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1. AN APPLICATION OF VOLUNTEER SCHEDULING AND THE PLANT LOCATION PROBLEM: A
CASE STUDY OF THE USACF PROGRAMME
Ayisolwainkosi Ncube
National University of Science and Technology, Faculty of Applied Sciences, Department of Mathematics, P.O
Box AC 939, Ascot, Bulawayo, Zimbabwe, Email:ayisoncube@gmail.com
Abstract
This case study presents the results of the Volunteer assignment model and a Plant Location model for the
USACF programme that is run by the non-profit Zimele Institute. The two stage capacitated plant location
model (TSCPLP) is formulated in order to reduce the distribution costs associated with the educational
paraphernalia the institute distributes. The TSCPLP model formulation took advantage of the infrastructure that
the Institution and its partners have. A volunteer labour assignment model is also formulated in order to
maintain and manage the pool of volunteers. The two models were formulated and solved in LINGO 10.An
efficient frontier was plotted for the volunteer assignment model. The optimal solution for the TSCPLP
identified the set of suitable warehouses and depots. The solution indicated that the current distribution costs
would be reduced by 41%.This paper would be particularly of interest to practitioners in development logistics,
operations research and management sciences.
Keywords: Volunteer Scheduling, Plant Location, Integer programming, Zimele Institute, Non Profit
Organisations, Operations Research, Humanitarian OR

2. 1.0 Introduction
The Zimele Institute is a Zimbabwean non-profit organisation whose purpose and obligation is to fight poverty
and foster development through education at grassroots levels in rural communities. The Organisation runs a
Fellowship programme that links 35 American Schools with 75 Zimbabwean Schools. The Zimbabwean
Schools receive donations of various materials such as clothing, textbooks, stationery, science equipment and
sporting equipment from the American schools. A shipment of all this paraphernalia is received at the Institute’s
main warehouse in Richmond and then distributed to the 75 partner schools. The programme has been affected
by high transportation costs and the resigning of the volunteer labour force that assists in sorting out and
distribution processes of the shipment.
Hillier and Lieberman (2009) loosely define Operations research as an approach that resemble the way research
is conducted in established scientific fields. It is applied to problems that concern how to conduct and coordinate
the operations within an organisation. Ergun et al (2013 points out that humanitarian OR differs from other OR
applications because it deals with particularly unique and variable events, often in resource poor and limited
infrastructure environments.
Ergun et al (2013) says disaster supply chain management is a new area with potential to have a positive impact
in society. Martinez et al (2010) in his publication says Operations Research (OR) has a valuable role to play in
the assisting of humanitarian organisations in order to improve operations. His assertions were exemplified by
discussing several applications of OR in the Haiti earthquake that occurred on January 12 2010.Table 1 below
shows an example of how operations research can be applied to address challenges that humanitarian
organisations face
Stage/ Cluster Main Operations research problems First weeks of response
Search and Rescue(SAR) 1. How to optimally deploy the rescue teams in vast urban area
2. How and where to transport rescued patients with grave traumatic injuries and
urgent surgery needs to maximise their chances of living
Access and Logistics 1. How to prioritise the use of ramp space at the airport
2. How to efficiently plan the use of heavy equipment to clear the roads
3. How to minimise fuel consumption in a road network with uncertain available
paths
4. How to prioritise repair efforts to guarantee access by the sea in the presence
of dynamic and noisy seaport capacity seaport assessments
Health 1. How to allocate scarce medical personnel and limited medical supplies to
demand points in an efficient way.
2. How to establish mobile open air hospitals provided by different humanitarian
organisations
Food Aid 1. How to transport the required amount of food to Haiti
2. What warehouses are used to stock food items
3.How many distribution points to use
4. Where to locate the distribution points to optimise the trade-off of coverage
vs. security
Table 1: Summary of main OR Problems faced during the immediate response phase after the Haiti earthquake-
source Martinez et al (2010)
In this case study the focus is on the Fellowship programme that the institute runs, a volunteer assignment
model is utilised and a Two stage Capacitated Plant Location Model (TCPLP) are utilised in order to try and
improve the process of sorting and distributing the educational paraphernalia. The volunteer allocation model
aims to ensure that the tasks at hand are dealt with swiftly and at the same time maintaining the volunteer
morale. On the other hand the TCPLP model aims to reduce the high costs associated with distributing the
shipment.
The plant location problem is concerned with locating facilities for operations in order to operate at optimal
levels by reducing transportation costs. According to Wildbore (2008) the problem of locating plants and
facilities has been researched under the name of plant, facility or warehouse location problem and these names
refer to the same principles and are interchangeable. The area of the (TSCPLP) is relatively new but its
foundations are rooted in the capacitated plant location (CPLP), which is a mixed Integer Linear Programming
model with potential plants that have limited capacity. As a result the solution methods that are readily available
for the TSCPLP are those that were initially developed for the CPLP.

