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In many production/distribution systems, materials flow in fixed lot sizes (e.g., in full truckloads or full containers) and under regular schedules (e.g., delivery every week). In this paper, we study a multiechelon serial system with batch ordering and fixed replenishment intervals. We derive the optimal inventory control policy, provide a distribution-function solution for its optimal control parameters, and present an efficient algorithm for computing those parameters. Further, we show that the optimal expected system cost is minimized when the ordering times for all stages are synchronized. In contrast to the known approach in the literature that develops a lower bound for the average cost of a given period for the classical serial system, we develop a lower bound for the average total cost over an appropriately defined cycle and then construct a policy that reaches the lower bound. We also discuss its extension to the nonlinear shortage cost case (i.e., the nonlinear cost case). This paper generalizes several recent results on the analysis of multiechelon systems.

Numerous mapping projects conducted on different species have generated an abundance of mapping data. Consequently, many multilocus maps have been constructed using diverse mapping populations and marker sets for the same organism. The quality of maps varies broadly among populations, marker sets, and software used, necessitating efforts to integrate the mapping information and generate consensus maps. The problem of consensus genetic mapping (MCGM) is by far more challenging compared with genetic mapping based on a single dataset, which by itself is also cumbersome. The additional complications introduced by consensus analysis include inter-population differences in recombination rate and exchange distribution along chromosomes; variations in dominance of the employed markers; and use of different subsets of markers in different labs. Hence, it is necessary to handle arbitrary patterns of shared sets of markers and different level of mapping data quality. In this article, we introduce a two-phase approach for solving MCGM. In phase 1, for each dataset, multilocus ordering is performed combined with iterative jackknife resampling to evaluate the stability of marker orders. In this phase, the ordering problem is reduced to the well-known traveling salesperson problem (TSP). Namely, for each dataset, we look for order that gives minimum sum of recombination distances between adjacent markers. In phase 2, the optimal consensus order of shared markers is selected from the set of allowed orders and gives the minimal sum of total lengths of nonconflicting maps of the chromosome. This criterion may be used in different modifications to take into account the variation in quality of the original data (population size, marker quality, etc.). In the foregoing formulation, consensus mapping is considered as a specific version of TSP that can be referred to as “synchronized TSP.” The conflicts detected after phase 1 are resolved using either a heuristic algorithm over the entire chromosome or an exact/heuristic algorithm applied subsequently to the revealed small non-overlapping regions with conflicts separated by non-conflicting regions. The proposed approach was tested on a wide range of simulated data and real datasets from maize.

The paper is devoted to the problem of multipoint gene ordering with a particular focus on \"dominance\" complication that acts differently in conditions of coupling-phase and repulsion-phase markers. To solve the problem we split the dataset into two complementary subsets each containing shared codominant markers and dominant markers in the coupling-phase only. Multilocus ordering in the proposed algorithm is based on pairwise recombination frequencies and using the well-known travelling salesman problem (TSP) formalization. To obtain accurate results, we developed a multiphase algorithm that includes synchronized-marker ordering of two subsets assisted by re-sampling-based map verification, combining the resulting maps into an integrated map followed by verification of the integrated map. A new synchronized Evolution-Strategy discrete optimization algorithm was developed here for the proposed multilocus ordering approach in which common codominant markers facilitate stabilization of the marker order of the two complementary maps. High performance of the employed algorithm allows systematic treatment for the problem of verification of the obtained multilocus orders, based on computing-intensive bootstrap and jackknife technologies for detection and removing unreliable marker scores. The efficiency of the proposed algorithm was demonstrated on simulated and real data.

This study examined performer, rater, occasion, and sequence as sources of variability in music performance assessment. Generalizability theory served as the study's basis. Performers were 8 high school wind instrumentalists who had recently performed a solo. The author audio-recorded performers playing excerpts from their solo three times, establishing an occasion variable. To establish a rater variable, 10 certified adjudicators were asked to rate the performances from 0 (poor) to 100 (excellent). Raters were randomly assigned to one of five performance sequences, thus nesting raters within a sequence variable. Two G (generalizability) studies established that occasion and sequence produced virtually no measurement error. Raters were a strong source of error. D (decision) studies established the one-rater, one-occasion scenario as unreliable. In scenarios using the generalizability coefficient as a criterion, 5 hypothetical raters were necessary to reach the .80 benchmark. Using the dependability index, 17 hypothetical raters were necessary to reach .80.