**Appendix A**

The basic MILP model for optimizing the polygeneration system during abnormal operations is described by Equations (A1)–(A7) and is similar to the model introduced in [14].

$$\mathbf{max} = \mathbf{c}^{\mathrm{T}} \mathbf{y}^\* \tag{A1}$$

$$\mathbf{A} \cdot \mathbf{x} = \mathbf{y}^\* \tag{A2}$$

$$\mathbf{b}^{\mathsf{T}}\mathbf{x}^{l} \le \mathbf{x} \le \mathbf{b}^{\mathsf{T}}\mathbf{x}^{u} \tag{A3}$$

$$\mathbf{b} \in \langle 0, 1 \rangle \tag{A4}$$

$$\text{y}^{\text{\*}}\_{\text{"river\\_water}} = (1 - \text{D}) \text{ y}\_{\text{"river\\_water}} \tag{A5}$$

$$\mathbf{y}^\* \ge \mathbf{y}^l \tag{A6}$$

$$\mathbf{f}^{l} \le \mathbf{b}^{\mathsf{T}} \mathbf{e} \le \mathbf{f}^{\mu} \tag{A7}$$

The objective function (Equation (A1)) is to maximize the profit of the system, excluding capital cost recovery, where **c**T represents the price vector for the material or energy streams and **y**\* is the net output vector during abnormal operations. The model is subject to material and energy balances (Equation (A2)) dependent on the process operational conditions where **A** is the balanced process matrix during normal operating conditions and **x** is the process scaling vector during abnormal conditions. The scaling vector is bound by the lower (**x***<sup>l</sup>*) and upper (**x***<sup>u</sup>*) operating capacity limits of each available technology (Equation (A3)) where **b**<sup>T</sup> is a binary variable (Equation (A4)) indicating whether a technology is operational (**b**i = 1) or not (**b**i = 0) during abnormal operations. The abnormal conditions occur when there is insufficient river water (Equation (A5)) defined by the drought intensity factor, D. Furthermore, a minimum production level (**y***<sup>l</sup>*) for identified product streams must be met (Equation (A6)). There is also a minimum (f*<sup>l</sup>*) and maximum (f*u*) number of operational technologies at any given time (Equation (A7)), vector **e** represents a column vector with all elements equal to 1.
