This study addresses a pricing problem of two substitutable products in a two‐echelon supply chain including two manufacturers and one retailer. The manufacturers sell their products through two distribution channels, namely traditional and Internet channels. The linear demand functions of products depend on selling prices, service value of channels, and quality level of products. Moreover, various market power structures are considered for the members of the supply chain. This study focuses on the specific game‐theoretical approaches to highlight the effect of market power structures and leadership between firms. The manufacturer–leader Stackelberg (MSS) game, retailer–leader Stackelberg game (RSS), manufacturer‐Bertrand competition (MSB), and retailer‐Bertrand competitions (RSB) are applied to analyze equilibrium solutions. The models help both manufacturers and retailer not only to maximize their profits but also to see the influences of their powers and decisions under different strategies. As a result, the leader has enough power to get higher profit, and the maximum profit of the whole supply chain is affected by the market powers of manufacturers and retailer. The best strategies for the retailer are those that are based on the RS games. The results illustrate that lower price does not lead to lower profit, and more sales does not necessarily result in higher profit. Moreover, the Bertrand strategy considered by the manufacturers to determine their optimal decisions is the best strategy from the customers’ perspective.

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The performance of crop models in simulating various aspects of the cropping system is sensitive to parameter calibration. Parameter estimation is challenging, especially for time-dependent parameters such as cultivar parameters with 2–3 years of lifespan. Manual calibration of the parameters is time-consuming, requires expertise, and is prone to error. This research develops a new automated framework to estimate time-dependent parameters for crop models using a parallel Bayesian optimization algorithm. This approach integrates the power of optimization and machine learning with prior agronomic knowledge. To test the proposed time-dependent parameter estimation method, we simulated historical yield increase (from 1985 to 2018) in 25 environments in the US Corn Belt with APSIM. Then we compared yield simulation results and nine parameter estimates from our proposed parallel Bayesian framework, with Bayesian optimization and manual calibration. Results indicated that parameters calibrated using the proposed framework achieved an 11.6% reduction in the prediction error over Bayesian optimization and a 52.1% reduction over manual calibration. We also trained nine machine learning models for yield prediction and found that none of them was able to outperform the proposed method in terms of root mean square error and R2. The most significant contribution of the new automated framework for time-dependent parameter estimation is its capability to find close-to-optimal parameters for the crop model. The proposed approach also produced explainable insight into cultivar traits’ trends over 34 years (1985–2018).

Motivation Epistasis, which is the phenomenon of genetic interactions, plays a central role in many scientific discoveries. However, due to the combinatorial nature of the problem, it is extremely challenging to decipher the exact combinations of genes that trigger the epistatic effects. Many existing methods only focus on two-way interactions. Some of the most effective methods used machine learning techniques, but many were designed for special case-and-control studies or suffer from overfitting. We propose three new algorithms for multi-effect and multi-way epistases detection, with one guaranteeing global optimality and the other two being local optimization oriented heuristics. Results The computational performance of the proposed heuristic algorithm was compared with several state-of-the-art methods using a yeast dataset. Results suggested that searching for the global optimal solution could be extremely time consuming, but the proposed heuristic algorithm was much more effective and efficient than others at finding a close-to-optimal solution. Moreover, it was able to provide biological insight on the exact configurations of epistases, besides achieving a higher prediction accuracy than the state-of-the-art methods. Availability and implementation Data source was publicly available and details are provided in the text.

Performance prediction of potential crosses plays a significant role in plant breeding, which aims to produce new crop varieties that have higher yields, require fewer resources, and are more adaptable to the changing environments. In the 2020 Syngenta crop challenge, Syngenta challenged participants to predict the yield performance of a list of potential breeding crosses of inbreds and testers based on their historical yield data in different environments. They released a dataset that contained the observed yields for 294,128 corn hybrids through the crossing of 593 unique inbreds and 496 unique testers across multiple environments between 2016 and 2018. To address this challenge, we designed a new predictive approach that integrates random forest and an optimization model for G E interaction detection. Our computational experiment found that our approach achieved a relative root-mean-square-error (RMSE) of 0.0869 for the validation data, outperforming other state-of-the-art models such as factorization machine and extreme gradient boosting tree. Our model was also able to detect genotype by environment interactions that are potentially biologically insightful. This model won the first place in the 2020 Syngenta crop challenge in analytics.