Near-optimal operation of a multiplant manufacturing system with central procurement.

摘要

The problem of scheduling a system of N manufacturing plants, called producers, with raw materials supplied from a single procurement center, called the warehouse, is studied. The warehouse receives N types of raw materials and delivers them to the producers, one type to each producer. These raw materials are then transformed by the producers into finished goods. There is an external demand at each producer for finished goods. The demand rate per unit time is product-dependent and constant. The production rate at each producer is also facility-dependent and constant. There are setup and convex production costs at each producer. These are also setup charges for ordering raw materials at all facilities as well as linear holding costs for raw materials and finished goods. No backorders are allowed. The objective is to find a production schedule that minimizes the continuous-time average cost over an infinite horizon.;Towards solving this scheduling problem, the special case of a single producer is considered first. This special case is of interest in its own rights since it is equivalent to finding a production schedule for a single machine with continuous buffer feed. Furnished with the results obtained for the single facility case, it is shown under some assumptions on the data that for the N-producer system, policies with guaranteed performance can be obtained. This is done by considering a subset of feasible policies called integer-ratio-multi-run policies. These policies have the property that the inter-ordering times at each producer for raw materials from the warehouse are multiples of the inter-ordering times at the warehouse, or vice versa. Also between arrivals of raw materials at each producer, many production runs are scheduled. A lower bound on the average cost of all integer-ratio-multi-run policies is obtained by relaxing some of the constraints involved in the optimization problem. It is shown that in fact this lower bound is also a lower bound on the average cost of all feasible policies. This relaxed solution is then rounded off to obtain provably highly effective policies. Different types of production cost functions are studied. Policies with guaranteed performance are presented for general convex production functions, and for some special cases provably near-optimal policies are obtained.