Preemptive repayment policy for multiple loans

Ng, C. T.; Ding, Qingqing; Cheng, T.C.E.; Lam, S.S.

doi:10.1007/s10479-011-0872-9

Cited by 3 publications

(5 citation statements)

References 13 publications

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“…The simplified version of the RPML problem considered in references [ 1 ] and [ 2 ] would correspond to a linear programming with the same objective function (3) , but considering only restrictions Eqs ( 4 ) and ( 6 ). Notice that the only variables needed in this case are positive real variables.…”

Section: Methodsmentioning

confidence: 99%

“…Meanwhile the simplified versions of RPML considered in [1] and [2] belongs to the polynomial class, that is, there is an algorithm to efficiently solve this tractable problem. For more details on computational complexity see [5, 6], or [7].…”

Section: Introductionmentioning

confidence: 99%

“…This problem is known in the literature as the Repayment Policy for Multiple Loans (RPML). A simplified version of the RPML problem has been previously modeled as a single machine scheduling problem with the objective of minimizing the maximum completion time of the debts, where the principals of the debts increase as functions of their starting times [ 1 , 2 ]. In the work by [ 1 ], the debts are non-preemptive, that is, once debtors start repaying a loan, they cannot stop paying it until it is completely paid, which is an unrealistic assumption.…”

Section: Introductionmentioning

confidence: 99%

“…In the work by [ 1 ], the debts are non-preemptive, that is, once debtors start repaying a loan, they cannot stop paying it until it is completely paid, which is an unrealistic assumption. On the other hand, [ 2 ] assumed a simplified version of the RPML problem and transformed it into a scheduling problem with preemptive processing times, that is, the debtor can stop repaying a loan and then resume it. The scheduling problem is then approximated with a continuous nonlinear optimization problem.…”

Section: Introductionmentioning

confidence: 99%

“…By proposing a mathematical model for the RPML problem, we close the almost 20 year old open question about the complexity of the RPML which, we find, belongs to the NP-hard complexity class, that is, the time required to solve the problem using any currently known algorithm increases very quickly as the size of the problem grows. Meanwhile the simplified versions of RPML considered in [ 1 ] and [ 2 ] belongs to the polynomial class, that is, there is an algorithm to efficiently solve this tractable problem. For more details on computational complexity see [ 5 , 6 ], or [ 7 ].…”

Section: Introductionmentioning

confidence: 99%

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Repayment policy for multiple loans

2017

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The Repayment Policy for Multiple Loans is about a given set of loans and a monthly incoming cash flow: what is the best way to allocate the monthly income to repay such loans? In this article, we close the almost 20-year-old open question about how to model the repayment policy for multiple loans problem together with its computational complexity. Thus, we propose a mixed integer linear programming model that establishes an optimal repayment schedule by minimizing the total amount of cash required to repay the loans. We prove that the most employed repayment strategies, such as the highest interest debt and the debt snowball methods, are not optimal. Experimental results on simulated cases based on real data show that our methodology obtains on average more than 4% of savings, that is, the debtor pays approximately 4% less to the bank or loaner, which is a considerable amount in finances. In certain cases, the debtor can save up to 40%.

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Section: Methodsmentioning

confidence: 99%