The below compressed files are for the Capacitated Task Allocation problem expressed in Cplex .lp format. Only one instance for each Task <--> Processor assignment problem is presented below, however multiple capacitated instances can be created from a single instance given they have the same coefficients and structure except for the capacity on the number of tasks that can be assigned to a processor.
Problem sets used in Capacitated Task Allocation
LK15_10_5F.zip
LK15_10_9E.zip
LK20_10_5.zip
LK50_10_50.zip
LK100_10_100.zip
To create various capacitated problem instances, simply change the right hand side of the capacity constraints for a given problem. For example, below are portions of the problem LK15_10_5F.lp, which models the assignment of 15 tasks to 10 processors, each with a capacity for handling 5 tasks. Changing the <= 5 to <=10 creates a new problem instance.
Minimize
+ 79 x1_1+ 84 x1_2+ 115 x1_3+ 72 x1_4+ 70 x1_5+ 113 x1_6+ 142 x1_7+ 74 x1_8+
141 x1_9+ 95 x1_10
+ 119 x2_1+ 71 x2_2+ 95 x2_3+ 124 x2_4+ 99 x2_5+ 82 x2_6+ 129 x2_7+ 144 x2_8+
105 x2_9+ 100 x2_10
+ 121 x3_1+ 104 x3_2+ 66 x3_3+ 143 x3_4+ 136 x3_5+ 132 x3_6+ 93 x3_7+ 154 x3_8+
156 x3_9+ 139 x3_10
+ 94 x4_1+ 130 x4_2+ 167 x4_3+ 167 x4_4+ 104 x4_5+ 74 x4_6+ 142 x4_7+ 148 x4_8+
168 x4_9+ 94 x4_10
+ 63 x5_1+ 86 x5_2+ 86 x5_3+ 70 x5_4+ 82 x5_5+ 98 x5_6+ 63 x5_7+ 120 x5_8+ 116
x5_9+ 70 x5_10
+ 132 x6_1+ 44 x6_2+ 54 x6_3+ 133 x6_4+ 133 x6_5+ 117 x6_6+ 136 x6_7+ 113 x6_8+
46 x6_9+ 48 x6_10
+ 56 x7_1+ 103 x7_2+ 64 x7_3+ 66 x7_4+ 126 x7_5+ 95 x7_6+ 115 x7_7+ 64 x7_8+ 102
x7_9+ 74 x7_10
+ 69 x8_1+ 123 x8_2+ 116 x8_3+ 116 x8_4+ 49 x8_5+ 42 x8_6+ 111 x8_7+ 104 x8_8+
93 x8_9+ 118 x8_10
+ 87 x9_1+ 124 x9_2+ 99 x9_3+ 112 x9_4+ 74 x9_5+ 123 x9_6+ 42 x9_7+ 85 x9_8+ 72
x9_9+ 108 x9_10
+ 78 x10_1+ 116 x10_2+ 55 x10_3+ 124 x10_4+ 123 x10_5+ 104 x10_6+ 49 x10_7+ 98
x10_8+ 67 x10_9+ 101 x10_10
+ 81 x11_1+ 59 x11_2+ 115 x11_3+ 70 x11_4+ 58 x11_5+ 82 x11_6+ 109 x11_7+ 24
x11_8+ 110 x11_9+ 104 x11_10
+ 28 x12_1+ 52 x12_2+ 90 x12_3+ 90 x12_4+ 17 x12_5+ 56 x12_6+ 100 x12_7+ 27
x12_8+ 36 x12_9+ 29 x12_10
+ 23 x13_1+ 31 x13_2+ 100 x13_3+ 106 x13_4+ 73 x13_5+ 58 x13_6+ 112 x13_7+ 21
x13_8+ 101 x13_9+ 80 x13_10
+ 40 x14_1+ 100 x14_2+ 23 x14_3+ 87 x14_4+ 63 x14_5+ 26 x14_6+ 83 x14_7+ 14
x14_8+ 85 x14_9+ 74 x14_10
+ 17 x15_1+ 75 x15_2+ 71 x15_3+ 63 x15_4+ 70 x15_5+ 50 x15_6+ 74 x15_7+ 0 x15_8+
43 x15_9+ 98 x15_10
+ [ - 46 x1_1*x2_1 - 102 x1_1*x3_1 - 10 x1_1*x4_1 - 44 x1_1*x5_1 - 116
x1_1*x6_1 - 18 x1_1*x7_1 - 168 x1_1*x8_1 - 130 x1_1*x9_1 - 64 x1_1*x10_1 - 148
x1_1*x11_1 - 156 x1_1*x12_1 - 90 x1_1*x13_1 - 122 x1_1*x14_1 - 72 x1_1*x15_1
- 8 x2_1*x3_1 - 34 x2_1*x4_1 - 152 x2_1*x5_1 - 74 x2_1*x6_1 - 14 x2_1*x7_1 - 68
x2_1*x8_1 - 124 x2_1*x9_1 - 102 x2_1*x10_1 - 44 x2_1*x11_1 - 190 x2_1*x12_1 - 28
x2_1*x13_1 - 38 x2_1*x14_1 - 34 x2_1*x15_1
and so on ...
subject to
\\ each processor can handle only so many tasks workload
+ x1_1 + x2_1 + x3_1 + x4_1 + x5_1 + x6_1 + x7_1 + x8_1 + x9_1 + x10_1
+ x11_1 + x12_1 + x13_1 + x14_1 + x15_1
<= 5
+ x1_2 + x2_2 + x3_2 + x4_2 + x5_2 + x6_2 + x7_2 + x8_2 + x9_2 + x10_2
+ x11_2 + x12_2 + x13_2 + x14_2 + x15_2
<= 5
and so on for the remaining tasks to be assigned...