ISyE 3104 – Fall 2012
Homework 11
Due Tuesday November 13th, 2012 (35 points)
1. (8 points) Read the article “Broken links: The disruption to manufacturers worldwide from
Japan’s disasters will force a rethink of how they manage production” The Economist.
March, 2011. (http://www.economist.com/node/18486015). Answer briefly (a paragraph) the
following questions:
a. (2 points) Just-in-time (JIT) concept has spread down the global manufacturing to
keep inventories down. Discuss the shortcomings that JIT global manufacturers
experienced after disasters like Japan’s earthquake and tsunami or Iceland's volcano
eruption.
Solution:
In the aftermath of these disasters, suppliers located in the affected areas found hard to fulfill the
demand of their customers downstream in the supply chain because their production capacity, the
transportation capabilities, or their own suppliers were affected. The problem was even harder
under a JIT environment, since by definition the held inventory is minimum, so even if the
suppliers were back in line relatively quick, there was some impact if downstream the supply
chain companies didn’t have the inventories or backup plans to overcome the sudden changes in
supply. The results were scarce supplies that may have raised prices and/or decrease products
availability.
b.
(2 points) In this article, JIT shortcomings are discussed in a natural disaster setting.
Discuss other situations when similar shortcomings may arise.
Solution:
These shortcomings are not unique to disasters. Sudden changes in demand can cause similar
impact, for instance if there is a promotion downstream the supply chain, a sudden increase of
the product’s popularity, a wrong forecast, etc. Also, smaller incidents may occur that stop
production such as factory accidents, power shortage, equipment malfunction, etc. Social and
political environment can also disrupt the supply chain: new commerce trades and fees, strikes,
etc.
c. (4 points) Does this mean that JIT does not work or it is “too risky” to implement?
What can be done to reduce the JIT associated risks (at least two recommendations)?
Discuss the potential trade-offs of your recommendations.
Solution:
The idea behind JIT “pull over push” brings inventories to low levels which results in potential
savings. However, this also comes with risks as the capacity to respond to quick changes in
supply or demand is compromised when there is not a buffer available (i.e., inventories).
Nevertheless, this does not mean that the JIT idea should be completely discarded. There are
some actions that could be taken to reduce risk, for instance; holding more days of inventory for
products that are of strategic importance or under a higher risk of supply chain disruption;
increasing the portfolio of suppliers (instead of having “all the eggs in one basket”), using
overtime to catch up with production requirements, etc. Evaluating the different trade-offs and
doing scenario analysis can help to define the adequate measures and adjustments for the
company’s different products.
2. (4 points) Recall the Penville game you played in the class.
a. (1 point) Explain why there was more WIP inventory in the “push” system compared
to the “pull” system where we used Kanbans.
Solution:
In the “pull” system WIP inventory is limited by the Kanbans, whereas in the “push” system
each person kept producing whenever possible, no matter the how much WIP inventory was
accumulated in the station.
b. (1 point) In the “team” system there were only 3 players, but their overall production
was close to that of the “pull” system which had 5 players. Explain why this is the
case.
Solution:
Because in the case of the “team” system, idle time is minimized since everyone can do all the
tasks so everyone is producing at all times, whereas in the “pull” system a person sometimes
waited for the next person in the production line.
c. (1 point) Which of the three systems you would expect to perform worse in terms of
catching defects in the production line?
Solution:
That would likely to be the “push” system, since the production is continuous and pushed, no
matter the current state of demand, defective WIP inventory and final products can be rapidly
accumulated before a defect is caught.
d. (1 point) Suppose that the workers at the workstations need to take frequent (and
sometimes long) breaks. Which of these systems would be affected more, in terms of
the impact on the throughput?
Solution:
In both “push” and “pull” systems the production line could be interrupted if there is not enough
WIP inventory available to cover the break; however, since in the “pull” system the WIP
inventory is lower or constricted than in the “push” system, we would expect the impact to be
greater, since there is less buffer to mitigate it.
