Scheduling manufacturing systems with work-in-process inventory control: single-part-type systems

Abstract

In this paper, a real-time feedback control algorithm is developed for scheduling single-part-type production lines in which there are three important classes of activities: operations, failures, and starvation or blockage. The scheduling objectives are to keep the actual production as close to the demand as possible, and to keep the level of work-in-process inventory as low as possible. By relating the starvation and blockage to the system capacity, the buffer sizes and the target buffer levels are chosen according to the demands and machine parameters.The processing time for each operation is deterministic. Failure and repair times are random. Whenever a machine fails or is starved or blocked, the scheduling system recalculates short term production rates.To begin with, we study a very simple case, a two machine and one part type system, to get insight into the buffer effects and production control policies. Using the relationship between system capacity and starvation or blockage, we find desirable buffer levels and buffer sizes. The production control policy is determined to meet the system performance requirements concerning low WIP inventory and tardiness.The results from the simple case are extended to N-machine, one-part-type systems.

Production Control for a Tandem Two-Machine System

“…By observing the behavior of the optimal control for this system, we can develop approximate extensions for more complex systems. Indeed, this has already been done in [3], [4], [5J and [6] for quite elaborate systems (multiple machines, multiple part types, arbitrary routing including reentrant flow) and practical controls have been developed using modifications of our ideas. A brief discussion of these extensions is given later.…”

“…Equations (8) in which Au" is the transition rate from state a to state p. and where the minimization is performed subject to (3), (4) and (5). IfJ were known, the control law would be to choose u" Ul so as to minimize subject to (3), (4) and (5).…”

“…A brief discussion of these extensions is given later. (4) o :=;; Ul(t) -s 0I1(t) U 1 (5) The initial conditions x. (O) and X2(0) are given.…”

“…subject to (l )- (5) where g(.) is a convex function ofx, and Xl, and {3 is a discount rate between 0 and 1.…”

Stability Analysis of Large Scale Networks of Autonomous Work Systems with Delays

“…In prior work, sharing of capacity information between work systems has been modelled [6] along with the benefits of alternative control laws and reducing delay in capacity changes [7]- [8]. Several authors have described both linear and nonlinear dynamical models for control of variables such as inventory levels and work in progress (WIP), including the use of pipeline flow concepts to represent lead times and production delays ( [9], [10]). Delivery reliability and delivery time have established themselves as equivalent buying criteria alongside product quality and price (see [1], [11]).…”