Problem 1
If the optimal number of facilities that minimizes the total logistical cost for a certain supply chain is five, what would be a logical justification for decision makers of this supply chain to build more than five facilities?
Problem 2
What would happen to the Implied Uncertainty in the following scenarios (fill in the blank increase, decrease, or stay the same)
a) A company introducing five new products to the market at the same time.
b) A retail store introducing a web site for the first time for its customers to shop on line.
c) A company shooting for enhancing its service level from 90% to 95%.
d) A company reducing its workforce from three shifts to two shifts.
e) A main supplier matching its demand exactly with its capacity.
Problem 3
Most companies use more than one type of distribution network depending on products characteristics and the company's competitive strategy. Seating Solutions is a company that sells three types of office chairs: Comfy, Ergo, and Exec. The first type Comfy is a very popular chair with a stable demand as it is of a good quality and inexpensive. Ergo is an ergonomic chair that is more expensive as it is highly adjustable. It is popular among customers whose job requires them to sit for long hours. Therefore, the demand on is not that high. Exec on the other hand is made of very expensive leather and therefore it is the least demanded type. What distribution network or networks would you recommend for Seating Solutions? Justify your answer.
Problem 4
Would it be better for a supply chain to centralize or decentralize its facilities in the following scenarios. Provide a brief explanation of your answer.
a) A supply chain that needs to reduce spending on outbound transportation.
b) A supply chain with a high average inbound transportation cost.
c) A company that wants to exploit economies of scale by increasing their batch size.
d) A company that uses very complex and technologically advanced manufacturing processes.
Problem 5:
Suppose that total transportation cost for a product can be approximated by the function:
T(f)= 2.1612f2 - 25.9 f + 121.1
Where f is the number of facilities.
a) Ignoring any other costs, find the optimal number of facilities with the minimum total transportation cost?
b) How much is the total transportation cost for that number of facilities?
Ouestion 6:
A company has three supply plants in Baltimore, Memphis and Wichita with the capacities shown below. The main markets for this company are in Atlanta, Boston and Chicago with the demands also shown below. It turns out that the optimal amounts to ship from plants to markets are as given below. All units for capacities, demands and shipments are in thousands:
|
Markets
|
|
Supply
|
|
|
|
Unused
|
|
Plants
|
Capacity
|
Atlanta Boston Chicago
|
Total shipped
|
Capacity
|
|
Baltimore
|
10
|
0 8 (a)
|
10
|
(b)
|
|
Memphis
|
(e)
|
10 (d) 12
|
22
|
0
|
|
Wichita
|
8
|
0 (e) 0
|
(f)
|
8
|
|
Demand 10 8 16
|
I. Fill in the missing amounts in the table (Show your calculations or justification)
a.
b.
c.
d.
C.
1.
2. Is this a minimization or maximization problem? Justify your answer
3. If the company has some additional capacity that can be used, to which plant (or plants) would you allocate the additional capacity and why?
4. Do you think any of the plants can be shut down without affecting the solution? Explain.
Problem 7:
Winter's model was used to forecast the demand in the table below. Answer the following provided that all smoothing factors are equal to 0.1 and the periodicity is 12:
a) Find the values of X I, X2, ..., X9 in the table below and show your calculations.
b) What conclusions can you make from the Bias values of this forecasting model
|
Period
|
Actual
Demand
|
Level
|
Trend
|
Seasonal
Factor
|
Forecast
|
E,
|
At
|
bias
|
MAD
|
|
|
|
445
|
0.37
|
|
|
|
|
|
|
|
1
|
387
|
448
|
0.67
|
0.82
|
362.88
|
-24.12
|
24.12
|
-24.12
|
24.12
|
|
2
|
362
|
449
|
0.70
|
0.80
|
359.57
|
-2.43
|
2.43
|
-26.55
|
13.28
|
|
3
|
402
|
450
|
0.77
|
0.88
|
395.79
|
-6.21
|
6.21
|
-32.76
|
10.92
|
|
4
|
394
|
448
|
0.45
|
0.94
|
423.74
|
29.74
|
29.74
|
-3.02
|
15.63
|
|
5
|
453
|
448
|
0.40
|
1.02
|
458.10
|
5.10
|
5.10
|
2.08
|
13.52
|
|
6
|
491
|
448
|
0.35
|
1.11
|
496.95
|
5.95
|
5.95
|
8.04
|
12.26
|
|
7
|
462
|
448
|
036
|
1.03
|
460.25
|
-1.75
|
1.75
|
6.29
|
10.76
|
|
8
|
518
|
447
|
0.18
|
1.20
|
539.56
|
21.56
|
21.56
|
27.85
|
12.11
|
|
9
|
391
|
450
|
0.47
|
0.82
|
367.55
|
-23.45
|
23.45
|
4.40
|
13.37
|
|
10
|
343
|
450
|
0.40
|
0.77
|
348.27
|
5.27
|
5.27
|
9.67
|
12.56
|
|
11
|
624
|
448
|
0.21
|
1.45
|
650.98
|
26.98
|
26.98
|
36.65
|
13.87
|
|
12
|
586
|
X1
|
X2
|
1.26
|
X3
|
X4
|
XS
|
X6
|
X7
|
|
13
|
|
|
|
X8
|
X9
|
|
|
|
|