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## No-holdback allocation rules for continuous-time assemble-to-order systems

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Venue: | Operations Research |

Citations: | 4 - 0 self |

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130 | Foundations of Inventory Management - Zipkin - 1997 |

48 | A threshold inventory rationing policy for service-differentiated demand classes.
- Deshpande, Cohen, et al.
- 2003
(Show Context)
Citation Context ... do not carry over to the general system considered here. Interestingly, both studies identify similar cost structures to guarantee optimality, even though the approaches taken are very different. The analysis of Dogru et al. (2010) is based on a stochastic programming (SP) formulation and a lower bound approach, whereas we use a sample path approach, supplemented with a system reduction technique that reduces the original ATO systems to a single-item inventory system. Finally, there is a large body of literature on single-item inventory systems with multiple demand classes; see, for example, Deshpande et al. (2003) and references therein. These systems can be viewed as special cases of an ATO system containing only a single common component but no product-specific components. Thus, there is no assembly issue. In particular, the fulfillment of a demand does not need to consider the availability of the product-specific components. Most papers in this literature study variants of a rationing (or reservation) policy, which is a hold-back rule, whereas we consider NHB rules. 3. Model Description and Preliminaries In this section, we introduce the basic model setting. In §8 we will discuss several generalizat... |

48 |
Order-fulfillment performance measure in an assemble-to-order system with stochastic lead-times,
- Song, Xu, et al.
- 1999
(Show Context)
Citation Context ...tain allocation rule and then evaluate and/or optimize the replenishment policy. Our paper also focuses on specific types of control policies. For the given type of replenishment policy, we evaluate the performance of NHB allocation rules and show that under certain conditions NHB rules are optimal in the allocation policy space. To our knowledge, most papers that address continuousreview models (the focus of the present article) assume the FCFS allocation rule and develop tools to evaluate and/or optimize the independent base-stock replenishment policies. See, for example, Song (1998, 2002), Song et al. (1999), Song and Yao (2002), Lu et al. (2003, 2005), and Zhao and Simchi-Levi (2006). For periodic-review models, because the demand during each period is batched and filled at the end of the period, different allocation rules have been considered. These include a fixed priority rule (Zhang 1997), the FCFS rule (Hausman et al. 1998), and a fair-share rule (Agrawal and Cohen 2001). Akcay and Xu (2004) studied a product-based allocation rule that makes optimal or near-optimal allocation decisions within each period. However, all these prior studies apply FCFS to demand between periods. In other words,... |

38 | Performance analysis and optimization of assemble-to-order systems with random lead-times, Working Paper,
- Song, Yao
- 2000
(Show Context)
Citation Context ... and then evaluate and/or optimize the replenishment policy. Our paper also focuses on specific types of control policies. For the given type of replenishment policy, we evaluate the performance of NHB allocation rules and show that under certain conditions NHB rules are optimal in the allocation policy space. To our knowledge, most papers that address continuousreview models (the focus of the present article) assume the FCFS allocation rule and develop tools to evaluate and/or optimize the independent base-stock replenishment policies. See, for example, Song (1998, 2002), Song et al. (1999), Song and Yao (2002), Lu et al. (2003, 2005), and Zhao and Simchi-Levi (2006). For periodic-review models, because the demand during each period is batched and filled at the end of the period, different allocation rules have been considered. These include a fixed priority rule (Zhang 1997), the FCFS rule (Hausman et al. 1998), and a fair-share rule (Agrawal and Cohen 2001). Akcay and Xu (2004) studied a product-based allocation rule that makes optimal or near-optimal allocation decisions within each period. However, all these prior studies apply FCFS to demand between periods. In other words, these alternative al... |

