Solved at Scale

A Bigger Item List

Eleven integer-weight items and one shared bin capacity form the real instance the external solver reads. The weights are parsed from the solver's model file at build time, and the total size feeds the lower-bound technique from the previous chapter.

highlighted = computed this step

Eleven items

Eleven items, labeled A through K, each with an exact integer weight: item A weighs 48, item G weighs 42, and item K weighs 30. Why: this is the real model the external solver reads, parsed from its model file at build time, not hand-typed into the lesson.

sA=48s_A=48
A bigger item listEleven integer-weight items and one shared bin capacity, parsed from the solver's model file.11 items, capacity 100sizeA48B30C19D36E36F27G42H42I36J24K30capacity100total370

Shared capacity

Every bin has capacity 100. Why: the one-dimensional feasibility rule is unchanged from the earlier chapters, so a bin is feasible only when its exact fill stays at most capacity.

capacity=100\text{capacity}=100
A bigger item listEleven integer-weight items and one shared bin capacity, parsed from the solver's model file.11 items, capacity 100sizeA48B30C19D36E36F27G42H42I36J24K30capacity100total370

Total size

The total item size is 370. Why: the weights are integers, so their sum is exact, and the total is the input to the lower-bound technique from the previous chapter. No solving happens in this lesson.

total size=370\text{total size}=370
A bigger item listEleven integer-weight items and one shared bin capacity, parsed from the solver's model file.11 items, capacity 100sizeA48B30C19D36E36F27G42H42I36J24K30capacity100total370

Diagram note

The table lists one row per item, A through K, plus the capacity and total rows; those row labels are the labels this chapter uses everywhere. Pixel positions are rounded for layout; every item size, fill, total size, and bound is exact.

exact integer weights, parsed not typed\text{exact integer weights, parsed not typed}
A bigger item listEleven integer-weight items and one shared bin capacity, parsed from the solver's model file.11 items, capacity 100sizeA48B30C19D36E36F27G42H42I36J24K30capacity100total370