3. In the TSCPLP there are three stages, where there are three decision levels. Warehouses or Production plants are
in the first level and the decision under consideration will be which sites to open. The second stage is the
distribution depots and the decision is how many depots to open and which ones. Finally the third stage involves
customers and the decisions to be made here are to assign customers to specific depots. The figure 1 below is an
illustration of this model
Figure 1: Two stage capacitated plant location problem
The plant location has been used in various applications beyond logistics or the planning of distributions.
Tanebaum (1981) discusses an application in the design of telecommunication networks. The problem was one
of access design, in which concentrators must be located to connect terminals to a central processor. This
particular problem is often modelled additional facility becomes a negative valued and solved as a plant location
problem.
Heuristics have been the prevalent solution method for this problem the common one being the ADD heuristic
which falls under the class of greedy heuristics. The Heuristic opens facilities one at a time until the marginal
saving for opening an additional facility become negative. Most solutions for the CPLP are adaptations of the
algorithms of the incapacitated problem.
A volunteer is any individual who offers him/herself to a service to a service without an expectation of monetary
compensation, Shin and Kleiner (2003).Volunteer management has gained interest in the social sciences in
recent years. The different areas that have been researched include the motives for volunteering. According to
Van Vianen (2008) the incentives for people volunteering are opportunities for personal growth, recognition,
achievement and a desire to contribute to the community. Lammers (1991) says issues with regards to
demographics are also a factor characteristics such as education and gender .The subject of retaining volunteers
and the analysis of practises that encourage renewed volunteerism is key in volunteer management. Gidron
(1984) for example cites task achievement and the quality of the work itself as some of the variables that could
better predict volunteer retention.
There are numerous features that separate a volunteer decision model from a profit making model, the table
below by Sampson (2006) gives an account of some of these differences. The differences shown are very useful
in the formulation of any volunteer assignment model.
Potential Plants
…………..
…………..
…………..
Potential Depots Partner Schools
1
2
n
1
2 2
m
k
1

4. Table 2 Differences in models.
Model Attribute Paid workforce Volunteer Workforce
Objective Maximise profits by minimising labour costs Maximise task completion by minimising
shortages
Key Constraint Required tasks Committed Labour
Labour costs Non trivial Low yet
Labour pool size Assumed to be sufficient or unconstrained Determined by size of committed labour
Labour Preferences Some models consider time preferences Models must consider volunteers time
and task preferences
Task Labour
Shortages
Not an Issue Shortages need to be balanced among
tasks
In this study all the programme operations are discussed and formulated in the section that follows. Section 3
gives a detailed account of the methodology and model computational results. Finally section 4 concludes the
study.
2.0 Description of programme operations
The procedure of bringing these shipments starts off with liaising with the American partners about feasible
arrival dates in order for the Institute to be able to arrange warehouse space and mobilise volunteers in ample
time. Once the shipment arrives in Zimbabwe it is transported to the main warehouse in Richmond, Bulawayo
where the headquarters of the organisation are located .At the warehouse during the offloading process the
contents which are usually packaged in boxes are placed categorically The stages listed below describe what
happens once the shipment is in the warehouse. Volunteer labour force is usually available during all these
stages.
Stage 1: Offloading contents off the shipping container.
Stage 2: Placing of contents in designated areas of the warehouse according to the box labels.
Stage 3: Counting and verification of boxes.
Stage 4: Opening boxes and grouping of similar contents.
Stage5: Counting and recording the grouped contents of the boxes.
Stage 6: Assigning the contents to partner schools
Stage 7: Packaging and labelling of boxes to be distributed to partners
Stage 8: Restacking boxes and grouping them according to their geographical clusters
Stage 9: Loading distribution trucks
The educational paraphernalia is delivered to all 75 schools individually however this has turned out to be a
costly exercise for the organisation since they rely on donor funding.
Since the organisation works with a volunteer labour force through most of these stages and the ability to hire
extra labour force is not guaranteed, it has become a challenge for the organisation to strike a balance between
utilising the available volunteers and the making sure they do tasks that are fulfilling and they are comfortable
with. Furthermore the transportation costs to each partner school are high thus there is need to explore other
alternatives in the distribution process
This study seeks to optimise the use of volunteer labour force and minimise the distribution costs, this has also
been necessitated by the fact that the organisation is considering expanding the programme to include more
partner schools from their operational provinces. This will be done by investigating possible combinations in
different stages that would allow the shipment to be processed in the least possible time and maintain the
existing pool of volunteers by assigning them tasks they comfortable with. Overall the study endeavours to
create an effective way of managing the activities of the programme.