32 | Order fill rate, leadtime variability, and advance demand information in an assemble-to-order system.
- Lu, Song, et al.
- 2003
(Show Context)
Citation Context ...d/or optimize the replenishment policy. Our paper also focuses on specific types of control policies. For the given type of replenishment policy, we evaluate the performance of NHB allocation rules and show that under certain conditions NHB rules are optimal in the allocation policy space. To our knowledge, most papers that address continuousreview models (the focus of the present article) assume the FCFS allocation rule and develop tools to evaluate and/or optimize the independent base-stock replenishment policies. See, for example, Song (1998, 2002), Song et al. (1999), Song and Yao (2002), Lu et al. (2003, 2005), and Zhao and Simchi-Levi (2006). For periodic-review models, because the demand during each period is batched and filled at the end of the period, different allocation rules have been considered. These include a fixed priority rule (Zhang 1997), the FCFS rule (Hausman et al. 1998), and a fair-share rule (Agrawal and Cohen 2001). Akcay and Xu (2004) studied a product-based allocation rule that makes optimal or near-optimal allocation decisions within each period. However, all these prior studies apply FCFS to demand between periods. In other words, these alternative allocation rules, i... |

29 |
On the order fill rate in a multi-item, base-stock inventory system,
- Song
- 1998
(Show Context)
Citation Context ...papers assume a certain allocation rule and then evaluate and/or optimize the replenishment policy. Our paper also focuses on specific types of control policies. For the given type of replenishment policy, we evaluate the performance of NHB allocation rules and show that under certain conditions NHB rules are optimal in the allocation policy space. To our knowledge, most papers that address continuousreview models (the focus of the present article) assume the FCFS allocation rule and develop tools to evaluate and/or optimize the independent base-stock replenishment policies. See, for example, Song (1998, 2002), Song et al. (1999), Song and Yao (2002), Lu et al. (2003, 2005), and Zhao and Simchi-Levi (2006). For periodic-review models, because the demand during each period is batched and filled at the end of the period, different allocation rules have been considered. These include a fixed priority rule (Zhang 1997), the FCFS rule (Hausman et al. 1998), and a fair-share rule (Agrawal and Cohen 2001). Akcay and Xu (2004) studied a product-based allocation rule that makes optimal or near-optimal allocation decisions within each period. However, all these prior studies apply FCFS to demand betwe... |

26 |
Joint demand fulfillment probability in a multi-item inventory system with independent order-up-to policies,
- Hausman, Lee, et al.
- 1998
(Show Context)
Citation Context ...pace. To our knowledge, most papers that address continuousreview models (the focus of the present article) assume the FCFS allocation rule and develop tools to evaluate and/or optimize the independent base-stock replenishment policies. See, for example, Song (1998, 2002), Song et al. (1999), Song and Yao (2002), Lu et al. (2003, 2005), and Zhao and Simchi-Levi (2006). For periodic-review models, because the demand during each period is batched and filled at the end of the period, different allocation rules have been considered. These include a fixed priority rule (Zhang 1997), the FCFS rule (Hausman et al. 1998), and a fair-share rule (Agrawal and Cohen 2001). Akcay and Xu (2004) studied a product-based allocation rule that makes optimal or near-optimal allocation decisions within each period. However, all these prior studies apply FCFS to demand between periods. In other words, these alternative allocation rules, if implemented in a continuous-review environment, reduce to FCFS. Similarly, Bernstein et al. (2007) considered the W system in a single selling season that can be divided into multiple time buckets. At the end of each bucket, stock allocation decisions can be made. Their objective is to s... |

26 | Supply chain operations: assembleto-order systems,” in Handbooks in - Song, Zipkin - 2003 |

21 | Inventory decisions in Dell's supply chain. - Kapuscinski, Zhang, et al. - 2004 |

