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The objective of the RBP is to develop a feasible blocking plan which, in conjunction with other operating policies, minimizes the total cost of delivering the commodities.
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This paper studies the design structures of feasible block designs when the block sizes are unequal.
However, in a practical application, the number of feasible blocks will be limited.
Constraint (8) makes sure that sufficient output quantities are allocated from the feasible blocks ( i in I (k ) ), i.e. from those preceding the due date of demand element k, to each of the demand elements.
Let t0 denote the maximum number of tag SNPs required among all feasible blocks.
The data in arrays E, F, and S were calculated in preprocessing, and the size of each array is L, the number of all feasible blocks.
Finding a segmentation that consists of k feasible blocks and maximum total length can be completed using dynamic programming based on the recurrence relation.
Here | B i | denote the length of block B i. Assuming that all of the feasible blocks and tag SNPs required for each block have been preprocessed, the longest-blocks- t-tags problem can be solved in O tL) time, where L denotes the total number of feasible blocks.
While k = 1, the boundaries of the block can be found by scanning the leftmost marker array and appending the longest feasible block in [ i, j] to a global data structure.
We point out that these efficiency results of our algorithms can be applied in many different definitions of diversity functions, provided that we can precompute the boundaries of all feasible blocks and tag SNPs required for these blocks.
The algorithm is shown in Algorithm 3. Theorem 7 (longest-blocks- t -tags) Assume that the maximum number of tag SNPs required among all feasible blocks, t 0, is a constant.
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