The Functional Relationship of Lead-Time and Inventory
The objective of this article is to ‘refresh our memories’ about one of the most fundamental relationships in supply chain management:
Inventory is proportional to Lead Time
Let us remind ourselves where this started. This relationship was first defined in the context of the semiconductor industry, managing complex material flows through a production plant. Known as “Little’s Law”, the relationship is expressed as follows:
LT (Lead-Time) = CT (Cycle-Time) * I (Inventory)
CT = 1 / Tact Rate, or described in business language: CT = 1 / (PROCESS TIME per Piece)
If the cycle time stays constant, then lead-time will be longer in proportion to the amount of inventory. However, lead-time increases may result from a variety of additional factors. Let us explore those.
Increasing Lead – Time through Disturbance
The proportional relationship is disturbed through either ‘clogging’ or a material shortage – the result of an issue with managing the flow of parts efficiently. This is expressed as follows:
WAIT TIME(PART) = f(Load) = f(material availability) = EXCESS BUFFER = Work in Progress / CT
The proportional relationship can also be impacted by ‘starvation’ (unused capacity) – the result of an issue with resource utilisation due to the wrong mix of work in front of the resource. This is expressed as follows:
WAIT TIME(RESOURCE) = IDLE TIME
At any given point in time, for a given part or resource, the WAIT TIME is either caused by clogging or starvation. In a system comprising many resources and parts, both types of WAIT TIME will co-exist at any point in time.
Increasing Lead-Time through Load and Batching
Queuing is caused by clogging (effect of utilisation) and follows a hyperbolic relationship. We explored in another article the relationship between lead time and load on a plant. This is expressed as follows:
Batch = Customer Order (for a MTO Business)
Batch = Replenishment Quantity (for a MTS Business)
The lead-time, in the context of a supply chain, of a batch can be expressed as follows:
LT(One Batch) = PROCESS TIME per Piece * BATCH SIZE + SETUP TIME + WAIT TIME + MOVE TIME(Internal and External Shipments(3PL)) + STORAGE TIME(DC) + HANDLING TIME(DC)
Through the “Bill of Materials” a number of lead-times are connected ie for each part, and as “The Goal” taught us, lead times are not static. The dynamic element is the wait time component of the equation. What makes it
dynamic, as we have seen above, is the effect of queuing, material shortage or starvation. In the real-world supply chain, this can happen in multiple areas, such as:
- Transportation (finite capacity of trucks and containers, shipping schedules, FTL constraint, etc)
- Production (load of production orders, batch sizes)
- Distribution Center (order load, inbound and outbound load (slots), picks, etc)
Increasing Lead-Time through Frequency and Granularity
Another impact area on lead-time is the process or event frequency, and the time granularity of an underlying planning process. As shown below, when transitioning from monthly to weekly time granularity, the resulting factor is 4. This results into the same impact on average inventory, hence the difference of the average inventory a system carries is reduced by the factor of 4. The frequency of an activity has the same impact. If I release a PO once a month or once a week, it will impact the corresponding inventory levels the same way
Whilst the first 2 impact areas are material flow related, the last one is information flow related. As a consequence, managing both material flow and information flow impact on the lead-time must be managed by a business operating a global supply chain.
Many companies have traditionally focused on the physical material flow impact, the information flow impact is often ignored or not understood.