Author: Michael Gamper
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The relationship between lead-time and inventory in operations management follows the derivation, published in the textbook Factory Physics from Hopp and Spearman (2000), of the original “Little’s Law” developed to describe the arrival and departure rate in a queuing system. The “Little’s Law” used in operations management states that inventory levels inside a system are proportional to the lead-time of the system, and is described by the following formula:

The formula’s components are:

TH = Throughput of a System in units per time period (equal to sales or shipments of a given system)

WIP = Work in Process in units (equal to Inventory in a given system)

CT = Cycle Time in time (equal to Lead-Time (LT))

If we calculate the WIP or inventory needs in a system with constant output per time period, then we find the following result using the rearranged formula WIP = TH * CT:

Another way to describe the proportional relationship between lead time and inventory is described below, assuming the throughput is constant (as described in the example above):

Lead-time (LT), however, is composed of different lead-time components and often the source of those lead-time components is not properly understood. In general, lead-time has two main components, the physical lead time and the information lead-time. Whilst the physical lead time has been subject to many improvements over the years, the information flow lead time is sometimes still a mystery as to what the source of that lead time is as well as how it impacts inventory along the supply chain.

Lead-Time Composition

The following universal formula applies to total lead-time if we are dealing with independent lead time components:

total lead-time with independent lead time components

Physical Lead-Time

Decomposing physical lead time is related to the physical properties of handling resources, materials and products along the supply chain. Physical properties can be found in production, distribution, transportation, stores etc. The sub-components of physical lead time are (non-exhaustive):

  • Processing Time
  • Set-up Time
  • Cleaning or Tear-down Time
  • Wait Time
  • Idle Time
  • Move Time
  • Storage Time

Information Lead-Time

Decomposing information lead-time is more difficult because it including not only the time of processing and order but also the time lags of making decisions and releasing information to other departments or trading partners. The sub-components of information lead time are (exhaustive):

  • Processing Time, the time is takes to complete a task or process
  • Frequency (repeating event), the time delay between 2 or more tasks or processes
  • Time Fence (single event), the cut off time to make commitments to suppliers or production processes, usually a single task or process which releases a decision
  • Granularity, the aggregation of time to be used for a task or process

Excluded from this statement on information lead-time is any inventory caused by variability, the bull-whip effect of sequential decision making or incomplete information at the time of decision making. This only adds to the total inventory is a system and hence lead-time.

Example

The following example demonstrate the relationship between lead time and inventory. Lead time in the example below is the granularity used in a planning task, first a month and then reduced to a week:

relationship between lead time and inventory

What can be clearly seen is that the average inventory in a system drop by a factor 4 if the granularity is reduced from 4 weeks (ie a month) to 1 week, which is the same factor of 4.

Total Lead-Time Management and Practical Considerations

In today’s world information lead time is a significant source for inventory in any given supply chain system. Before

Information lead time can be removed or optimised it has to be properly understood as to what the source exactly is. When removing information lead time one has to always analyse the relationship to the physical lead time of a system and understand how they interact and where constraints appears. Practical limits such as physical lead time or simply working hours have to be observed, example: flying product from China to Germany will require time and hence becomes a lead time constraint.

On the other hand, addressing the sequential flow of information in many processes through use of a broadcasting system such as collaborative platforms is one example of how to remove information flow lead time for a supply chain system.

Reducing lead time will always reduce inventory. In an ideal system the reduction will always follow the Little’s Law. In a real life system, however, other factors such as human interpretation and second guessing can make such a reduction less impactful.

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