to name a business model which behave like chicken pecks

Piecemeal (= By a small amount at a time; in stages) supply

Micro retailing

Consider using incremental. The definition of increment is

1.an increase or addition, esp one of a series

2.the act of increasing; augmentation

The term incremental is often used to connote a small increase

of, relating to, being, or occurring in especially small increments - incremental additions; incremental change

Some possible phrases are

incremental implementation

incremental marketing

incremental retailing

If you want it to sound "businessy", how about one of these:

• Micro Demand Fulfilment
• Short Order Supply

You could call it just-in-time inventory, or the just-in-time model.

Just-in-time (JIT) inventory concepts can be used at all levels of production; for example, a car manufacturer might strive to not overstock on parts. But JIT can also be used to describe a retail model between sellers and customers.

One textbook describes the paradigm as follows:

A perfectly synchronized process always supplies just he right quantity of the right quality product, at just the right time, in just the right place. These four "just rights" of synchronization form the core of the just-in-time paradigm. Just-in-time refers to an action taken only when it becomes necessary.

(from Managing Business Process Flows: Principles of Operations Management, by R. Anupindi, et al., 2012; emphasis in the original)

Those who try to use this paradigm find it a challenge to anticipate demand. But you acknowledge thi,s when you said that it was "seemingly impossible but it works in the Internet era when the supplier is a software program."

You can find links to other definitions of just-in-time by visiting this page, including links to business dictionaries.