5. 3.0Methodology
3.1 Volunteer Assignment Model Formulation
In a given week the Institute’s warehouse has four working day shifts that span 7.5 hours and a single 4.5 hour
working shift. Data collection on the number of volunteers at different stages of sorting the shipment was
collected and analysed. The results of this survey helped in determining the minimum number of volunteers to
be assigned at every stage. These statistics were then fed into the Volunteer assignment model. A survey was
also carried out to determine the volunteers’ task preferences. These findings influenced the model formulation,
for example to split the volunteers into males and females in the formulation. This was necessitated by the
discovery that most females didn’t favour the physically demanding arduous activities whilst the males seemed
not to mind
A binary integer model was formulated. The model had two conflicting objective functions which were:
1) Utilise the available volunteers to the fullest extent regardless of their preferences in order to finish
off tasks at the earliest time possible.
2) Ensure that volunteers were assigned to tasks they preferred in order to try and keep the current
pool of available volunteers.
The Integer Programing (IP) model is as follows:
Objective Function 1:
Maximise
∑ ∑ ∑ (1)
Objective Function 2:
Minimise
∑ ∑ ∑ (2)
Subject to:
∑ , (3)
∑ , (4)
∑ =0 , (5)
∑ ∑ ∑ (6)
Where
I = the set of all volunteers
J= the set of all stages in the model
K=the set of all tasks in the model
= set of all volunteers who do not prefer to do stage j
if a volunteer prefers not to be assigned to stage j
u = maximum number of shift blocks to assign to female volunteer i
e = minimum number of shift blocks to assign female volunteer i
h = maximum number of time blocks to assign to male volunteer i
f = minimum number of time blocks to assign to male volunteer i
= minimum number of volunteers to assign to stage k task j
Decision variables:
= assignment of a female volunteer i to stage j task k
= assignment of a female volunteer i to stage j task k
{ }

6. Objective function (1) is to utilise the current volunteer labour to its fullest extent, while on the other hand
objective function (2) aims at minimising the assignment of volunteers to tasks they do not prefer. Constraints
(3) and (4) make it a point that that the pool of volunteers available is fully utilised bearing in mind the survey
findings that indicated that volunteers want to be useful. Constraint (5) ensures that female volunteers are
assigned to tasks they prefer the most. Constraint (6) includes the findings of the survey that ensured that the
minimum number of volunteers that would ensure minimal delays in the warehouse.
The above formulation was solved using LINGO 10. The initial step was to solve objective function 1 subject to
all constraints. After solving the first formulation it is assumed to be pareto optimal. To find other pareto
optimal solutions the initial model is solved but in this instance objective function (2) is a constraint and the
Right Hand Side (RHS) values are assigned arbitrarily as shown below:
∑ ∑ ∑
The values of objective function 2 were varied to obtain different values for objective function 1. The values of
the two objective functions were then plotted and the result was a trade-off curve.
The figure below shows the general relationship of the efficient frontier after plotting the values of the two
objective functions against each other. This was done using several combinations of past pools of volunteers that
have been available to the organisation in the past.
3.2 Optimal Solution
Using the data on past volunteer teams available the data was factored into the model to generate solutions. The
plots of the two objective functions indicated a linear relationship that becomes constant after a certain value is
reached .The general shape of the efficient frontier is shown below in figure 2. The frontier revealed that a linear
relationship exists between maximising the utilisation of the labour force and assigning volunteers to tasks they
preferred. Therefore taking into account when the shipment arrives and the level of urgency that is needed to
sort out and distribute the shipment to the partner schools, the decision maker will select a point in the efficient
frontier and implement the volunteer assignment.
Figure 2: Plot of objective function 1 vs. Objective function 2
3.3 The Plant Location Problem
A variation of the Two Stage Capacitated Plant Location Problem (TSCPLP) was formulated, the model is
different from the traditional model in that:
i) The available warehouses did not supply every depot from the initial formulation.
ii) Some of the depots served as depots and destinations.

