Production planning for mixed assembly/arborescent systems

Abstract

In the automotive industry, components are fabricated from raw materials; modules from components; and subassemblies from modules. Final assembly of the end item, the vehicle, then follows. Such a process would be called an “assembly system” if each lower-level entity (raw material, component. module) were used inonly oneimmediate successor entity (component, module, subassembly). It is common to represent the bill of materials as a directed network. The nodes of this network are entities in the bill of materials; arcs in the network point from lower level entities in the direction of higher level entities and toward the end product. For example, if components1and2were combined to produce modulea, there would be an arc from node1to nodea. Similarly, there would be an arrow pointing from node2to nodea. A pure assembly system may thus be described by saying that each node has at most one direct successor, although it may have several immediate predecessors. Similarly, a pure “arborescent network” is the prototype for adistributionsystem, whereby each node (say a warehouse) may have at most one immediatepredecessor(distribution center), but possibly many immediate successors (retailers or smaller warehouses). The focus of this paper is that a complex manufacturing system often has arborescent or non-assembly portions in its network. In automotive assembly, a given component frequently appears in more than one subassembly in the manufactured product. Certain components are used in each of four wheels; left- and right-side body subassemblies contain common modules. The result is amixed assembly/arborescentstructure. Mixed assembly/arborescent structures also merit consideration as the prototype for combined production/distribution systems. In this article, we consider such mixed structures by building on properties of pure assembly and pure arborescent systems. First, for a wide class of parameters and various pure assembly structures, we study several single-level lot-sizing algorithms in conjunction with the cost-parameter-revision method of Blackburn and Millen (1982b). Cost-parameter revision is a way to account for the impact at other stages, of decisions made at a given stage, in a pure assembly system. We also show it is better not to revise these cost parameters for apure arborescentsystem. Our approach to a mixed assembly/arborescent system is thus based on identifying its “largest, independent pure assembly sub-graph.” This is a significant subsystem of the original graph or network, the largest portion that is pure assembly in nature. Modification of the cost parameters there, followed by stage-by-stage application throughout the whole network of the best single-stage lot-sizing method, gives lower total costs than when no cost revision is applied in the mixed system. Suggestions are then made for further research.