Notations

q

The quantity of procurement

I

The set of growers

$I^{\ast }$

The winner set of growers

K

The set of nonmoney attributes

${\theta }_i$

The attribute bundle selected by grower i

${\Theta }_k$

Discrete valuations space of attribute k

$c_i\left(\theta \right)$

Planting cost function of grower i for each attribute bundle $\theta$

$v\left(\theta \right)$

The valuation function of the procurer

$p_i$

The price submitted by grower i for one unit produce

$p_i^q$

The price submitted by grower i for q unit of produces

$B_i$

The multidimensional bid of grower i

$y_i^q$

The constructed score of grower i

$y_{\ast }^q$

The q_th highest score in the constructed