7. The capacitated plant location model is useful in scenarios where there is need to minimise transportation costs
and satisfy demand from customers. In this case focus was on one province, which is the Matabeleland North
province where there are the customers are the 25 partner schools that receive the educational paraphernalia.
The formulation is as follows:
Objective function
Minimise
∑ ∑ ∑ ∑ ∑ ∑ (1)
Subject to:
∑ , (2)
∑ , (3)
, I, (4)
∑ , (5)
∑ ∑ , (6)
0 , (7)
Where
I= {1,….,25} is the set of partner schools
J= {1,……8} is the set of potential depot locations in partner schools
K= {1,…...4} is the set of potential warehouse locations in development centres
= total cost of transporting from depot j to serve location i, I,
= fixed cost associated with depot j,
fixed cost associated with plant k.
=unit cost of transportation from plant k to depot j, K,
=demand of destination I,
=capacity of depot j,
=capacity of plant k,
Decision Variables
=fraction of demand of the destination I supplied from depot j
={
=units of demand transported from plant k to depot j
={
The objective in this model is to minimise the costs of setting up of plants and depots including the
transportation costs of moving the educational paraphernalia from the warehouses to depots and from depots to
the respective partner schools. Constraint (2) stipulates that the depots should satisfy the demand at the
destinations. Then constraints (3) makes sure that the functioning depots don’t supply more than what they are
capable of supplying. Constraint (4) does not allow a scenario where a closed depot is active. Constraint (5)
ensures that the active plants do not exceed their capacities when making supplies .Constraint (6) is a
conservation of flow constraint.
3.3.1 Model Implementation and Computational results

8. The shipment size and the schools’ demand for paraphernalia varies with time, thus one shipment scenario was
chosen for analysis. The scope of this particular application was only in one of the three provinces of operations
i.e. Matabeleland North. In general the objectives of the model were to identify:
i) Suitable warehouses from a set of possible warehouses each for sorting and storing the shipment
with a maximum capacity and fixed costs.
ii) Suitable potential depots locations from a set of possible depots with each having demand and unit
transportation costs
Potential Warehouses
A warehouse’s function includes storage, reorganising and repackaging. In this instance the warehouses
were useful for storing and sorting of the shipment. For the Matabeleland North province the Richmond,
Hwange Development Centre (DC), Nkayi DC and the Tsholotsho DC warehouse were all under
consideration.
The criteria that was utilised for selecting the set of possible warehouses to be included in the model were
security, accessibility, practicality and availability of space during the period of shipment deliveries. Data
on fixed costs associated with plants and the holding capacities was collected in order to input into the
formulation. Table 3 below shows the capacities and fixed costs associated with these warehouses. The unit
size referred to is uniform sized boxes that were used for repackaging the shipment.
Table 3: Potential Warehouses
Warehouse Capacity(units) Fixed costs (US$)
Richmond 850 2150
Hwange 100 2500
Nkayi 250 2300
Tsholotsho 85 2400
Potential Depots
Depots in this context were taken to be school libraries and storerooms that can be utilised but they also had
attributes such as fixed costs and capacity associated with them. The depots were selected on the basis of their
accessibility and security. Table 4 below lists those potential depots.
Table 4: Potential Depots
Depot Capacity (units) Fixed costs (US$)
Bethseda 80 280
BH 36 70 350
Bubude 70 300
Siyangaya 85 320
Longwe 70 290
Lukona 60 275
Nkayi High 100 310
Nkayi Primary 90 280
Since some of these depots are not fully controlled by the Zimele Institute the assumption was that all these
depots are fully available during the distribution process.
Depot destination (Partner schools)
The graph below shows the 25 Partner schools in the province and the units that were allocated to each school.

9. Figure 3: Partner schools Demand
3.3.2 Model Results
In the model formulation there were a total of 4 warehouses and 8 depots that were intended to supply 25
partner schools. The binary Integer programming model was formulated and solved using LINGO 10.
Optimal solution
The optimal solution was US$ 4605.95 which is a huge saving comparing with US$7802.50 that was spent by
the Zimele Institute in doing the same exercise this translates to 41% in savings.
Appropriate warehouse
All warehouses are included in the optimal solution. Since only the main Richmond warehouse is fully
controlled by the Institute, sensitivity analysis was carried out in order to find out how the unavailability of these
other warehouses affects the costs incurred during distribution.
Hwange warehouse: If the Hwange warehouse is unavailable the Richmond warehouse takes over the
allocations however this would increase the distribution costs to US$ 4679.85
Tsholotsho Warehouse: Similarly when the Tsholotsho warehouse is unavailable the Richmond warehouse is
utilised. The optimal solution then becomes US$ 487.95
Nkayi warehouse: In the event that the Nkayi Warehouse is unavailable the Richmond warehouse also takes
over and the costs become US$4878.95
Table 4 below summarises the sensitivity analysis with closing each warehouse.
Table 4: Warehouse Sensitivity analysis
Closed Warehouse Percentage
increase of
optimal Value
Hwange 1.68%
Tsholotsho 0.33%
Nkayi 5.8%
The use of all warehouses in the distribution process is complimentary in reducing the distribution costs. The
model relies heavily on the Richmond warehouse, it was utilised in all scenarios because it has a large capacity.
The operating costs shoot up because of the distance of the warehouse from the depots and that. It is located
further from the depots than the rest of the warehouses. The scenario where storage space is not available at
Hwange and Tsholotsho will not amount to a lot of expenses but it might cause logistics challenges since the
15 15 16 15 16 15 13
16 17
20
15
18
14
17 18 17
22
16 14
23
35
38 40
36
41
Bethseda
BH36
Chewumba
Ndlovu
Chimbombo
Simakade
Jabula
Mizpah
Soluswe
Shaba
Dikili
Mbalibali
Bubude
Sec
Bubude
Pry
Lukona
Guwe
Pry
Guwe
Sec
Thame
Longwe
Mangubeni
Dimpamiwa
Mdlawuzweni
Hlangabeza
Nkayi
High
Nkayi
Pry
Demand (units)
Demand (units)

