Manufacturer Of Printing Inks Sample Assignment

Sunchem, a manufacturer of printing inks, has five manufacturing plants worldwide. Their locations and capacities are shown in Table 1 along with the cost of producing 1 ton of ink at each facility. The production costs are in the local currency of the country where the plant is located. The major markets for the inks are North America, South America, Europe, Japan, and the rest of Asia. Demand at each market is shown in Table 1. Transportation costs from each plant to each market in US dollars are shown in Table 1. Management must come up with a production plan for 2010.

	Table 1
	North America	South America	Europe	Japan	Asia	Capacity Tons/year	Production cost/ton
United States	600	1200	1300	2000	1700	185	$10,000
Germany	1300	1400	600	1400	1300	475	15000 Marks
Japan	2000	2100	1400	300	900	50	1800000Yen
Brazil	1200	800	1400	2100	2100	200	13000 Real
India	2200	2300	1300	1000	800	80	400000 Rupees
Demand (tons/year)	270	190	200	120	100

a. If exchange rates are expected as in Table 2, and no plant can run below 50 percent of capacity, how much should each plant produce and which markets should each plant supply?

	US$	Mark	Yen	Real	Rupee
US$	1	1.993	107.7	1.78	43.55
Mark	0.502	1	54.07	0.89	21.83
Yen	0.0093	0.0185	1	0.016	0.405
Real	0.562	1.124	60.65	1	24.52
Rupee	0.023	0.046	2.47	0.041	1

b. If there are no limits on the amount produced in a plant, how much should each plant produce?

c. Can adding 10 tons of capacity in any plant reduce costs?

d. How should Sunchem account for the fact that exchange rate fluctuate over time?

Solution

(a)

Sunchem can use the projections to build an optimization model as shown below. In this case, the shipments from each plant to every market are assumed to be variable and solved to find the minimum total cost. This is done by utilizing the following constraints:

Each plant runs at least at half capacity.
Sum of all shipments from the plant needs to be less than or equal to the capacity in that plant.
All production volumes are non-negative.
All calculations are performed at the exchange rates provided.

Optimization model:

n = 5: five manufacturing plants

m = 5: number of regional markets.

D_j = Annual tons of ink needed for regional market j

K_i = Maximum possible capacity of manufacturing plants.

Especially for (a) lower limit for capacity is 50%*K_i .

c_ij= Cost of shipping one ton of printing ink from plant i to regional market j

p_i = Cost of producing one ton of printing ink at plant i

x_ij = Tons of printing ink shipped from site i to regional market j.

It should be integral and non-negative

This is clearly influenced by the production cost per ton and the local market demand. Low cost structure plants need to operate at capacity.

(b)

If there are no limits on production we can perform the same exercise as in (a) but without the capacity constraints (5.2) and (5.3). This gives us the following results:

Clearly by having no restrictions on capacity SunChem can reduce costs by $557,590. The analysis shows that there are gains from shifting a significant portion of production to Brazil and having no production in Japan, US and India.

(c)

From the scenario in (a) we see that two of the plants are producing at full capacity. And in (b), we see that it is more economical to produce higher volumes in Brazil. Once we add 10 tons/year to Brazil, the cost reduces to $7,795,510.

(d)

It is clear that fluctuations in exchange rates will change the cost structure of each plant. If the cost at a plant becomes too high, there is merit in shifting some of the production to another plant. Similarly if a plant’s cost structure becomes more favorable, there is merit in shifting some of the production from other plants to this plant. Either of these scenarios requires that the plants have built in excess capacity. Sunchem should plan on making excess capacity available at its plants.