Indices t time period $c\text{ }\text{ }{c}^{\prime }\text{ }\text{ }{c}_{t}$ cells v vessel g tugboat ${p}_{i}$ path; ${p}_{i}=\left({c}_{1},\cdots ,{c}_{T}\right)$ ${\omega }_{v}$ scenario for vessel v; ${\omega }_{v}=\left(t,{p}_{i}\right)$ $\overline{\omega }$ scenario for all vessels $\overline{\omega }=\left({\omega }_{1},\cdots ,{\omega }_{v}\right)$ Sets $\mathcal{C}$ set of cells $\mathcal{V}$ set of vessels $\mathcal{G}$ set of tugboats $\mathcal{T}$ set of time period $\mathcal{F}\left(c\right)\subseteq \mathcal{C}$ set of cells adjacent to cell c ${\mathcal{P}}_{{\omega }_{v}t}$ set of paths for vessel scenario ${\omega }_{v}=\left(t,{p}_{i}\right)$ ${\Omega }_{v}$ set of scenarios for vessel v $\overline{\Omega }$ set of all possible scenarios $\overline{\Omega }={\Omega }_{1}×\cdots ×{\Omega }_{v}$ Parameters ${K}_{{\omega }_{v}}$ environmental consequence associated with vessel v in scenario ${\omega }_{v}$ ${R}_{{\omega }_{v}}$ failure probability for vessel scenario ${\omega }_{v}$ ${R}_{\overline{\omega }}$ probability for scenario $\overline{\omega }=\left({\omega }_{1},\cdots ,{\omega }_{v}\right)$ , ${R}_{\overline{\omega }}={\prod }_{v\in \mathcal{V}}\text{ }{R}_{{\omega }_{v}}$ ${Q}_{gc{\omega }_{v}}$ probability of successful hook-up by tugboat g with vessel v, given tugboat g is in cell c at time of distress call t and vessel v follows scenario ${\omega }_{v}=\left(t,{p}_{i}\right),{p}_{i}\in {\mathcal{P}}_{{\omega }_{v}t}$ ${c}_{0g}$ initial position of tugboat g Variables ${x}_{gct}$ binary variable taking the value 1 if tugboat g is in cell c at time t, 0 otherwise ${z}_{gc{\omega }_{v}}$ binary variable takes the value 1 if tugboat g is in cell c at time of distress call t and is allocated (nearest) to vessel v doing scenario ${\omega }_{v}$