Cash flow and Queueing Theory: The Lifeblood of Business

Cash flow is the life blood of any business and one of the best metrics to analyze cash flow is the Cash Conversion Cycle (Net Operating Cycle). It's a measure of liquidity by determining the time elapsed from when a company invests working capital to when it collects cash. It is calculated as:

CCC = DOH + DOS - number of days payables

• DSO - Days of sales outstanding (Account Receivable collection to cash)
  
• DOH - Days on hand - how long inventory is held
• Number of days payables - Accounts payable liquidated to cash instrument payments to suppliers
  

Recall that:

DSO = AR / Average days sales on credit or [AR turnover]
DOH = COGS / Average Inventory [Inv turnover]
Number of days payables = AP / Average day's COGS [AP turnover]

aka: How long is money sitting in any particular stage?

It logically follows that there are several operational strategies companies can use to influence these cycles. Depending on the nature of the business in question, the benchmarks for operations performance will be different, but can still be influenced in several ways:

• Extend / reduce time for collections terms
• Extend / reduce payment terms to suppliers
• Just-in-time / overstock inventory practices
• Aggressive sales practices
• Financing receivables / payables
  

Other issues that can arise are issues like churning. Abrupt halts in cash flow can result in expensive financing solutions. This must be counter balanced against the potential lost revenue in sales from out of stock scenarios. However, with proper planning and management these situations should generally be avoided altogether or at least optimized for maximum profit.

Looking at this financial model, there is an analogous model which can be taken in queuing theory:

• Throughput - cash flow (as COGS per period)
  
• Latency - float
  
• Arrival rate (λ)- incoming cash (AR conversion rate to cash)
  
• L - Inventory
  
• Processing rate (μ) - cash output (AP conversion rate to cash)
  

If you consider cash flow as a queue, you can suddenly use a whole host of queuing model formulas to describe your cash flow, things like Little's law:

L= λ W

And queue formulas such as utilization rate?

ρ = λ / μ

This formula essentially describes a short term profitability based on your most liquid assets (or an approximation of overall real profit margins). This has similar characteristics as the Current Quick ratio, but differs in that it describes financial performance as a partial derivative with respect to time (shorter term marginal performance - this metric describes the change in liquidity - rather than the current financial position of your liquidity).

While a good measure of liquidity, cash flow can also indicate if there are other problems going on as well. For instance, if cash conversion rates are too slow, that may be indicative of credit problems and possible default scenarios (a topic for another post).

* Quick note, in order for queuing theory to work, you HAVE to assume FIFO accounting (queues are FIFO in nature). LIFO would be better represented by memory stack models (push and pop flows).