Question
Note- I tried to solve and below is the answer provided please let me know this is okay or not? and I am stuck at
Note- I tried to solve and below is the answer provided please let me know this is okay or not? and I am stuck at last parts d and e. please solve d and e and modify the answer if need/ if I'm wrong. complete d and e like I did in table form.
Required -need d and e parts needs to be completed
qns
Sleekfon and Sturdyfon are two major cell phone manufacturers that have recently merged. Their current market sizes are as shown in Table 5-9. All demand is in millions of units.
Sleekfon has three production facilities in Europe (EU), North America, and South America. Sturdyfon also has three production facilities in Europe (EU), North America, and the rest of Asia/Australia. The capacity (in millions of units), annual fixed cost (in millions of $), and variable production costs ($ per unit) for each plant are as shown in Table 5-10.
Transportation costs between regions are as shown in Table 5-11. All transportation costs are shown in dollars per unit. Duties are applied on each unit based on the fixed cost per unit capacity, variable cost per unit, and transportation cost. Thus, a unit currently shipped from North America to Africa has a fixed cost per unit of capacity of $5.00, a variable production cost of $5.50, and a transportation cost of $2.20. The 25 percent import duty is thus applied on $12.70 (5.00 + 5.50 + 2.20) to give a total cost on import of $15.88. For the questions that follow, assume that market demand is as in Table 5-9.
The merged company has estimated that scaling back a 20-million-unit plant to 10 million units saves 30 percent in fixed costs. Variable costs at a scaled-back plant are unaffected. Shutting a plant down (either 10 million or 20 million units) saves 80 percent in fixed costs. Fixed costs are only partially recovered because of severance and other costs associated with a shutdown.
FOR THIS REVIEW QUESTION I NEED TO FIGURE OUT 1-5
a. What is the lowest cost achievable for the production and distribution network prior to the merger?Which plants serve which markets?
b. What is the lowest cost achievable for the production and distribution network after the merger if none of the plants is shut down?Which plants serve which markets?
c. What is the lowest cost achievable for the production and distribution network after the merger if plants can be scaled back or shut down in batches of 10 million units of capacity?Which plants serve which markets?
d. How is the optimal network configuration affected if all duties are reduced to 0?
e. How should the merged network be configured?
TABLE 5-9 Global Demand and Duties for Sleekfon and Sturdyfon
| MARKET | N.America | S.America | Europe (Eu) | Europe (Non-Eu) | Japan | Rest of Asia /Australia | Africa |
| Sleekfon demand | 10 | 4 | 20 | 3 | 2 | 2 | 1 |
| Sturdyfon Demand | 12 | 1 | 4 | 8 | 7 | 3 | 1 |
| Import Duties (%) | 3 | 20 | 4 | 15 | 4 | 22 | 25 |
| TABLE 5-9 Global Demand for Sleekfon and Sturdyfon |
| Capacity | FixedCost/Year | Variable cost/Unit | ||
| Sleekfon | Europe (EU) | 20 | 100 | 6.0 |
| N. America | 20 | 100 | 5.5 | |
| S. America | 10 | 60 | 5.3 | |
| Sturdyfon | Europe (EU) | 20 | 100 | 6.0 |
| N. America | 20 | 100 | 5.5 | |
| Rest of Asia | 10 | 50 | 5.0 | |
| TABLE 5-10 Plant Capacities and Costs for Sleekfon and Sturdyfon |
| N. America | S. America | Europe (Eu) | Europe (Non-Eu) | Japan | Rest of Asia/ Australia | Africa | |
| N. America | 1.00 | 1.50 | 1.50 | 1.80 | 1.70 | 2.00 | 2.20 |
| S. America | 1.50 | 1.00 | 1.70 | 2.00 | 1.90 | 2.20 | 2.20 |
| Europe (EU) | 1.50 | 1.70 | 1.00 | 1.20 | 1.80 | 1.70 | 1.40 |
| Europe (non Eu) | 1.80 | 2.00 | 1.20 | 1.00 | 1.80 | 1.60 | 1.50 |
| Japan | 1.70 | 1.90 | 1.80 | 1.80 | 1.00 | 1.20 | 1.90 |
| rest of Asia/Australia | 2.00 | 2.20 | 1.70 | 1.60 | 1.20 | 1.00 | 1.80 |
| Africa | 2.20 | 2.20 | 1.40 | 1.50 | 1.90 | 1.80 | 1.00 |
| TABLE 5-11 Transportation costs Between regions ($ per unit) |
Answer starts from here
a)
Starting from the basic models in (a), we will build more advanced models in the subsequent parts of this question. Prior to merger, Sleekfon and Sturdyfon operate independently, and so we need to build separate models for each of them.
