High crop densities are valuable to increase weed suppression, but growers might be reluctant to implement this practice due to increased seed cost. Because it is also possible to lower planting densities in areas with no or low weed interference risk, the area allocated to each planting density must be optimized considering seed cost and productivity per plant. In this study, the growth and yield of maize (Zea mays L.), cotton (Gossypium hirsutum L.), and soybean [Glycine max (L.) Merr.] were characterized in response to low planting densities and arrangements. The results were used to develop a bioeconomic model to optimize the area devoted to high- and low-density plantings to increase weed suppression without increasing seed cost. Physiological differences seen in each crop varied with the densities tested; however, maize was the only crop that had differences in yield (per area) between densities. When a model to optimize low and high planting densities was used, maize and cotton showed the most plasticity in yield per planted seed (g seed−1) and area of low density to compensate for high-density area unit. Maize grown at 75% planting density compared with the high-planting density (200%) increased yield (g seed−1) by 229%, return by 43%, and profit by 79% while decreasing the low-density area needed to compensate for high-density area. Cotton planted at 25% planting density compared with the 200% planting density increased yield (g seed−1) by 1,099%, return by 46%, and profit by 62% while decreasing the low-density area needed to compensate for high-density area. In contrast, the high morphological plasticity of soybean did not translate into changes in area optimization, as soybean maintained return, profit, and a 1:1 ratio for area compensation. This optimization model could allow for the use of variable planting at large scales to increase weed suppression while minimizing costs to producers.

As a new business form, the buy-online and pick-up-in-store (BOPS) mode allows consumers to pay for goods online and pick them up in a physical store. In this paper, an equilibrium model is constructed to formulate an optimal decision-making problem for online and offline retailers under the BOPS mode, where the online retailer determines the retail price of the goods and the consignment quantity in a physical store, while the offline retailer chooses the revenue share of profit by a consignment contract. Different to the existing models, the cost of overstocking and loss of understocking are incorporated into the profit function of the online retailer due to the randomness of demand. For the objective function of the offline retailer, the cross-sale quantity generated by the BOPS mode is taken into account. Then the game between the online and offline retailers is expressed as a stochastic Nash equilibrium model. Based on the analytic properties of the model, necessary conditions for the equilibrium solution are obtained. A case study and sensitivity analysis are employed to reveal the managerial implications of the model, which can provide a number of valuable suggestions on optimizing the strategies for the online and offline retailers under the BOPS mode.

The cost-effectiveness of total maximum daily load (TMDL) programs depends heavily on program design. We develop an optimization framework to evaluate design choices for the TMDL for the Potomac River, a Chesapeake Bay sub-basin. Scenario results suggest that policies inhibiting nutrient trading or offsets between point and nonpoint sources increase compliance costs markedly and reduce ecosystem service co-benefits relative to a least-cost solution. Key decision tradeoffs highlighted by the analysis include whether agricultural production should be exchanged for low-cost pollution abatement and other environmental benefits and whether lower compliance costs and higher co-benefits provide adequate compensation for lower certainty of water-quality outcomes.