Question 2 (25 points) The testing department at a TV production facility has to schedule the TV tests. They are going to perform several tests including shock test, thermal test, stacking test, panel measurement, etc. In total, there are 20 tests to be performed. The manager of the testing department has to decide which operator is going to perform which test. Operators can only perform the tests they are trained for. Each test is going to be performed by one operator. Obviously, more than one test is going to assigned to some operators. Otherwise, there is no feasible assignment. Moreover, at least one test has to be assigned to each operator. The time (in minutes) it takes to perform a certain test for each operator is given in the following table. If the operator cannot conduct the test, the relevant cell is left empty. 1 2 185 96 Operator 5 6 93 148 111 53 20 267 112 274 9 205 164 299 8 80 174 245 114 143 10 80 43 55 71 52 278 130 a 200 7 267 88 129 176 247 269 127 44 110 16 223 196 266 108 104 ola 26 210 201 251 282 101 240 3 4 134 43 93 36 238 22 140 180 85 129 278 265 35 152 150 288 157 236 145 124 38 176 102 252 117 41 32 221 200 289 271 Test 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 84 278 73 125 218 48 189 107 96 180 182 20 90 62 65 | 103 40 31 266 17 281 170 209 72 42 214188 154 238 130 134 42 82 291 46 33 286 223 180 115 253 149 38 22 28 33 128 54 290 291 107 207 298 186 121 129 100 132 193 46 193 189 58 59 39 163 72 250 97 285 Develop an integer programming formulation to determine the assignment of tests to the operators such that the difference between the maximum and minimum among the total duration of the tests assigned to the operators is minimized. (For example, if the total duration of the tests assigned to these 10 operators are 202, 152, 93, 79,95, 145, 156, 185, 192 and 173 minutes, then the difference between the maximum and minimum is 202 79 2 = 123.) Define your decision variables clearly. You may want to define additional notation for the duration parameters given in the table above in order to write down the model in a compact form. If you do so, please clearly define it as well and explain how you are going to handle the empty cells in the table. (Hint: You have to define additional variables to determine the maximum and minimum total test durations among all operators.) Question 2 (25 points) The testing department at a TV production facility has to schedule the TV tests. They are going to perform several tests including shock test, thermal test, stacking test, panel measurement, etc. In total, there are 20 tests to be performed. The manager of the testing department has to decide which operator is going to perform which test. Operators can only perform the tests they are trained for. Each test is going to be performed by one operator. Obviously, more than one test is going to assigned to some operators. Otherwise, there is no feasible assignment. Moreover, at least one test has to be assigned to each operator. The time (in minutes) it takes to perform a certain test for each operator is given in the following table. If the operator cannot conduct the test, the relevant cell is left empty. 1 2 185 96 Operator 5 6 93 148 111 53 20 267 112 274 9 205 164 299 8 80 174 245 114 143 10 80 43 55 71 52 278 130 a 200 7 267 88 129 176 247 269 127 44 110 16 223 196 266 108 104 ola 26 210 201 251 282 101 240 3 4 134 43 93 36 238 22 140 180 85 129 278 265 35 152 150 288 157 236 145 124 38 176 102 252 117 41 32 221 200 289 271 Test 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 84 278 73 125 218 48 189 107 96 180 182 20 90 62 65 | 103 40 31 266 17 281 170 209 72 42 214188 154 238 130 134 42 82 291 46 33 286 223 180 115 253 149 38 22 28 33 128 54 290 291 107 207 298 186 121 129 100 132 193 46 193 189 58 59 39 163 72 250 97 285 Develop an integer programming formulation to determine the assignment of tests to the operators such that the difference between the maximum and minimum among the total duration of the tests assigned to the operators is minimized. (For example, if the total duration of the tests assigned to these 10 operators are 202, 152, 93, 79,95, 145, 156, 185, 192 and 173 minutes, then the difference between the maximum and minimum is 202 79 2 = 123.) Define your decision variables clearly. You may want to define additional notation for the duration parameters given in the table above in order to write down the model in a compact form. If you do so, please clearly define it as well and explain how you are going to handle the empty cells in the table. (Hint: You have to define additional variables to determine the maximum and minimum total test durations among all operators.)