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

Abstract

A two-level flexible manufacturing system is considered to be composed of several different production units U i , 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 U i has several possible speeds v i1 , v i2 ,…, v im , 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. We recently have developed a cost-optimization on-line control model which for a single production unit determines both control points and speeds to be introduced at those points, in order to minimize the unit’s expenses within the planning horizon, subject to the chance constraint. We present a two-level on-line control model under random disturbances, which centers on minimizing the section’s expenses subject to the chance constraint. The suggested two-level heuristic algorithm is based on rescheduling the section’s target among the production units both at t=0, when the system starts functioning, and at each emergency point, when it is anticipated that a certain unit is unable to meet its local target on time subject to a chance constraint. At any emergency point t the remaining section’s target V t is rescheduled among the units; thus, new local targets V it , 1≤ i≤ n, ∑ i V it=V t , are determined. New local chance constraint values p it are determined too. Those values enable the system to meet its overall target at the due date subject to the pregiven chance constraint p. A numerical example is given. Extensive experimentation has been undertaken to illustrate the efficiency of the algorithm.