20 |
Demand fulfillment rates in an assemble-to-order system with multiple products and dependent demand’,
- Zhang
- 1997
(Show Context)
Citation Context ...l in the allocation policy space. To our knowledge, most papers that address continuousreview models (the focus of the present article) assume the FCFS allocation rule and develop tools to evaluate and/or optimize the independent base-stock replenishment policies. See, for example, Song (1998, 2002), Song et al. (1999), Song and Yao (2002), Lu et al. (2003, 2005), and Zhao and Simchi-Levi (2006). For periodic-review models, because the demand during each period is batched and filled at the end of the period, different allocation rules have been considered. These include a fixed priority rule (Zhang 1997), the FCFS rule (Hausman et al. 1998), and a fair-share rule (Agrawal and Cohen 2001). Akcay and Xu (2004) studied a product-based allocation rule that makes optimal or near-optimal allocation decisions within each period. However, all these prior studies apply FCFS to demand between periods. In other words, these alternative allocation rules, if implemented in a continuous-review environment, reduce to FCFS. Similarly, Bernstein et al. (2007) considered the W system in a single selling season that can be divided into multiple time buckets. At the end of each bucket, stock allocation decisions... |

19 | Joint inventory replenishment and component allocation optimization in an assemble-to-order system”.
- Akcay, Xu
- 2004
(Show Context)
Citation Context ...ls (the focus of the present article) assume the FCFS allocation rule and develop tools to evaluate and/or optimize the independent base-stock replenishment policies. See, for example, Song (1998, 2002), Song et al. (1999), Song and Yao (2002), Lu et al. (2003, 2005), and Zhao and Simchi-Levi (2006). For periodic-review models, because the demand during each period is batched and filled at the end of the period, different allocation rules have been considered. These include a fixed priority rule (Zhang 1997), the FCFS rule (Hausman et al. 1998), and a fair-share rule (Agrawal and Cohen 2001). Akcay and Xu (2004) studied a product-based allocation rule that makes optimal or near-optimal allocation decisions within each period. However, all these prior studies apply FCFS to demand between periods. In other words, these alternative allocation rules, if implemented in a continuous-review environment, reduce to FCFS. Similarly, Bernstein et al. (2007) considered the W system in a single selling season that can be divided into multiple time buckets. At the end of each bucket, stock allocation decisions can be made. Their objective is to study the impact of demand aggregation on profits, sales, and initial ... |

18 | Optimal control of a high-volume assemble-to-order system.
- Plambeck, Ward
- 2006
(Show Context)
Citation Context ...er words, these alternative allocation rules, if implemented in a continuous-review environment, reduce to FCFS. Similarly, Bernstein et al. (2007) considered the W system in a single selling season that can be divided into multiple time buckets. At the end of each bucket, stock allocation decisions can be made. Their objective is to study the impact of demand aggregation on profits, sales, and initial stock decisions. The model has neither replenishment nor lead time, so both the setting and the focus are quite different from the present paper. The policy choices in the asymptotic studies by Plambeck and Ward (2006a, b) on high-volume ATO systems are exceptions, but their setting also is quite different from ours. In their setting, the decision variables include the component production capacities, assembled product production sequence, and product prices. Once a component’s production capacity is chosen, the production facility produces the component at full capacity, so there is no inventory decision. Our paper differs from the studies cited above in several ways: (i) We analyze the base-stock ATO system under a different type of allocation rule—an NHB rule—that is IN F O R M S ho ld s co p yr ig h t ... |

14 |
Production and inventory control of a single product assemble-to-order system with multiple customer classes,
- Benjaafar, Elhafsi
- 2006
(Show Context)
Citation Context ...B and FCFS whenever possible. Section 8 discusses extensions of the results to general replenishment policies, lead time models, and demand processes, as well as general BOM matrices. Finally, §9 concludes the paper. Proofs are available in an electronic companion to this paper at http://or.journal.informs.org. 2. Literature Review As mentioned above, inventory control of an ATO system consists of two decisions: inventory replenishment and inventory allocation. In general, the optimal decisions for any reasonable objective function are state dependent; see Song and Zipkin (2003). For example, Benjaafar and ElHafsi (2006) considered a special case: an assembly system with a single end-product and multiple demand classes. Each component supplier has a finite production capacity. They show that under Markovian assumptions on demand and production, the optimal replenishment policy is a statedependent base-stock policy, and the optimal allocation rule is a multilevel rationing policy that depends on the inventory levels of all other components. Dogru et al. (2010) considered a special case of the W system in which all components have identical constant lead times. They show that when a symmetric cost condition or ... |

