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

A two-level flexible manufacturing system is considered to be composed of s everal different production units U-i, 1 less than or equal to i less than or equal to n, at the lower level and a section at the upper one. The secti on is required to produce a given target amount V by a given due date D sub ject to a chance constraint, i.e. the least permissible probability p of me eting the target on time is pregiven. Each production unit U-i has several possible speeds nu(i1), v(i2), . . . , v(im), which are subject to random d isturbances. The unit's output can be measured only at preset inspection (c ontrol) points. The target amount is gauged by a single measure and may be rescheduled among the production units. For each unit, the average manufact uring 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 ou tput at that point, are given. We recently have developed a cost-optimization on-line control model which for a single production unit determines both control points and speeds to b e introduced at those points, in order to minimize the unit's expenses with in the planning horizon, subject to the chance constraint. We present a two -level on-line control model under random disturbances, which centers on mi nimizing the section's expenses subject to the chance constraint. The sugge sted two-level heuristic algorithm is based on rescheduling the section's t arget among the production units both at t=0, when the system starts functi oning, and at each emergency point, when it is anticipated that a certain u nit is unable to meet its local target on time subject to a chance constrai nt. At any emergency point t the remaining section's target V-t is reschedu led among the units; thus, new local targets V-it, 1 less than or equal to i less than or equal to n, Sigma(i)V(it) = V-t, are determined. New local c hance constraint values p(it) are determined too. Those values enable the s ystem to meet its overall target at the due date subject to the pregiven ch ance constraint p. A numerical example is given. Extensive experimentation has been undertaken to illustrate the efficiency of the algorithm. (C) 2000 IMACS. Published b y Elsevier Science B.V. All rights reserved.