### Table 1: Decomposing matrices of mixed integer programs.

1997

"... In PAGE 9: ... We used := (#rows) 1:05 2 rounded up as the block capacity, which allows a deviation of 10% of the actual block sizes in the decomposition. Table1 reports the results of our computational experiments for all instances with up to 400 rows. The format is as follows: Column 1 provides the name of the problem, Columns 2 to 4 contain the number of rows, columns and non-zeros of the matrix to be decomposed.... ..."

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### Table 2 Sizes of Mixed Integer Programs

"... In PAGE 23: ...0. Sizes of the reduced mixed-integer programs, as well as their computational times (in CPU seconds) are given in Table2 . In Table 3 we show the initial (default) solution, the heuristic solution derived from the mixed-integer program (15) - (18), and the optimal solution for each problem we considered.... ..."

### Table 2.1: Solving the adversarial problem as a mixed-integer program

2006

### Table 3: Decomposing transposed matrices of mixed integer programs.

"... In PAGE 24: ... The test set consists of all problems with up to 1,000 rows (1,000 columns in the original problem). Table3 shows the results of our computations. Surprisingly, the performance of our algorithm is not only similar to the \primal quot; case, in fact it is even better! We can solve almost all problems with up to 400 rows.... ..."

### Table 2: Decomposing matrices of mixed integer programs.

"... In PAGE 22: ...nder consideration. The rst interesting case in this context are two blocks and we set := 2. We used := (#rows) 1:05 2 rounded up as the block capacity, which allows a deviation of 10% of the actual block sizes in the decomposition. Table2 shows the results that we obtained for matrices of mixed integer programs taken from the Mipliby and preprocessed with the presolver of the general purpose MIP-solver SIP that is currently under devel- opment at the Konrad-Zuse-Zentrum. We again considered all instances with up to 1,000 rows.... ..."

### Table 12 Final fetch vector alphameric assignment scheme- values generated using mixed-integer linear programming.

"... In PAGE 13: ... The alphameric assignment scheme is shown in Table 12. Determination of fetch width constraints If the garbled word data were transformed into a magni- tude value using the alphameric assignment scheme shown in Table12 , it could be assumed that the garbled and correct forms of the same word would map into fair- ly similar (close) magnitude values. If the correct form W.... ..."

### Table 3. Mixed integer program for obtaining a combinatorial lower bound on the optimal number of moves for the stacking problem

### Table 2.3: Problem dimensions for test instances, number of integer and con- tinuous variables, p=q ratio and a comparison of mixed integer programming computing times.

### Table 2.4: Problem dimensions for test instances, number of integer and con- tinuous variables, p=q ratio and a comparison of mixed integer programming computing times.

### Table 1: The mixed integer formulation (ESPMIP) for the engine scheduling problem

2002

"... In PAGE 4: ... We now introduce the variables: ze P one if pattern P a18 a33 e is assigned to engine e a18a71a4 ; zero otherwise xe P1P2 one if pattern P2 a18 a33 e is immediately served after P1 a18 a33 e on e a18a72a4 ; zero otherwise Ti (non-negative) arrival time in location i a18a20a5 of the visiting engine Note, that for the arrival times we need not specify which engine arrives at a particular location since this information is already covered by the z variables. Table1 shows the entire formulation (2) through (11), denoted by (ESPMIP). The given objective function (2) serves as convenient example only.... ..."