13 | Backorder minimization in multiproduct assemble-to-order systems.
- Lu, Song, et al.
- 2005
(Show Context)
Citation Context ...ral system-W under any base-stock policy s and FRFS, we have Bt s =max { max i∈A Bit si ∑ K max i∈SK Bit si } Bs =max { max i∈A Bisi ∑ K max i∈SK Bisi } IN F O R M S ho ld s co p yr ig h t to th is ar tic le an d di st rib ut ed th is co py as a co ur te sy to th e au th or (s ). A dd iti on al in fo rm at io n, in cl ud in g rig ht s an d pe rm is si on po lic ie s, is av ai la bl e at ht tp :// jo ur na ls .in fo rm s. or g/ . Lu, Song, and Zhao: No-Holdback Allocation Rules for Continuous-Time ATO Systems 700 Operations Research 58(3), pp. 691–705, © 2010 INFORMS Lu et al. (2005) showed that the backorders for system-W under FCFS are given by B13t s = maxB133 t sB1t s1 and B23t s = maxB233 t s B2t s2 where B 13 3 t s + B233 t s = B3t s3. Thus, the total number of backorders under FCFS is maxB133 t sB1t s1 +maxB233 t sB2t s2, which is greater than or equal to the total number of backorders under FRFS, maxB3t s3B1t s1 + B2t s2, on any sample path. 5.1.2. Nested Structure. Consider a system with n products. The BOM sets of products satisfy = K0 ⊂ K1 ⊆ K2 ⊆ · · · ⊆ Kn = 12 m We call such a BOM st... |

13 | Order-based backorders and their implications in multiitem inventory systems. - Song - 2002 |

12 |
Optimal material control and performance evaluation in an assembly environment with component commonality.
- Agrawal, Cohen
- 2001
(Show Context)
Citation Context ...ess continuousreview models (the focus of the present article) assume the FCFS allocation rule and develop tools to evaluate and/or optimize the independent base-stock replenishment policies. See, for example, Song (1998, 2002), Song et al. (1999), Song and Yao (2002), Lu et al. (2003, 2005), and Zhao and Simchi-Levi (2006). For periodic-review models, because the demand during each period is batched and filled at the end of the period, different allocation rules have been considered. These include a fixed priority rule (Zhang 1997), the FCFS rule (Hausman et al. 1998), and a fair-share rule (Agrawal and Cohen 2001). Akcay and Xu (2004) studied a product-based allocation rule that makes optimal or near-optimal allocation decisions within each period. However, all these prior studies apply FCFS to demand between periods. In other words, these alternative allocation rules, if implemented in a continuous-review environment, reduce to FCFS. Similarly, Bernstein et al. (2007) considered the W system in a single selling season that can be divided into multiple time buckets. At the end of each bucket, stock allocation decisions can be made. Their objective is to study the impact of demand aggregation on profits... |

12 | Analysis and evaluation of an assemble-to-order system with batch ordering policy and compound Poisson demand,”European
- Zhao
- 2009
(Show Context)
Citation Context ...ent policy. Our paper also focuses on specific types of control policies. For the given type of replenishment policy, we evaluate the performance of NHB allocation rules and show that under certain conditions NHB rules are optimal in the allocation policy space. To our knowledge, most papers that address continuousreview models (the focus of the present article) assume the FCFS allocation rule and develop tools to evaluate and/or optimize the independent base-stock replenishment policies. See, for example, Song (1998, 2002), Song et al. (1999), Song and Yao (2002), Lu et al. (2003, 2005), and Zhao and Simchi-Levi (2006). For periodic-review models, because the demand during each period is batched and filled at the end of the period, different allocation rules have been considered. These include a fixed priority rule (Zhang 1997), the FCFS rule (Hausman et al. 1998), and a fair-share rule (Agrawal and Cohen 2001). Akcay and Xu (2004) studied a product-based allocation rule that makes optimal or near-optimal allocation decisions within each period. However, all these prior studies apply FCFS to demand between periods. In other words, these alternative allocation rules, if implemented in a continuous-review env... |

