Offsetting algorithms in liquidity-saving mechanisms (LSMs) reduce the liquidity needs of payment system participants by finding solutions to the bank clearing problem. In this paper, we propose a new offsetting algorithm based on mixed-integer linear programming solvers. We then perform simulations to compare the performance of our approach with that of two of the most well-known offsetting algorithms in the LSM literature. While our approach is not guaranteed to find the optimal solution to the bank clearing problem, it outperformed the two other algorithms in more than 91% of our simulations. In addition to performing better, our approach also presents four unique advantages: it enables payment system operators to explicitly formulate and dynamically amend the objective function they are using; it is extremely easy to implement as it uses external solver capabilities; it can be used as a benchmark by payment system operators to assess how well their LSM algorithm performs compared with optimal solutions; and it allows payment system operators to optimize over multiple variables (eg, maximize value cleared and minimize delay outstanding) and set up a maximum rate of substitution between those variables. In the current context of payment systems renewal and central bank digital currency implementation, this paper could be of interest to policy makers working on the design of new LSM features.