Optimizing Assemble-to-Order Systems: Decomposition Heuristics and Scalable Algorithms

Abstract

We consider continuous-review assemble-to-order (ATO) systems with a general bill of materials (BOM) and general leadtimes. ATO systems have the advantage of mass customization and are widely adopted in practice. However, characterizing the optimal inventory policy is notoriously challenging and computational intractable, especially in large-scale systems. We propose effective and computational scalable heuristics through asymptotics, sample-path, linear programming and primal-dual analyses. First, we characterize the asymptotically optimal policy for the M-system. The policy consists of a periodic review priority (PRP) allocation rule and a coordinated base-stock (CBS) replenishment policy. We then construct heuristic policies using insights from the asymptotically optimal policy. In particular, we adopt the PRP allocation rule and develop a decomposition approach for inventory replenishment. This approach decomposes a general system into assembly subsystems and a linear program is constructed to compute policy parameters. However, both the CBS and the assembly decomposition approach are limited to simple systems. We then consider a second approach, which decomposes a system into distribution subsystems and each subsystem has a straightforward solution, which is similar to the newsvendor problem. We use the primal-dual analysis to show that the expected cost under the optimal independent base-stock policy in a general system could be bounded by two newsvendor systems with properly set parameters. Finally, we examine the effectiveness and scalability of these two decomposition approaches in numerical tests. We find that the assembly decomposition is very effective but computationally expensive and thus only good for small-scale systems; the distribution decomposition performs as effective as the optimal independent base-stock (IBS) policy, but is highly scalable for large-scale systems. Numerical tests also provide some interesting insights on the impact of system parameters on the value of past demand information.