10. depots are far apart. This then indicates the importance of planning in advance and making sure other
warehouses in the model are booked in advance before the distribution exercise commences.
Appropriate depots
All depots were included in the optimal solution. Table 5 below shows the level of utilisation of all depots.
Table 5: Depot Utilisation
Depot Origin
Warehouse
Units
received
Depot
Utilisation
Bethseda Richmond 9 97.5%
Hwange 69
BH 36 Hwange 31 44.3%
Bubude Richmond 36 51.42%
Siyangaya Tsholotsho 84 99%
Longwe Richmond 70 100%
Mangubeni Richmond 40 66.67%
Nkayi High Nkayi DC 36 32.73%
Nkayi Pry Nkayi DC 119 95.2%
The Bethseda, Siyangaya, Longwe, Lukona and Nkayi Pry Depots are highly utilised and this is largely due to
their close proximity to the partner schools. These utilisations could also be indications on how to assign
volunteers in future.
4.0 Conclusions
This paper has presented a volunteer labour scheduling model and a TSCPLP model .The volunteer model took
into account their preferences and making sure the tasks were completed on time. The intention of introducing
these models was to have better management of the volunteer labour force and reduce distribution costs. The
solutions found for the volunteer scheduling model created a greater understanding and control of how to work
with Volunteers. On the other hand distribution costs of the shipment could be reduced by up to 41% if the
TSCPLP model is adopted. After formulation and utilising numerical examples in LINGO 10, integer
programming models were solved to obtain optimal solutions.
This case study has shown that volunteer management problems and Two stage capacitated Plant Location
Problems can be solved easily in the context of humanitarian organisations.

11. References
Ergun O,Karukus G,Keskinocak P,Swann J,Villarreal M.2013. Operations research to improve disaster supply
chain management. Available on http://eu.wiley.com
Gidron B 1984. Predictors of retention and turnover among service volunteer workers, Journal of social Service
Research,8,1,1-16.
Hillier, F. & Lieberman, G.2009. Introduction to Operations Research 9th Edition, McGraw-Hill
Science/Engineering/Match, Columbus OH.
Lammers J 1991. Attitudes, motives and demographic predictors of volunteer commitment and service duration,
Journal of social Service Research, 14, 3/4,125-140.
Martinez AJP,Stapleton O, Wassenhove LNV. Using OR to Support Humanitarian Operations:Learning from
Haiti Earthquake Available on http://www.insead.edu
Sampson S,E 2006 Optimisation of volunteer labour assignments, Journal of operations Management,24,4,363-
377.
Shin S and Kleiner B 2003, How to manage unpaid volunteers in Organisations, Management Research
News,26,2,63-71.
Tanenbaum A,S, 1981 Computer Networks Prentice-Hall, Englewood Cliffs, NJ.
Van Vianen A , 2008, A person-Enviroment Fit Approach to Volunteerism: Volunteer Personality Fit And
Culture Fit as Predictors Of Affective Outcomes, Basic and Applied Social Psychology,30,2,153-166.
Wildbore B, L,2008 Theoratical And Computational Analysis of the Two stage capacitated Plant Location
Model, Available on http://mro.massey.ac.nz/bitstream/handle/10179/660/02whole.pdf
Acknowledgements
Thanks to the Management of the Zimele Institute in providing relevant data for both models and for the
assistance they provided in the collection of new data for the volunteer management model. Special mention
goes to Miss Gudoshava and Mr M Moyo. Thanks also to the National University of science and Technology
for providing research facilities.