Managing Workload and Vacation for Analysts: A Complex Production Scenario

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The discussion centers on the challenges of managing workload and vacation for four analysts tasked with reviewing invoices, each with a daily quota of 475 lines. Analysts have varying authority levels based on invoice dollar amounts, complicating the distribution of work. The company mandates a 30-day turnaround for processing invoices while allowing each analyst to accrue up to 22 vacation days annually. Participants express skepticism about equally distributing the workload without using mathematical or statistical formulas, citing insufficient modeling and parameters. Ultimately, the consensus is that achieving a fair workload distribution under these conditions is unfeasible.
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The scenario is this: Four analysts work at a company reviewing invoices. Each analyst is expected to meet a quota of an average of 475 lines reviewed per day. The invoices vary in number of lines and dollar amount. Each analyst has an authority level based on a dollar amount set by management. Two analysts are at the same authority level and the other two are at different levels. In addition, the company must maintain a 30-day turn around for processing the invoices. Also, each analyst accrues up to 22 days of vacation per year. The question: How it is possible to equally distribute the workload with all of the variables discussed above and NOT apply a mathmatical or statistical formula of some sort?
 
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There is no way, and model as well as parameters are insufficiently described to answer that question.
 

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