Optimization model for Sleekfon:
| n = 3: Sleekfon production facilities. m = 7: number of regional markets. Dj= Annual market size of regional market j Ki= maximum possible capacity of production facility i cij = Variable cost of producing, transporting and duty from facility i to market j fi = Annual fixed cost of facility i xij= Number of units from facility i to regional market j. It should be integral and non-negative. |
Please note that we need to calculate the variable costcijbefore we plug it into the optimization model. Variable costcijis calculated as follows:
cij= production cost per unit at facility i + transportation cost per unit from facility i to market j + duty*(production cost per unit at facility i + transportation cost per unit from facility i to market j + fixed cost per unit of capacity)
| SYMBOL | INPUT | CELL |
| Dj | Annual market size of regional market j | B4:H4 |
| Ki | maximum possible capacity of production facility i | C12:C14 |
| cij | Variable cost of producing, transporting and duty from facility i to market j | B22:H28 |
| fi | Annual fixed cost of facility i | D12:D17 |
| xij | Number of units from facility i to regional market j. | C43:I45 |
| obj. | objective function | D48 |
| 5.1 | demand constraints | J43:J45 |
| 5.2 | capacity constraints | C46:I46 |
(Sheet sleekfon in workbook problem5.4)
The above model gives optimal result as in following table:
| Quantity Shipped | |||||||||
| N. America | S. America | Europe (EU) | Europe (Non EU) | Japan | Rest of Asia/Australia | Africa | Capacity | ||
| Europe (EU) | 0.00 | 0.00 | 20.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |
| Sleekfon | N. America | 10.00 | 0.00 | 0.00 | 3.00 | 2.00 | 2.00 | 0.00 | 3.00 |
| S. America | 0.00 | 4.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 5.00 | |
| Demand | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | ||
| Total Cost for Sleekfon = | $564.39 |
And we use the same model but with data from Sturdyfon to get following optimal production and distribution plan for Sturdyfon:
| Quantity Shipped | |||||||||
| N. America | S. America | Europe (EU) | Europe (Non EU) | Japan | Rest of Asia/Australia | Africa | Capacity | ||
| Europe (EU) | 0.00 | 0.00 | 4.00 | 8.00 | 0.00 | 0.00 | 1.00 | 7.00 | |
| Sturdyfon | N. America | 12.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 7.00 |
| Rest of Asia | 0.00 | 0.00 | 0.00 | 0.00 | 7.00 | 3.00 | 0.00 | 0.00 | |
| Demand | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | ||
| Total cost for Sturdyfon = | 512.68 |
(b)
Under conditions of no plant shutdowns, the previous model is still applicable. However, we need to increase the number of facilities to 6, i.e., 3 from Sleekfon and 3 from Sturdyfon. And the market demand at a region needs revised by combining the demands from the two companies. Decision maker has more facilities and greater market share in each region, and hence has more choices for production and distribution plans. The optimal result is summarized in the following table.
