Introduction
Banks depend on interests to generate profits. Without interest, banks do not have any other source of revenue ( Anderson et al. 2012). For Yeager, the expected gains will be lower than projected since the bank is collecting payment from one source. Therefore, the possible source of revenue in the form of interests is misplaced. However, by the bank looking at opening new lockboxes, it will enable them to get more lockboxes hence allowing the bank to receive more payments and therefore increase their profits.
Summary
Using integer linear programming, the bank will be able to determine if the program is worth the investment; i.e., opening more payment points or the venture will create more loss to the bank. Currently, Yeager National Bank is missing a total of $600,000 in potential interest due to the time it takes to receive the payments from clients. Moreover, given that it takes five days to collect and deposit payments, it is an indication of business inefficiency and especially since the bank depends on those avenues to gain profits in the form of interest.
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Method
Mixed integer linear programming (MILP) is the best method that can be employed to come up with a report for the manager. Given that the annual cost of operations is fixed, the bank does not know precisely the number of lockboxes to put in place. The model can be used to develop the exact number of lockbox to put up, including precise locations to place the lockbox. The formula will be solved four times. This will enable the bank to come up with the best locations to place the lockboxes ( Anderson et al. 2012). The model will also allow the bank to determine the location to put one lockbox, 2, 3 or four lockboxes. It will further assist the bank to identify the costs to place and maintain the lockboxes in those specific locations annually.
Result
Therefore, the following variables will be applicable in this case.
P= Phoenix, otherwise 0 (0 will represent the fact that the lockbox will not be placed in the identified location).
S= 1 lockbox in Salt Lake City or 0.
A= 1 lockbox in Atlanta or 0.
B= 1 lockbox in Boston or 0.
PNW=1 lockbox in the northern part of Phoenix or 0.
PSM= 1 lockbox in the southern part of Phoenix or 0.
BSE= 1 lockbox in south part of Boston else, 0.
The model will have 24 variables and 36 constraints. The primary goal is to minimize the amount of interest income that will be lost. Using the example of the Northwestern region, assuming that the banks decide to place one lockbox, each day, the bank collects $ 80,000 and takes four days to process those payments. At an interest rate of 15%, the bank can save a total of $ 48,000 = this is achieved through the following calculation 15/100 x 4 x $ 80,000 annually if the account of the northwest branch is credited directly. A similar computation will be done for other potential locations. The goal of the coefficient functions for P, S, A, and B are deemed to be zero. Therefore, the costs of operations do not come in at this stage.
Discussion
The first five constraints to be developed represent each location, and it is to ensure that each site gets a lockbox. The subsequent restrictions to be calculated are aimed at ensuring that each region receives an open lockbox. Moreover, during calculation, we have to consider the limitation to place each lockbox per the chosen area. The constraints will be varied further from 1 to 4 since the problem will be resolved four times.
Conclusion
For the bank to maximize and increase their profits, they will have to put up several outlets that will enable them to collects as much proceeds as possible. Moreover, given that the primary source of revenue for the bank is interests, the bank will have to ensure that a precise number of lockboxes is put up, so that they do not put up more which will eat up the revenues collect.
Reference
Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2012). Quantitative methods for business . Cengage Learning.