3. (15 points) A manufacturing company needs to plan the order releases for component Z.
Component Z’s gross requirements for weeks 2 to 6 are given in the table below. The
component’s lead time is 1 week. The cost per order is $50 and the holding cost is
$2/unit/period.
2 20 3 25 4 30 5 20 6 30 Compute the planned order releases using the given algorithm.
a. (4 points) Silver –Meal heuristic
Solution:
For Silver-Meal heuristic we calculate the average cost (setup + holding) per period if at period i
we produce the time-phased net requirements for periods i, i+1,…,j. We start with j=1, then
j=i+1, and we continue until the average cost increases.
For period i=1. If j=1 then the setup cost is $50 and there is no holding cost. If j=2, the setup cost
is $50 and the holding cost is 25*1*$2=$50 (25 units are carried during one period at a cost of $2
per unit). The total cost is $100 and the average cost is $100/2=$50. If j=3, the setup cost is $50
and the holding cost is 25*1*$2+ 30*2*$2=$170 (25 units are carried during one period and 30
units are carried during 2 period). The total cost is $220 and the average cost is $220/3=$73.33.
We stop, and j=2: we will produce 45 units at period 1 and will produce again on period 3.
We repeat the process starting at period 3: i=3. The average cost increases at j=5, so j=4 and we
will produce 50 units on period 3. We will produce again on period 5, and since it is the last
period, we produce exactly 30 units. The summary of these calculations is shown in the table
below:
Period i
1
3
5
1
50
2
50
C(j)
3
73.33333
50
4
5
45
70
50
Then, we get the planned release orders as follows:
1
Net Requirements
TP Net Requirements
Planned Order release
20
45
2
20
25
0
3
25
30
50
4
30
20
0
5
20
30
30
6
30
b. (4 points) Least Unit Cost
Solution:
The process is the same than a) but the average is compute per unit produced instead of per
period.
For period i=1. If j=1 then the setup cost is $50 and there is no holding cost, and the average cost
per unit is $50/20=$2.5. If j=2, the setup cost is $50 and the holding cost is 25*1*$2=$50 (25
units are carried during one period at a cost of $2 per unit). The total cost is $100 and the average
cost is $100/45=$2.22. If j=3, the setup cost is $50 and the holding cost is 25*1*$2+
30*2*$2=$170 (25 units are carried during one period and 30 units are carried during 2 period).
The total cost is $220 and the average cost is $220/75=$2.933. We stop, and j=2: we will
produce 45 units at period 1 and will produce again on period 3.
We repeat the process starting at period 3: i=3. The average cost increases at j=4, so j=3 and we
will produce 30 units on period 3. We will produce again on period 4, and j=5, so we will
produce 50 units on period 4 (for periods 4 and 5). The summary of these calculations is shown
in the table below:
Period i
1
3
4
1
2.5
C(j)
2
3
2.222222 2.933333
1.666667
4
5
1.8
2.5
2.2
Then, we get the planned release orders as follows:
1
Net Requirements
TP Net Requirements
Planned Order release
2
20
25
0
20
45
3
25
30
30
4
30
20
50
5
20
30
0
6
30
c. (4 points) Part Period balancing
Solution:
For the Part Period Balancing heuristic we calculate the holding costs if at period i we produce
the time-phased net requirements for period i, i+1…j. We choose the period j where the holding
costs approximate the setup cost.
For period i=1. If j=1 there is no holding cost. If j=2 the holding cost is 25*1*$2=$50, which
equals the setup cost. We stop, and j=2: we will produce 45 units at period 1 and will produce
again on period 3. We repeat the process starting at period 3: i=3. If j=3 there is no holding cost,
if j=4 the holding cost is 20*$2=$40, and if j=5 it is 20*1*$2+ 30*2*$2=$160, so we choose j=4.
We will produce again in period 5, so we have to produce 30 units then. The summary of these
calculations is shown in the next table.
