The claimant in this case was a waitress/manager, whose restaurant place of work closed and she was offered what she considered to be unsuitable alternative employment at one of the respondent's other restaurants. 

At the EAT the claimant gave sworn testimony. Maps were studied. The availability of public transport was detailed as were shift times. Child-minding arrangements were also discussed. Asked if she could have made use of a bicycle, she was not enthused. There was no mention of any examination of any exploration by her of the possibility of her getting a lift and so being dropped home or to the new restaurant.

The EAT accepted that a moderate increase in travel time and probable moderate additional expense would have arisen but noted that there was a written commitment given by the respondent to the claimant undertaking to preserve the same terms and conditions that were present in her former employment in the new position offered.

Therefore, the claimant was found to have unreasonably refused the offer of alternative employment and was not entitled to a redundancy payment.
http://www.workplacerelations.ie/en/Cases/2015/July/RP94_2014.html