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2. There is no standard format for the final document but make sure you treat this case
study as a professional technical report.
3. Make sure to include any analysis, tables, spreadsheets as part of your report.
4. Make sure to provide any reference when you cite work performed and/or published
by others.
Evaluation Rubric:
Criterion
Wt (%)
Content and
Context
70%
Organization
20%
Grammar
10%
Novice
50%: Two or more
required elements of the
question missing or not
fully addressed.
50%: Answers not clearly
organized; contains several
logical errors.
50%: Major grammar or
spelling errors or contains
significant grammar errors.
Level of Achievement
Competent
75%: Answers organized
but may contain one minor
logical argument error.
Proficient
100%:
All
required
elements
of
question
addressed
fully
and
clearly.
100%: Answer clearly
organized and contains no
logical argument errors.
75%:
Multiple
minor
grammar or spelling errors.
100%: 5 or fewer
grammar or spelling errors.
75%: One required element
of question missing or not
fully addressed.
1
The Washington Metropolitan Area Transit Authority (WMATA) is the transportation
infrastructure serving the DMV area providing rapid transit, fixed-route bus, and paratransit
services. WMATA has hired you to identify opportunities to optimize the transportation assets
operation and maintenance activities and assigned you two (2) specific task orders.
Task Order #1: Inventory policy optimization for bus and paratransit services maintenance
activities.
Vehicle’s Fleets Information
I.
WMATA has the following preventive maintenance (PM) schedule:
II.
Fleet
model
Units
Model-A
Model-B
Model-C
100
85
50
Fleet
model
Units
Model-A
Model-B
50
50
Oil per
service
(gallons)
12
10
18
Fixed-route buses fleet
Standard time
Service
per service
frequency
(hrs.)
Monthly
1.5
Bi-monthly
2
Monthly
1
Cost per service
(USD)
(L+M+OH)
$125
$100
$105
Oil per
service
(gallons)
5
5
Paratransit buses fleet
Standard time
Service
per service
frequency
(hrs.)
Bi-monthly
1
Bi-monthly
0.75
Cost per service
(USD)
(L+M+OH)
$25
$18
Support Facilities Information
1. Maintenance Facilities
• WMATA’s maintenance facilities has capacity to serve 50 units per day.
2. Supply Chain Process and Warehouse Facilities Information
• WMATA’s has allocated space in the warehouse to store 1-month worth of inventory.
• WMATA buys the oil in bulk at $3 per gallon discounted to $2.75 per gallon if the order
quantity is more than 3000 gallons.
• WMATA has a storage cost of $0.025 per gallon per day.
• The transactional cost (i.e., placing the order) is $75 per order and 3-day lead time.
WMATA wants to explore shorter lead time.
III.
Analysis outcome:
• Determine the optimal inventory policy
• Submit recommendations to WMATA
o Document and present underlying assumptions (if any) used to conduct your
analysis and to present your recommendation
2
Task Order #2: Overhaul and Inspection Processes Cost Reduction
WMATA has three (3) main rail yards in three jurisdictions, DC, MD and VA, where specialized
overhaul is performed to the train cars. After the overhaul, the train cars need to go to one of the
two (2) inspection centers in MD or VA where train cars must go for detailed inspection before
they are in service again. The quarterly capacities for the rail yards are 120, 150, and 120, and the
demands at the two inspection centers are 230 and 140 train cars.
Table 1. Mileage Chart
MD
VA
DC
MD
VA
10
5
12
20
15
8
Table 2. Transportation Cost per
Car
MD
VA
DC
MD
VA
$800
$500
$550
$1,000
$1,250
$600
Analysis outcome:




Represent the process in a diagrammatic for using the transportation model with nodes and
arcs.
Represent the process using linear programming (LP), including the objective function and
constraints.
Present the optimal solution to WMATA.
Document and present underlying assumptions (if any) used to conduct your analysis and to
present your recommendations.
3
Do you see that (C21) it has ( = (B18-B14)*0.025)
But (C22) has ( = (B19-B15)*0.025)…. How come like that!!!
There is nothing in (B19)… all schedule like that check it again!!
What is this
number?
From where?
Why is that?
Task 1:
: ordering cost per order,
: average demand p.a,
ℎ: inventory holding cost,
: order quantity
Q=√
2

Q=√
2(57600)(75)
(0.025∗30)
Q = 3394.113 or 3395 gallons per order.
Total orders in an year =

Total orders in an year =
57600
3395
Total orders in an year = 17 orders
The transit system should make a total of 17 orders per year with a quantity of 3395 gallons per order
which makes the cost $9336, which is an 8.34% discount per order. This further results in 17 orders per
annum to fulfil the average annual demand.
Assumptions;

Each unit is only held for 30 days in a given year averagely
The average demand is the same as this year’s demand
Task 2:
From
To
MD
VA
Supply
DC
$800
$1000
120
MD
VA
Demand
$500
$550
230
$1250
$600
140
150
120
= 800 1 + 1000 2 + 500 3 + 1250 4 + 550 5 + 600 6 , ℎ
1 , 2 , 3 , 4 , 5
The linear programming problem is to minimize Z subject to the constraints
1 + 2 ≤ 120 3 + 4 ≤ 150 5 + 6 ≤ 120 1 + 3 + 5 = 230 2 + 4 + 6 = 140 ≥ 0
The optimal solution for this case comes out to be (80, 20, 150, 0, 0, 120) with a Z value of $231,000.
From
To
MD
VA
DC
80
20
MD
VA
150
0
0
120
This is an unbalanced transportation model problem, it is assumed that the rail yards, specifically the rail
yard in DC can double as virtual inventory since supply exceeded demand in this case. The problem was
also optimized with a biasing condition of making sure the demand remains completely fulfilled and the
supply surplus is added to inventory.

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