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This paper develops a dynamic programming solution algorithm for the NLBP to obtain an optimal N-level batching with hierarchical clustering structure.
In the dynamic programming algorithm for the NLBP, stage n (n = 1, 2, ..., N) is represented by the level and the state at a stage n is the numbers of items of cluster not batched yet until level n: that is [mathematical expression not reproducible].
The forward DP recursive equations for the NLBP are
We find the range of [mathematical expression not reproducible] needed to be considered in the DP recursive equations to find an optimal solution of the NLBP when unit processing cost, [mathematical expression not reproducible], is charged for batched items.
In other words, it is sufficient to consider [mathematical expression not reproducible] to obtain an optimal solution of the NLBP. Here, note that [mathematical expression not reproducible] for all n.
Let [PHI]([l.sup.(n)]) be the set of [mathematical expression not reproducible] needed to be considered in DP recursive equations to obtain an optimal solution of the NLBP when unit processing cost, [mathematical expression not reproducible], is charged for batched items.
Responses from the questionnaire (Figure) were grouped into four categories comparing the use of opioids for treating cancer pain and NLBP:
Differences in ratings of responses for treating cancer pain with opioids compared with ratings for treating NLBP with opioids were tested using paired t-tests.
Residents expressed moderately high concern that prescribing opioids for patients with NLBP would cause addiction, abuse, and serious side effects and would reduce use of other pain treatments (Table 1).
They agreed that opioids were effective and well tolerated in patients with cancer but were less certain about NLBP. The belief was much stronger that cancer patients benefited more and tolerated opioids better compared with those with NLBP (Table 2).
Residents were much more comfortable prescribing opioids, regardless of doses needed, for patients with cancer than with NLBP (Table 2).
The study is a 12-week, randomised, double-blind, international (Germany, Italy, Poland, Romania, UK and India) Phase IIb/III trial in which 411 patients with chronic NLBP of at least moderate severity, as judged by the patients, have been randomised to treatment with ralfinamide at a daily oral dose of 160 mg, 320 mg, or matched placebo.
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