Optimization of Industrial-Scale Assemble-to-Order Systems

Abstract

U sing a novel stochastic programming (SP) formulation, we develop an algorithm for inventory control in industrial-size assemble-to-order (ATO) systems that has unparalleled efficiency and scalability. Applying our algorithm to several numerical examples, we generate new insights regarding the control and optimization of these systems.We consider a continuous time model, seeking base-stock levels for components that minimize the sum of holding costs and product-specific backorder costs. Our initial focus is on first-come, first-served (FCFS) allocation of components to products; for this setting our algorithm quickly computes solutions for which the asymptotic optimality gap with the optimal FCFS base-stock policy is less than 1%. We then turn to two related questions: How do common heuristics used in practice compare to our performance, and how costly is the FCFS assumption?For the first question, we investigate the effectiveness of ignoring simultaneous stock-outs (ISS), a heuristic that has been used by companies such as IBM and Dell. Our experiments indicate that ISS performance, when compared to the optimal FCFS base-stock policy, improves as the average newsvendor (NV) fractiles increase but suffers under lead-time demand correlations.For the second question, we develop an efficiently computable upper bound on the benefit of optimal allocation over FCFS. We find that for many large ATO systems, FCFS performs surprisingly well and that its performance improves with decreasing NV fractile asymmetry among products and, again, with increasing average NV fractiles. We also investigate simple no-holdback allocation policies and find that they tend to outperform the best FCFS policies.

Optimal and asymptotically optimal policies for assemble-to-order n- and W-systems

“…In particular, for continuous‐review models, most papers assume the FCFS allocation rule, and develop tools to evaluate and optimize the IBS replenishment policies. See, for example, . For periodic‐review models, because the demand during each period is batched and filled at the end of the period, different allocations rules have been considered.…”

On the use of independent base-stock policies in assemble-to-order inventory systems with nonidentical lead times

“…Policies that vary inventory positions of some components to satisfy certain optimality criteria have been considered ( [3], [5], [7]), but their developments have been so far limited to systems with special Bill of Materials (BOM). As a result, base stock policies, such as the ones that Ignore Simultaneous Stock-outs (ISS) of components ( [10]), are still commonly employed in practice. This paper considers a family of IBS policies with different choices of base stock levels from existing schemes such as ISS.…”

“…Previous studies have used stochastic programs (SP) to set a lower bound on the average inventory cost of ATO systems ( [5], [6], [10])). We start from a similar launching pad by formulating an SP and proving its optimal solution is below the inventory cost under any feasible policy.…”

“…Unlike the bound in [6], ours applies to systems with any number of distinct lead times rather than one lead time only. Unlike the bound in [10], ours covers all feasible policies, not just IBS policies. Inventory control is optimal if it keeps the total expected cost at the lower bound for all time.…”

Optimal FCFS allocation rules for periodic‐review assemble‐to‐order systems

“…Importantly, they found that the optimal component allocation policy obtained for a special W system violated the FCFS principle. van Jaarsveld and Scheller‐Wolf developed an algorithm for the joint optimization of inventory replenishment and component allocation, and studied the performance of this algorithm for industrial‐scale ATO systems. Nevertheless, all these studies assume continuous review ATO systems.…”