6 | Optimal scheduling control of a multiclass fluid network - Chen, Yao - 1989 |

6 | Note: A separation principle for a class of assemble-to-order systems with expediting.
- Plambeck, Ward
- 2006
(Show Context)
Citation Context ...er words, these alternative allocation rules, if implemented in a continuous-review environment, reduce to FCFS. Similarly, Bernstein et al. (2007) considered the W system in a single selling season that can be divided into multiple time buckets. At the end of each bucket, stock allocation decisions can be made. Their objective is to study the impact of demand aggregation on profits, sales, and initial stock decisions. The model has neither replenishment nor lead time, so both the setting and the focus are quite different from the present paper. The policy choices in the asymptotic studies by Plambeck and Ward (2006a, b) on high-volume ATO systems are exceptions, but their setting also is quite different from ours. In their setting, the decision variables include the component production capacities, assembled product production sequence, and product prices. Once a component’s production capacity is chosen, the production facility produces the component at full capacity, so there is no inventory decision. Our paper differs from the studies cited above in several ways: (i) We analyze the base-stock ATO system under a different type of allocation rule—an NHB rule—that is IN F O R M S ho ld s co p yr ig h t ... |

5 |
A stochastic programming based inventory policy for assemble-to-order systems with application to theWmodel,”Operations Research,
- Dogru, Reiman, et al.
- 2010
(Show Context)
Citation Context ...location. In general, the optimal decisions for any reasonable objective function are state dependent; see Song and Zipkin (2003). For example, Benjaafar and ElHafsi (2006) considered a special case: an assembly system with a single end-product and multiple demand classes. Each component supplier has a finite production capacity. They show that under Markovian assumptions on demand and production, the optimal replenishment policy is a statedependent base-stock policy, and the optimal allocation rule is a multilevel rationing policy that depends on the inventory levels of all other components. Dogru et al. (2010) considered a special case of the W system in which all components have identical constant lead times. They show that when a symmetric cost condition or a “balanced capacity” condition is satisfied, the optimal replenishment policy is a state-independent base-stock policy and the optimal allocation policy is an NHB policy (which they call myopic policies). Clearly, the optimal policy for the general multiproduct ATO system having different component lead times, such as the one we consider here, is likely more complex. In fact, neither the optimal replenishment policy nor the optimal allocation... |

5 | The value of component commonality in a dynamic inventory system with lead times.
- Song, Zhao
- 2009
(Show Context)
Citation Context ... at io n, in cl ud in g rig ht s an d pe rm is si on po lic ie s, is av ai la bl e at ht tp :// jo ur na ls .in fo rm s. or g/ . Lu, Song, and Zhao: No-Holdback Allocation Rules for Continuous-Time ATO Systems 694 Operations Research 58(3), pp. 691–705, © 2010 INFORMS non-FCFS. (ii) For any given base-stock policy, we compare the performances of NHB and FCFS whenever possible. (iii) We establish certain optimality properties of NHB rules over all allocation rules in the base-stock systems. We are aware of only two other works that analyze nonFCFS rules in continuous-review ATO systems. First, Song and Zhao (2009) considered FRFS and the general NHB rules but focused on a model with only one common component (including system-W), which is a special case of the model studied here. Also, these authors only studied performance evaluation of the fill rates and did not consider backorders and optimality conditions. Second, Dogru et al. (2010) incidentally noticed the general class of the NHB rules. In particular, they considered a priority-based backlog clearing policy as well as a reservation policy. However, as mentioned above, their focus is the W system with equal constant lead times. The system conside... |

