Please do not give me the answer in Chegg textbook solutions, the question I\'m
ID: 464387 • Letter: P
Question
Please do not give me the answer in Chegg textbook solutions, the question I'm asking is different.
Question: Formulate an 0-1 integer programming model for this problem
A sports apparel company has received an order for a college basketball team’s national championship T-shirt. The company can purchase the T-shirts from textile factories in Mexico, Puerto Rico, and Haiti. The shirts are shipped from the factories to companies in the United States that silk-screen the shirts before they are shipped to distribution centers. Following are the production and transportation costs ($/shirt) from the T-shirt factories to the silk-screen companies to the distribution centers, plus the supply of T-shirts at the factories and demand for the shirts at the distribution centers.
Determine the optimal shipments that will minimize total production and transportation costs for the apparel company. Formulate an 0-1 integer programming model for this problem
T-shirt factory 4. Miami 5. Atlanta 6. Houston Supply 1. Mexico 4 6 3 18 2. Puerto Rico 3 5 5 15 3. Haiti 2 4 4 23Explanation / Answer
There are three factories located at three different places( say represented by 'i' taking the values 1, 2, and 3) and three silk screen companies located at three different places( say represented by 'j' taking the values 4, 5, and 6) and finally three different demand centres( say represented by 'k' taking the values 7, 8, and 9). In other words the places are represented by their respective numbers as given in the question.
Decision variables are defined as Xijk representing the number ( positive integer ) that are produced at ith factory and silk screen at jth silk screen company and delivered at kth demand center.
The Objective function is to minimize the total production and transportation costs. The cost co-efficients denoted as Cijk corresponding to decision variables are calculated as follows: Cijk = Cij + Cjk
In simple terms Objective function is to Minimize Sigma (over i, j, k ) Cijk * Xijk
Constraints are on account of supply and demand. For supply i is kept constant and for demand k is kept constant as follows:
Sigma ( i is fixed and j varying) Xijk <= (less than equal to ) Si for i = 1,2,3 S1=18, S2=15, S3=23
Sigma ( k is fixed and j varying) Xijk >= ( greater than equal to ) Dk for k= 7, 8, 9 D7=20, D8=12, D9=20
For screen companies total quantity into must match with the total quantity supplied that is for fixed j Sigma (i varying ) Xijk = Sigma (k varying) Xijk
Total demand (52) is less than total supply (56)
Variable Coefficient X147 8 X148 10 X149 7 X157 9 X158 11 X159 11 X167 5 X168 7 X169 7 X247 7 X248 9 X249 6 X257 8 X258 10 X259 10 X267 7 X268 9 X269 9 X347 6 X348 8 X349 5 X357 7 X358 9 X359 9 X367 6 X368 8 X369 8