Period i
1
3
5
Holding cost (j)
2
3
4
50
0
40
1
0
5
160
0
Then, we get the planned release orders as follows:
1
Net Requirements
TP Net Requirements
Planned Order release
20
45
2
20
25
0
3
25
30
50
4
30
20
0
5
20
30
30
6
30
d. (3 points) Assume that the company can order up to 25 units of component Z per
week due to space limitations. Can there be a feasible order release plan considering
this constraint? If so, give one feasible plan. Can you further improve this feasible
plan to reduce the total setup and holding costs?
The total production required in the 5 period is 125, and since the capacity is 25 per period, there
is a feasible solution, in fact, the only feasible solution: to produce up to capacity each period.
1
Net Requirements
TP Net Requirements
Planned Order release
20
25
2
20
25
25
3
25
30
25
4
30
20
25
5
20
30
25
6
30
4. (8 points) The demands for an assembly for weeks 1-5 are: 40, 30, 25, 35, and 20. The setup
cost is $100 and the holding cost is $4/unit/period. There can be at most one setup per week
of this assembly. Assume there is enough capacity to produce any number of assemblies per
week. Find the optimal production schedule and its cost (holding and setup costs). If there are
more than one optimal schedule, state all of them. You can use either a shortest path or a
dynamic programming approach.
Solution:
We will use the Dynamic Programming approach. You can consult the appendix of chapter 7 for
additional details.
We have 5 periods; therefore, we have 5 nodes plus a sink node 6. Fk is the minimum cost from
node k to sink node 6. It is computed as:
min
Where ckj is the cost from going to node j from node k, and it represents the cost of producing in
period k the time-phased net requirements of periods k,k+1,…j-1, and producing again until
period j.
To compute ckj we add the setup cost and the holding cost of the inventory that is carried during
different periods of time. For instance:
c12= 100 (produce 20 at period 1. We will produce again in period 2)
c13= 100 + 30(1)(4)= 220 (produce 70 units at period 1, we need 40 units at period 1 and we
carry 30 units –the time-phased requirements for period 2- one period. We will produce again
until period 3)
c14= 100 + 30(1)(4) + 25(2)(4) = 420 (produce 95 units at period 1, we need 40 at period 1, carry
30 one period, and carry 25 two periods. We will produce again until period 4)
c15= 100 + 30(1)(4) + 25(2)(4) + 35(3)(4) = 840
c16= 100 + 30(1)(4) + 25(2)(4) + 35(3)(4) + 20(4)(4)= 1160
The summary of these costs is shown in the table below. Note that not all the costs have to be
computed from the beginning. We can compute them as we need them.
ckj
1
2
3
4
5
2
100
3
220
100
4
420
200
100
5
840
480
240
100
6
1160
720
400
180
100
We start the process with the default initial condition f6=0.
f6= 0
f5=min(c56 + f6)= 100+0=100; j=6
f4=min(c45 + f5, c46 + f6)= min(100+100, 180+0)= 180; j=6
f3=min(c34 + f4, c35 + f5, c36 + f6)= min(100+180, 240+100,400+0)=280; j=4
f2=min(c23 + f3, c24 + f4, c25 + f5, c26 + f6)= min(100+280,200+180,480+100,720+0)=380; j=3,4
f1=min(c12 + f2, c13 + f3, c14 + f4, c15 + f5, c16 + f6)= min(100+380,
220+280,420+180,840+100,1160+0)=480; j=2
Since j=2 for period 1, we produce at period 1 and then also at period 2. There are two optimal
production schedules since at period 2 we can produce only for period 2 or for period 2 and 3
(since j=3 or j=4). In the first case since j=4 for period 3, we only produce for period 3 and then
again in period 4. Since j=6 for period 4, we will produce for period 4 and period 5. The two
optimal planned release orders are as follow:
TP Net Requirements
Planned Order release
1
40
40
2
30
30
3
25
25
4
35
55
5
20
0
TP Net Requirements
Planned Order release
1
40
40
2
30
55
3
25
0
4
35
55
5
20
0