OPERTIONS RESEARCH QUESTION DUE 23 rd March 2018, before 15:00 1. A company has
ID: 3281963 • Letter: O
Question
OPERTIONS RESEARCH QUESTION DUE 23 rd March 2018, before 15:00
1. A company has 4 production facilities. Each facility is eligible to produce Product A, Product B or Product C, but it can only produce one of these products. The annual fixed cost of operating each facility and the variable cost of producing a product of each type at each facility are given in the table. Facility Fixed Cost (S) Facility 1 Facility 2 Facility 3 Facility 4 8,000,000 6,000,000 4,000,000 3,000,000 Variable Cost (S) Product A Product B Product C 1600 1800 1900 2200 1200 1500 1700 1900 900 1100 1200 1400 The company must produce 5000 units of each type of product in a year. Formulate an IP to minimize the total annual production cost satisfying the following constraints Each facility can produce only one type of product The total production of each type of product must be at a single facility. For instance, if any Products A are produced at facility 1, then all Products A must be produced there. e If facilities 3 and 4 are used, then facility 1 must also be used.Explanation / Answer
IP model is following
Let Xij be a binary variable such that Xij=1 indicates that product j is produced at facility i
Min (X11+X12+X13)*8000000+5000*(1200X11+1600X12+900X13)+(X21+X22+X23)*6000000+5000*(1500X21+1800X22+1100X23)+(X31+X32+X33)*4000000+5000*(1700X31+1900X32+1200X33)+(X41+X42+X43)*8000000+5000*(1900X41+2200X42+1400X43)
s.t.
X11+X21+X31+X41 = 1 (Total production of product A must be at a single facility)
X12+X22+X32+X42 = 1 (Total production of product B must be at a single facility)
X13+X23+X33+X43 = 1 (Total production of product C must be at a single facility)
X11+X12+X13 <= 1 (Facility 1 can only produce one type of product)
X21+X22+X23 <= 1 (Facility 2 can only produce one type of product)
X31+X32+X33 <= 1 (Facility 3 can only produce one type of product)
X41+X42+X43 <= 1 (Facility 4 can only produce one type of product)
(X31+X32+X33)+(X41+X42+X43)-(X11+X12+X13) <= 1 (If facilities 3 and 4 are used, then facility 1 must also be used)
Xij {0,1}
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