4 | 2006. Production and inventory control of a single product assemble-to-order system with multiple customer classes - Benjaafar, ElHafsi |

3 |
The benefits of reevaluating real-time order fulfillment decisions.
- Xu, Allgor, et al.
- 2009
(Show Context)
Citation Context ...oldest backorder for which all required components are available. Under other NHB rules, one can satisfy the backorders for which all required components are available in different sequences. An NHB rule is a product-based allocation rule; the allocation of one component’s inventory to a demand depends on the inventory status of other components. Consequently, it requires more information and more coordination than FCFS. It also may make some orders wait longer than under FCFS. Both FCFS and FRFS are commonly seen in practice. Kapuscinski et al. (2004) describe an example of FRFS at Dell, and Xu et al. (2009) describe an example of FCFS at Amazon.com. Using a sample path argument, we show that, for basestock systems with certain material-flow topologies, NHB Figure 1. System-W, N, M. 1 23 13 System-W 1 2 1 12 System-N 1 2 1 2 System-M 12 23 rules minimize both the total backorder and the total onhand inventory. The minimum is achieved for each sample path at any time, similar to the concept of global optimality studied in fluid networks; see, for example, Chen and Yao (1993). In addition, for these systems, assuming certain symmetric cost structures, NHB rules are optimal among all allocation rule... |

3 |
Dynamic scheduling control of a multi-class fluid network.
- Chen, Yao
- 1993
(Show Context)
Citation Context ...ze both the total backorder and the total on-hand inventory. The minimum is achieved for each sample path at any time, similar to the concept of global optimality studied in fluid networks, see, e.g. =-=[5]-=-. In addition, for these systems, assuming certain symmetric cost structures, NHB rules are optimal among all allocation rules in the sense that they minimize systemwide average inventory and backorde... |

3 |
Supply Chain Operations: Assemble-to-Order,”
- Song, Zipkin
- 2003
(Show Context)
Citation Context ...ts. Also, because a common component can be used to fulfill several product orders, how one allocates that component among the products determines customer waiting times. Thus, a reasonable allocation rule should also be state dependent. However, we have little knowledge at present about the structures of the these replenishment and allocation policies; see §2 for more detail. As a result, only simple, heuristic control policies are implemented in practice, and the majority of the academic literature focuses on performance evaluation and optimization of specific types of control policies; see Song and Zipkin (2003) for a review. In particular, most prior works assume independent base-stock component replenishment policies, as we do in the current paper. For convenience, we refer to such systems as base-stock (ATO) systems. For continuous-review base-stock systems, in which an allocation decision must be made at the time of a customer order and at the time of a component replenishment delivery, most of the literature assumes the first-come-first-served (FCFS) allocation rule and studies the performance evaluation and optimization of the base-stock policies. 691 IN F O R M S ho ld s co p yr ig h t to th i... |

1 |
Allocation policies based on demand aggregation in an assemble-to-order system. Working paper,
- Bernstein, DeCroix, et al.
- 2007
(Show Context)
Citation Context ... the demand during each period is batched and filled at the end of the period, different allocation rules have been considered. These include a fixed priority rule (Zhang 1997), the FCFS rule (Hausman et al. 1998), and a fair-share rule (Agrawal and Cohen 2001). Akcay and Xu (2004) studied a product-based allocation rule that makes optimal or near-optimal allocation decisions within each period. However, all these prior studies apply FCFS to demand between periods. In other words, these alternative allocation rules, if implemented in a continuous-review environment, reduce to FCFS. Similarly, Bernstein et al. (2007) considered the W system in a single selling season that can be divided into multiple time buckets. At the end of each bucket, stock allocation decisions can be made. Their objective is to study the impact of demand aggregation on profits, sales, and initial stock decisions. The model has neither replenishment nor lead time, so both the setting and the focus are quite different from the present paper. The policy choices in the asymptotic studies by Plambeck and Ward (2006a, b) on high-volume ATO systems are exceptions, but their setting also is quite different from ours. In their setting, the ... |