ISyE 3104 – Fall 2012
Homework 10
Due Tuesday October 30, 2012 (30 points)
1. (6 points) Answer briefly (one paragraph) the following questions about the “Big Depot
Hurricane Planning Game”.
a. (2 points) Two common decisions for disaster planning were analyzed in this case study:
to contract and reserve inventory in advance, and to allocate the reserved inventory.
Discuss other (at least two) important decisions to prepare and respond to a disaster in an
efficient and timely way.
Solution:
Most of supply chain management processes and decisions apply: how to forecast the demand,
how to transport (routes, mode) supplies to required locations, etc. However, decisions must take
into account the very uncertain setting of a disaster and be robust enough given the different
possible outcomes. For example, while deciding the best transportation mode or the best
transportation route, the decision maker should consider damaged road infrastructure, airport
possible conditions, etc. When forecasting the demand, we need to make sure the assumptions
made consider the possibility of extreme scenarios of damage, as it is the case in a disaster
setting.
b. (2 points) Demand uncertainty (size and location) was identified in this case study as a
very important logistics challenge when planning for a disaster. Discuss other (at least
two) logistics challenges that may not have been explicitly mentioned, but that could
arise in disaster planning and response. How are these challenges similar or different
from the ones faced during day-to-day operations of a company such as Big-Depot?
Solution:
There is not only demand uncertainty in size and location, but there is also uncertainty in timing.
This timing uncertainty requires a constant state of preparedness from the supply chain which
could be achieved with strategies such as inventory propositioning. Also, there is uncertainty in
supply. Suppliers’ supply chains may be disrupted as well, compromising the timely delivery of
the supply, or high demand items might become scarce. There is a strong dependency of lastmile operations on the disaster severity, e.g. transportation infrastructure might be disrupted, or it
might require equipment that may not be locally available. Information and communication
might be limited as well, stressing the management and control of operations. There are multiple
players involved in the disaster response (NGOs, military, government, etc.) and efficient
collaboration could be challenging given the different objectives and incentives of the players.
Even though supply chain decisions are somewhat similar to day-to-day operations (inventory,
purchasing, transportation, etc.), disaster response poses additional challenges beyond traditional
supply chain planning, which means additional opportunities on how operations researchers and
supply chain management professionals could apply their knowledge and skills to positively
impact lives.
c. (2 points) The given budget for the purchasing decisions in the Home Depot game is
$950,000. If the budget is increased, what would happen with the minimum expected
total purchasing cost (expected cost of reserved plus expedited quantities)? Explain.
Solution:
First, assume that there is not a budget constraint. Then, the optimal quantities for this
unconstrained problem (the News Vendor quantity for each product in this case) may require a
larger budget. In that case the quantities will need to be adjusted, but then this implies that new
expected minimum cost cannot be smaller than in the unconstrained problem since these adjusted
quantities were also a feasible solution in the unconstrained problem. Increasing the budget
makes the problem less constrained, and a less constrained problem will have an equal or better
(expected) objective value. In this specific case, the budget constraint is binding (the News
Vendor quantities exceed the budget), so if we increase the budget the minimum expected
purchasing cost value should decrease.
2. (18 points) A company manufacturers item X. The product structure is described below. The
number in parenthesis is the lead time for purchasing or making the given component.
 Item X:
o Composed of 1 unit of component A, 1 unit of component B and 2 units of
component C.
 Component A (1 week):
o Composed of 2 units of component B and 1 unit of component D.
 Component B (2 weeks):
o Composed of 2 units of component D and 3 units of component E.
 Component C (2 weeks)
 Component D (1 week)
 Component E (1 week)
a. (4 points) Draw the product structure.
Solution:
b. (2 points) What is the lead time of making the item X from scratch? Explain.
Solution:
We assume no inventory is available (made from scratch) and that ordering and/or making tasks
can be done in parallel when possible (no restrictions on capacity are given). The lead time is
four weeks. First order D and E and after 1 week both components are available to make B. Then
after 2 weeks B is ready. After that, it takes 1 week to make A. This makes a total of 4 weeks.
Component C can be made/order in week 2.
We can also find this by looking at the critical route in the diagram below. The arrows show the
time needed to be in that position of the product structure. For instance it takes 3 weeks to have
component B ready (arrow above B).
c. (1 point) The demand for item X for weeks 5-15 is given below. The company has an
initial inventory of 20 units of item X and wants a final inventory of 30 units at the end of
week 15. Determine the net demand for weeks 5-15 of item X.
Week
Demand
5
90
6
80
7
70
8
100
9
110
10
120
11
90
12
85
13
80
14
80
15
70
Solution:
To compute the net demand we just need to subtract the initial inventory from the demand in
period 5 and add the final inventory to the demand in period 15.
Week
Demand
Net Demand
1
2
3
4
5
90
70
6
80
80
7
70
70
8
100
100
9
110
110
10
120
120
11
90
90
12
85
85
13
80
80
14
80
80
15
70
100
d. (4 points) Determine the planned order release (lot for lot) for component B.
Solution:
Since component B is needed for both item X and component A, we need to determine when
these components A are going to be produced so we can make sure we have enough units of
component B. From c), we know when we are producing item X. We now need to compute the
same for component A, which is equivalent to compute the planned order release for A.
