Six different beta distributions, with parameters α, β listed below, were used as base distributions:
α = 0.5, β = 0.5
α = 1.0, β = 2.0
α = 2.0, β = 3.0
α = 2.0, β = 2.0
α = 3.0, β = 1.0
α = 3.0, β = 2.0
Each such distribution was discretized at s equally spaced points, where s is the number of sizes. These base probabilities were then each independently multiplied by a random factor uniformly distributed over the interval [1 – ε, 1 + ε]. Since the resulting values do not in general sum to 1, we renormalized the values to produce genuine probabilities for the s sizes in this generated profile for this store. The store volume, randomly generated from [5, 180], was then multiplied by the profile values to obtain the demand distributions tabulated later.
Data sets were produced for n = 30, 90, 150 stores with equal numbers of profiles generated from each of the m = 6 base distributions. In the problems below, the number of sizes is s = 4 and the perturbation parameter ε was selected from {0.15, 0.20, 0.25}. For each pair (n, ε) five replications were randomly generated.
The three tables below correspond to n = 30, 90, 150 stores. The three columns of each table correspond to the values 0.15, 0.20, 0.25 of the perturbation parameter ε. The five rows correspond to the five replications for each pair (n, ε).
Each data set in the table has a header record containing the value n, s, m. The succeeding records contain a store number (repeated in the first and second columns) followed by the s demand values generated for that store.
In the majority of the cases, the best solution found was the “natural” solution with bins containing all the n/m profiles generated from the same base distribution. Specifically, the natural binning has the first n/m stores from {1, 2, ..., n} in the first bin, the next n/m stores from {1, 2, ..., n} in the second bin, and so forth. In 8 of the 45 test problems, however, the natural solution was not the best found, and the best solutions known in these cases are given in the files soln(1), soln(2), ..., soln(8).
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0.15 |
0.20 |
0.25 |
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replication 1 |
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replication 2 |
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replication 3 |
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replication 4 |
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replication 5 |
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0.15 |
0.20 |
0.25 |
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replication 1 |
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replication 2 |
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replication 3 |
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replication 4 |
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replication 5 |
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0.15 |
0.20 |
0.25 |
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replication 1 |
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replication 2 |
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replication 3 |
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replication 4 |
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replication 5 |