| Quantity Shipped | |||||||||
| N. America | S. America | Europe (EU) | Europe (Non EU) | Japan | Rest of Asia/Australia | Africa | Capacity | ||
| Europe (EU) | 0.00 | 0.00 | 4.00 | 11.00 | 0.00 | 0.00 | 2.00 | 3.00 | |
| Sleekfon | N. America | 16.00 | 0.00 | 0.00 | 0.00 | 4.00 | 0.00 | 0.00 | 0.00 |
| S. America | 0.00 | 5.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.00 | |
| Europe (EU) | 0.00 | 0.00 | 20.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |
| Sturdyfon | N. America | 6.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 14.00 |
| Rest of Asia | 0.00 | 0.00 | 0.00 | 0.00 | 5.00 | 5.00 | 0.00 | 0.00 | |
| Demand | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | ||
| Total Cost for Merged Network = | 1066.82 |
(c)
This model is more advanced since it allows facilities to be scaled down or shutdown. Accordingly we need more variables to reflect this new complexity.
Optimization model for Sleekfon:
| n = 6: Sleekfon and Sturdyfon production facilities. m = 7: number of regional markets. Dj= Annual market size of regional market j, sum of the Sleekfon and Sturdyfon market share. Ki=capacity of production facility i Li=capacity of production facility if it is scaled back cij = Variable cost of producing, transporting and duty from facility i to market j fi = Annual fixed cost of facility i gi= Annual fixed cost of facility i if it is scaled back hi= Shutdown cost of facility i xij= Number of units from facility i to regional market j. It should be integral and non-negative. yi= Binary variable indicating whether to scale back facility i. yi= 1 means to scale it back, 0 otherwise. Since two facilities, Sleekfon S America and Sturdyfon Rest of Asia, can not be scaled back, the index i doesn't include these two facilities. zi= Binary variable indicating whether to shutdown facility i. zi=1 means to shutdown it, 0 otherwise. (1-yi-zi) would be the binary variable indicating whether the facility is unaffected. |
Please note that we need to calculate the variable costcijbefore we plug it into the optimization model. Variable costcijis calculated as following:
cij= production cost per unit at facility i + transportation cost per unit from facility i to market j + duty*(production cost per unit at facility i + transportation cost per unit from facility i to market j + fixed cost per unit of capacity)
And we also need to prepare fixed cost data for the two new scenarios: shutdown and scale back. As explained in the problem description, fixed cost for a scaled back facility is 70% of the original one; and it costs 20% of the original annual fixed cost to shutdown it.
Above model gives optimal solution as summarized in the following table. The lowest cost possible in this model is $988.93, much lower than the result we got in (b) $1066.82. As shown in the result, the Sleekfon N.America facility is shutdown, and the market is mainly served by Sturdyfon N.America facility. The N.America market share is 22, and there are 40 in terms of production capacity, hence it is wise to shutdown one facility whichever is more expensive.
| Quantity Shipped | ||||||||||||
| N. America | S. America | Europe (EU) | Europe (Non EU) | Japan | Rest of Asia/Australia | Africa | Scale back | Shut down | Plant unaffected | Capacity | ||
| Europe (EU) | 0.00 | 0.00 | 5.00 | 11.00 | 0.00 | 0.00 | 2.00 | 0.00 | 0.00 | 1.00 | 2.00 | |
| Sleekfon | N. America | 20.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 |
| S. America | 2.00 | 5.00 | 0.00 | 0.00 | 3.00 | 0.00 | 0.00 | 0 | 0.00 | 1.00 | 0.00 | |
| Europe (EU) | 0.00 | 0.00 | 19.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | |
| Sturdyfon | N. America | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 |
| Rest of Asia | 0.00 | 0.00 | 0.00 | 0.00 | 5.00 | 5.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | |
| Demand | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |||||
| Total Cost for Merged Network = | 988.93 |
For questions (d) and (e), we need to change the duty to zero and run the optimization model again to get the result. We can achieve this by resetting B7:H7 to zeros in sheet merger (shutdown) in workbook problem5.4.xls.
(d) ?
(e) ?
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Fundamentals of quality control and improvement
Authors: amitava mitra
3rd edition
978-0470226537
