somvoorwaarde

Somvoorwaarde is a term used in Dutch mathematical language to describe a constraint that restricts the sum of a set of quantities or variables. It expresses that the total amount of some resources, parts, or signals must satisfy a specified condition. In formal notation, a somvoorwaarde often takes the form of a linear equation or inequality involving a sum, for example sum_{i=1}^n x_i = B or sum_{i=1}^n x_i ≤ B, sometimes with additional requirements such as x_i ≥ 0 or x_i integral.

In optimization and operations research, somvoorwaarden define the feasible region together with other constraints. They are common in resource allocation problems, budgeting, scheduling, and network flow, where the total usage or total available amount must match a capacity or target. In combinatorics, somvoorwaarden appear when counting structures with a fixed total size, such as partitions of an integer or the distribution of a fixed budget among categories.

Examples help illustrate the concept. If two decision variables x1 and x2 represent numbers of two item types and a somvoorwaarde requires x1 + x2 = 5, the feasible pairs are (0,5), (1,4), (2,3), (3,2), (4,1), (5,0). More generally, weighted sums may be constrained, as in sum_{i} w_i x_i ≤ W, where weights w_i and capacity W define the condition.

Terminology notes: somvoorwaarde is a descriptive term found in Dutch textbooks and problem statements. It is often translated as “sum constraint” or “sum condition,” though exact usage can vary.