Two-level cost-optimization production control model under random disturbances

A two-level flexible manufacturing system is considered to be composed of several different production units Ui, 1≤i≤n, at the lower level and a section at the upper one. The section is required to produce a given target amount V by a given due date D subject to a chance constraint, i.e. the least permissible probability p of meeting the target on time is pregiven. Each production unit Ui has several possible speeds vi1,vi2,…,vim, which are subject to random disturbances. The unit’s output can be measured only at preset inspection (control) points. The target amount is gauged by a single measure and may be rescheduled among the production units. For each unit, the average manufacturing costs per time unit for each production speed and the average cost of performing a single inspection at a control point to observe the actual output at that point, are given.