BOSTON (SHNS) – Weighing whether public transit riders are entitled discounts or rebates following weeks where snow and cold disrupted MBTA services, state transportation policymakers on Tuesday greeted five such proposals with a mix of skepticism and interest.

Shutdowns and limited service on the transit system have led to some public calls for rider compensation, and Gov. Charlie Baker said he is “open” to the idea of refunds. Baker on Wednesday plans to recommend a major funding hike for the MBTA, part of a bid to improve service.

Massachusetts Department of Transportation Board of Directors Chairman John Jenkins said he is concerned about “setting a precedent” and questioned what the rebates or discounts aimed to accomplish.

Dominic Blue, a MassDOT board member, said that for commuter rail customers, monthly passes are fairly “expensive,” and he believes a rebate or discount program could help the goal of “gaining the trust back from our customers” and could attract new riders.

“It would be nice but given where we are today . . . I do not think it makes sense. I feel pretty strongly about it. We do not have the money,” said board member Janice Loux. She said the resources spent studying the issue are “just appalling to me.”

The board’s Finance and Audit Committee did not recommend a course of action Tuesday.

Transportation Secretary Stephanie Pollack said the state should either give riders a monetary benefit or a plan for how to improve service.

“The same money we would use to give back to people is the same money we would use to fix the system,” Pollack said on WBZ radio Monday night. On Tuesday, Pollack reiterated that point and said if the board doesn’t want to move forward on a refund or discount program it should think of “what else can we do for our passengers.”

Pollack told reporters she hadn’t made up her mind on the issue and said it would need to be decided before the board sets the budget in April.

Public transit is subsidized, so part of the cost of every trip is already discounted by taxpayers, who may also be riders.

MBTA Chief Financial Officer Jonathan Davis presented five potential options, providing free fares, discounted monthly passes and rebates or refunds. One option to accept monthly commuter rail passes an extra month would be “easy to implement,” but is the most expensive option, costing $10.5 million.

The costs associated with the five alternatives add up to $32.5 million. One $6 million plan would make fares free for a week and another would give temporary discounts to monthly and weekly pass-holders throughout the system, which would take an estimated two months to implement and cost $3.6 million. A cash rebate program for monthly pass-holders would take longer and cost about $6.4 million, including $360,000 on shipping and handling.

Davis also said the T would consider waiving fees for paratransit trips that were canceled because of weather conditions. Marilyn McNab, a Boston resident, suggested refunds for canceled trips.

Board member Andrew Whittle suggested fines against the new commuter rail operator Keolis could be used to fund refunds or discounts. Davis said so far the T has assessed about $3 million in penalties.