
We have developed an SD simulation model as a decisionsupport system to model resource-constrained multi-project foreffective management of human resource allocation. We
performed the case study by exploring three different resource
allocation scenarios. The simulation results would help
understand efficient resource allocation and its impact on
performance while working in an MPE. Project managers canuse this allocation category based on their primary objective andmanagement style.
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