Traditional multiple-discrete continuous choice models that have been formulated and applied in recent years consider a single linear resource constraint, which, when combined with consumer preferences, determines the optimal consumption point. However, in reality, consumers may face multiple resource constraints, such as those associated with time, money, and storage capacity. Ignoring such multiple constraints and instead using a single constraint can, and in general will, lead to poor data fit and inconsistent preference estimation, which can then have a serious negative downstream effect on forecasting and welfare/policy analysis. Unlike earlier attempts to address this multiple constraint situation, we formulate a new multiple-constraint (MC) multiple discrete continuous extreme value (MDCEV) model (or the MC-MDCEV model) that retains a closed-form probability structure and is as simple to estimate as the MDCEV model with one constraint. We achieve this by assuming a type-I extreme value distribution for the error term in its minimization form in the baseline utility preference of each good rather than a maximization form as in Bhat's (2005; 2008) original MDCEV formulation. The statistical foundation of the proposed model is based on the fact that the difference between a minimal type-I extreme value random variable with scale σ and the weighted sum of the exponential of standardized minimal type-I extreme value random variables (scaled up by σ) leads to an apparently new multivariate distribution that has an elegant and closed-form survival distribution function. Results from a simulation experiment show that our proposed model substantially outperforms single-constraint models; the results also highlight the serious mis-estimation that is likely to occur if only a subset of active constraints is used. The proposed model is applied to a case of week-long activity participation where individuals are assumed to maximize their utility from time-use subject to time and money budgets.It is hoped that our proposed simple closed-form multi-constraint MDCEV model will contribute to a new direction of application possibilities and to new research into situations where consumers face multiple constraints within a multiple discrete-continuous choice context.

近年来制定和应用的传统多离散连续选择模型考虑的是单个线性资源约束，当与消费者偏好结合时，可确定最佳的消费点。但是，实际上，消费者可能会面临多种资源约束，例如与时间，金钱和存储容量相关的资源约束。忽略这样的多个约束，而是使用单个约束，通常会导致数据拟合差和偏好估计不一致，从而对预测和福利/政策分析产生严重的负面负面影响。与早期解决这种多重约束情况的尝试不同，我们制定了一个新的多重约束（MC）多重离散连续极值（MDCEV）模型（或MC-MDCEV模型），该模型保留了封闭形式的概率结构，并且与具有一个约束的MDCEV模型一样容易估算。我们通过假设误差项的I型极值分布以其最小化形式出现在每种商品的基准效用偏好中，而不是像Bhat（2005; 2008）原始MDCEV公式那样以最大化形式来实现。所提出模型的统计基础基于以下事实：标度为σ的最小I型极值随机变量与标准化的I类极小值随机变量的指数加权和之间的差（按σ放大） ）导致出现了新的多元分布，该分布具有优雅且封闭形式的生存分布函数。仿真实验的结果表明，我们提出的模型明显优于单约束模型。结果还突出表明，如果仅使用活动约束的子集，很可能会发生严重的错误估计。提议的模型适用于为期一周的活动参与的情况，其中假定个人在时间和金钱预算的约束下，从时间使用中最大化自己的效用。