## Urgent problem, (simple?) linear programming,

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
Potentin
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Joined: Sun Jul 12, 2015 10:27 am
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### Urgent problem, (simple?) linear programming,

Hey guys I really feeling kind of lost. I have to hand in an assignment which includes one small linear programming problem.
Mex Hex Data Sheet

Plant Production Cost__________Capacity________Running
(in \$ per unit)___________(in million)_________(in million \$)

Brasil_______0,23_____________1,5__________0,7
Germany______0,37____________3,0________ 1,2
India________ 0,17____________2,5_________0,5
Japan________0,29____________1,5_________0,9
South Africa ___0,21 ____________2,5_________1,2

Region_____Demand (in million)

South America 1,5
North America 1,2
Europe____ 2,4
Asia ___4,0
Africa ___0,9

Transportation costs (in \$ per unit)

______South America___North America___Europe ___Asia____ Africa
Brasil ______0,11_________0,15________0,21____0,30_____0,25
Germany_____0,24_________0,17________0,05_____0,20_____0,24
India ______0,20_________0,25________0,15_____0,10_____0,19
Japan _______0,27_________0,22_________0,15_____0,07_____0,32
South Afri ______0,29_________0,23_________0,17_____0,24_____0,13

Differences in local labor costs and other regional factors created significant differences in the cost to produce MexHex in the various locations. The data tables give details on the costs to produce each unit and the capacity of each plant. Additionally, the running costs for each plant are given (only needed for problem 3).
MexHex is needed on all continents and the demand for each continent is also given in the data tables. Moreover, you are given the costs to ship one vaccination from each plant to each region.
1. Compute the total production and transportation costs if each plant only serves its region (Japan and India both ship to Asia).

2. Compute the minimal production and transportation costs and the corresponding plan. Compute the savings w.r.t. to the solution of 1.

3. Now also take running costs into account. The running costs for each plant are added for each operating plant. First compute the total costs for the case that each plant only serves its region. Then compute the minimal production, transportation and running costs and the corresponding plan. This means if a plant is not producing anything, its running costs do not need to be added. [Note: your solution must be an integer linear program, i.e. it must run when the ’linear model’ option is checked. You cannot use ’IF’ in an formula.]

buddy
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### Re: Urgent problem, (simple?) linear programming,

What have you done so far?

Potentin
Posts: 3
Joined: Sun Jul 12, 2015 10:27 am
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### Re: Urgent problem, (simple?) linear programming,

Variables:
Bp________number of units produced in Brasil
Cp________ number of units produced in Canada
Gp________ number of units produced in Germany
Ip_________ number of units produced in India
Jp_________ number of units produced in Japan
SAp_______ number of units produced in South Africa

All integer and non-negative

a) Objective function:

Production costs per plant and transportation costs restricted to the region

MINIMIZE: 0,23Bp+0,34Cp+0,37Gp+0,17Ip+0,29Jp+0,21SAp
+0,11Bp+0,07Cp+0,05Gp+0,1Ip+0,07Jp+0,13SAp

Constraints:
Demand contraints:
Bp>=1.500.000
Cp>=1.200.000
Gp>=2.400.000
Ip+Jp>=4.000.000
SAp>=900.000

Capacity
Bp<=1.500.000
Cp<=3.000.000
Gp<=3.000.000
Ip<=2.500.000
Jp<=1.500.000

By doing this I found out that you actually don’t need linear programming for the first question, since the capacity if India and Japan is equal to the demand of Asia and there is region restriction in point a).However do I miss sth.?
i gonna upload my "approaches" for b) and d) tomorrow. I really would appreciate if you guys have a look at it.

Potentin
Posts: 3
Joined: Sun Jul 12, 2015 10:27 am
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### Re: Urgent problem, (simple?) linear programming,

Actually main problem is c).

I need to apply a linking constraint with the binary variables.
In my option it should be
Produced units in X <= Capacity of X * binary variable Y

However excel solver don't accept my approach =/