Fillingremain

Fillingremain is a term used in operations research and computer science to describe the amount of unused capacity left after attempting to fill a container, buffer, or dataset according to a predefined filling policy. It serves as a measure of how far a system is from full utilization under the chosen filling rule.

Formal notion: Given a container with capacity C and a set of items with sizes, a filling policy selects a subset (and possibly partial items) to fill up to C. The fillingremain R is the remaining capacity, often defined as R = max(0, C - V_eff), where V_eff is the total size placed under the policy. Depending on the policy, V_eff may reflect whole items only, or allow fractional placement of the final item, which alters the resulting remainder.

Computation and examples: In a greedy filling scenario with capacity 100 and items of sizes 40 and 50, selecting 40 and 50 fills 90 units, leaving a remainder of 10. If a policy permits splitting the last item, one could place 40 and 60 of a 50-sized item (if allowed by the model), achieving a remainder of 0. The concept thus captures both discrete and fractional filling scenarios.

Applications: Fillingremain is used in bin packing, memory allocation, warehouse and production planning, and network packetization, where understanding residual capacity informs efficiency and decision making.

Variants and interpretation: The exact definition of fillingremain can vary with policy assumptions, such as whether partial items are permitted and how ties are broken among equal-sized options. The term is thus a modeling convenience rather than a universally standardized metric.

See also: bin packing, capacity planning, residual capacity.