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

Abstract

Abstract:In Assemble-To-Order (ATO) systems, situations may arise in which customer demand must be backlogged due to a shortage of some components, leaving available stock of other components unused. Such unused component stock is called remnant stock. Remnant stock is a consequence of both component ordering decisions and decisions regarding allocation of components to end-product demand. In this article, we examine periodic-review ATO systems under linear holding and backlogging costs with a component installation stock policy and a First-Come-First-Served (FCFS) allocation policy. We show that the FCFS allocation policy decouples the problem of optimal component allocation over time into deterministic period-by-period optimal component allocation problems. We denote the optimal allocation of components to end-product demand as multimatching. We solve the multi-matching problem by an iterative algorithm. In addition, an approximation scheme for the joint replenishment and allocation optimization problem with both upper and lower bounds is proposed. Numerical experiments for base-stock component replenishment policies show that under optimal base-stock policies and optimal allocation, remnant stock holding costs must be taken into account. Finally, joint optimization incorporating optimal FCFS component allocation is valuable because it provides a benchmark against which heuristic methods can be compared.

Asymptotically Optimal Inventory Control for Assemble-to-Order Systems with Identical Lead Times

“…One may find a thorough review of the related literature in [30], and a more recent one in [3]. Many previous studies focus on particular types of policies, such as base stock replenishment policies, FIFO or No-Hold-Back allocation policies (see [18], [19], [14] for some samples), and for periodic-review systems, allocation policies that always satisfy demands from previous periods first (e.g., [1], [2], [13], [35]).…”

Optimization of Industrial-Scale Assemble-to-Order Systems

“…Because computation times are quite a different concern from the performance of the policies, we first benchmark the scalability of the SAA algorithm developed in §3.2 against the algorithms proposed by Akçay and Xu (2004) and Huang and de Kok (2011 For each test case, we determine the amount of computation time that is needed to obtain a solution of good quality using the different algorithms (i.e., within 1% of the corresponding asymptotic lower bound). For details, see Online Supplement D. Computation times are limited to 2 hours per sample, i.e., 100 hours over 50 samples.…”

“…Both SP formulations Xu 2004, Huang andde Kok 2011) are structurally similar to the SPs proposed for the zero lead time case: They use the base-stock levels directly as decision variables, which gives rise to a nonlinear sampling-based problem. To overcome this difficulty, they use auxiliary variables to linearize sampling-based bounds, that is, the big-M method (Huang andde Kok 2011, Akçay andXu 2012). However, this approach gives rise to weak LP relaxations and severe scalability issues.…”

“…Unlike the studies discussed earlier, they investigate the performance of a heuristic that dynamically allocates components to products arriving in the same period, using an SP to optimize the base-stock levels. Huang and de Kok (2011) note that many models exclude the holding costs of inventory committed to product demands; they include these costs in their model. Their computational results show that committed stock may comprise a large fraction of total inventory.…”

“…We focus on base-stock policies for the same reason. And although many studies have addressed the optimization of base-stock levels in FCFS ATO systems (e.g., Zhang 1997, Song and Yao 2002, Akçay and Xu 2004, Huang and de Kok 2011, none of the proposed methods can compute close-to-optimal solutions for large-scale systems.…”