Component A planned order release:
Week
Gross. Requirements
Net requirements
Time‐phased
Planned release
1
2
3
4
70
70
5
70
70
80
80
6
80
80
70
70
7
70
70
100
100
8
100
100
110
110
9
110
110
120
120
10
120
120
90
90
11
90
90
85
85
12
85
85
80
80
13
80
80
80
80
14
80
80
100
100
15
100
100
Now, we can compute the gross requirements of B. At each period we add the production of item
X plus the order release of A times 2 (since two units of B are needed for each unit of A
produced)
Component B planned order release:
Week
Gross. Requirements
Net requirements
Time‐phased
Planned release
1
2
3
140
140
230
230
4
140
140
220
220
5
230
230
270
270
6
220
220
320
320
7
270
270
350
350
8
320
320
300
300
9
350
350
260
260
10
300
300
245
245
11
260
260
240
240
12
245
245
280
280
13
240
240
100
100
14
280
280
15
100
100
e. (2 points) Determine the planned order release (lot for lot) for component D.
Solution:
Now that we have the planned order release of A and B, we can compute the gross requirements
for component D: one for each component A produced, plus 2 for each component B produced at
any given period.
Component D planned order release:
Week
Gross. Requirements
Net requirements
Time‐phased
Planned release
1
280
280
2
280
280
460
460
3
460
460
510
510
4
510
510
620
620
5
620
620
710
710
6
710
710
800
800
7
800
800
710
710
8
710
710
640
640
9
640
640
580
580
10
580
580
565
565
11
565
565
640
640
12
640
640
280
280
13
280
280
100
100
14
100
100
15
f. (5 points) Determine the planned order release (lot for lot) for component C. Consider
that there is an initial inventory of this component of 200 units at week 1 and a
scheduled receipt of 200 units in week 6 and another of 300 units in week 8.
Solution:
We need to incorporate the initial inventory in week 1 and the scheduled receipts. The initial
inventory of each period is just the final inventory of the previous period. The final inventory of
each period is found by adding the initial inventory of the period plus the scheduled receipts and
subtracting the gross requirements, if this quantity is negative then this equals the net
requirements for the period and the final inventory is zero for that period.
Component C planned order release:
Week
Gross. Requirements
Sch. Receipts
Initial inventory
Net requirements
Time‐phased
Planned release
Final inventory
1
2
3
4
5
140
200
200
200
200
200
0
0
200
0
0
200
200
0
40
40
60
200
6
160
200
60
0
0
0
100
7
140
100
40
120
120
0
8
200
300
0
0
240
240
100
9
220
10
240
11
180
12
170
13
160
14
160
15
200
100
120
180
180
0
0
240
170
170
0
0
180
160
160
0
0
170
160
160
0
0
160
200
200
0
0
160
0
0
0
0
200
0
0
0
3. (6 points) Another component used by the manufacturing company in Problem 2,
Component Y, is imported from Europe and the order cost is $2,000. Given this high order
cost, the company is analyzing to use an EOQ lot sizing instead of lot for lot. The cost of
component Y is $350 per unit. The company uses an annual interest rate of 22% for holding
inventory. Order lead-time is 2 weeks. Net requirements for this component are given below
for weeks 5-15. Determine the planned order release (EOQ) for component Y. Assuming that
the inventory holding cost is charged against the inventory at the end of each week, what are
the ordering and inventory holding costs associated with this EOQ lot sizing strategy and the
net requirements in the table below? Based on these costs, is it this EOQ lot sizing strategy
better than a lot for lot sizing strategy for this component? Why?
Week
Net requirements
5
155
6
150
7
165
8
150
9
120
10
110
11
100
12
110
13
120
14
125
the
EOQ
15
110
Solution:
The
average
demand
.
.
/
rate
is
128.63.
We
compute
and
get
589.
We use this EOQ to compute the planned order release. To compute when we need an order
release we look at the time-phased requirements and every time that for a given period the
accumulated time-phased requirements are greater than the accumulated production, a new lot
with size Q needs to be released. The final inventory of a period is computed by adding the
previous period ending inventory (initial inventory for the current period) plus any delivery
planned for the period minus the requirements for the period.
Component Y planned order release: EOQ
Week
Net requirements
Time‐phased
Planned release
Planned deliveries
Ending Inventory
3
4
155
589
150
0
5
155
165
0
589
434
6
150
150
589
0
284
7
165
120
0
0
119
8
150
110
0
589
558
9
120
100
0
0
438
10
110
110
0
0
328
11
100
120
589
0
228
12
110
125
0
0
118
13
120
110
0
589
587
14
125
15
110
0
462
0
352
During these periods Q is ordered 3 times, so the ordering cost is $2,000*3= $6,000. The holding
cost is the sum of the ending inventory times the weekly holding cost: 3908*1.48=$5,787. The
sum of these costs is $11,787
We now compute the cost for a lot-for-lot strategy. Since we produce exactly the amount we
need for the period, the carried inventory is zero. However, we will need to order every period,
so the ordering cost is $2,000*11=$22,000. The EOQ lot sizing is therefore a better option
(lower cost).
Component Y planned order release: lot-for-lot
Week
Net requirements
Time‐phased
Planned release
Planned deliveries
Ending Inventory
3
4
155
155
150
150
5
155
165
165
155
0
6
150
150
150
150
0
7
165
120
120
165
0
8
150
110
110
150
0
9
120
100
100
120
0
10
110
110
110
110
0
11
100
120
120
100
0
12
110
125
125
110
0
13
120
110
110
120
0
14
125
15
110
125
0
110
0