Production and Inventory Control of a Single Product Assemble-to-Order System with Multiple Customer Classes

Benjaafar, Saif; Elhafsi, Mohsen

doi:10.1287/mnsc.1060.0588

Cited by 163 publications

(140 citation statements)

References 22 publications

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“…Also, because component orders are not part of our system state, these can in effect be cancelled upon transition to a new state. Both of these assumptions are standard in the literature (see, for example, Ha 1997, Benjaafar and ElHafsi 2006, ElHafsi et al 2008.…”

Section: Problem Formulationmentioning

confidence: 99%

“…ATO production not only allows companies to reduce their response window by stocking components, but also gives them the flexibility of postponing final assembly until demand is realized (Benjaafar and ElHafsi 2006). Many high-tech firms, facing shorter product life cycles and higher demand for product varieties, use ATO production to extend customized product offerings, lower inventory cost, and mitigate the effect of product obsolescence.…”

Section: Introductionmentioning

confidence: 99%

“…Optimal cost functions for multivariate MDPs (like ours) are typically shown to be convex in each dimension of the state space. For examples of such results, see Benjaafar and ElHafsi (2006), ElHafsi et al (2008), ElHafsi (2009), and Benjaafar et al (2011. See also Smith and McCardle (2002) for sufficient conditions ensuring convexity in a multivariate Markovian inventory model.…”

Section: Introductionmentioning

confidence: 99%

“…Song and Zipkin (2003) provide a comprehensive survey of this literature. The paper that is most closely related to ours is Benjaafar and ElHafsi (2006). They consider an ATO assembly system with a single end product that uses one unit of multiple components.…”

Section: Introductionmentioning

confidence: 99%

“…They show that, under Markovian assumptions on production and demand, the optimal replenishment is a state-dependent base-stock policy, and the optimal allocation is a state-dependent rationing policy. We extend the model of Benjaafar and ElHafsi (2006) in several directions: (i) we allow our components to be demanded individually as well; (ii) unlike their end product, our master product may use multiple units from each component; and, furthermore, (iii) our master product and each of our individual products may require the same component in different quantities.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Technical Note—Optimal Structural Results for Assemble-to-Order Generalized M-Systems

Nadar

Akan

Scheller‐Wolf

2014

Operations Research

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We consider an assemble-to-order generalized M-system with multiple components and multiple products, batch ordering of components, random lead times, and lost sales. We model the system as an infinite-horizon Markov decision process and seek an optimal policy that specifies when a batch of components should be produced (i.e., inventory replenishment) and whether an arriving demand for each product should be satisfied (i.e., inventory allocation). We characterize optimal inventory replenishment and allocation policies under a mild condition on component batch sizes via a new type of policy: lattice-dependent base stock and lattice-dependent rationing.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Technical Note—Optimal Structural Results for Assemble-to-Order Generalized M-Systems

Nadar

Akan

Scheller‐Wolf

2014

Operations Research

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Optimal control of a production‐inventory system with both backorders and lost sales

Benjaafar

Elhafsi

Huang

2010

Naval Research Logistics

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We consider the optimal control of a production inventory‐system with a single product and two customer classes where items are produced one unit at a time. Upon arrival, customer orders can be fulfilled from existing inventory, if there is any, backordered, or rejected. The two classes are differentiated by their backorder and lost sales costs. At each decision epoch, we must determine whether or not to produce an item and if so, whether to use this item to increase inventory or to reduce backlog. At each decision epoch, we must also determine whether or not to satisfy demand from a particular class (should one arise), backorder it, or reject it. In doing so, we must balance inventory holding costs against the costs of backordering and lost sales. We formulate the problem as a Markov decision process and use it to characterize the structure of the optimal policy. We show that the optimal policy can be described by three state‐dependent thresholds: a production base‐stock level and two order‐admission levels, one for each class. The production base‐stock level determines when production takes place and how to allocate items that are produced. This base‐stock level also determines when orders from the class with the lower shortage costs (Class 2) are backordered and not fulfilled from inventory. The order‐admission levels determine when orders should be rejected. We show that the threshold levels are monotonic (either nonincreasing or nondecreasing) in the backorder level of Class 2. We also characterize analytically the sensitivity of these thresholds to the various cost parameters. Using numerical results, we compare the performance of the optimal policy against several heuristics and show that those that do not allow for the possibility of both backordering and rejecting orders can perform poorly.© 2010 Wiley Periodicals, Inc. Naval Research Logistics 2010

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A partial characterization of the optimal ordering/rationing policy for a periodic review system with two demand classes and backordering

Chen

Feng

2010

Naval Research Logistics

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Abstract:We consider a finite horizon periodic review, single product inventory system with a fixed setup cost and two stochastic demand classes that differ in their backordering costs. In each period, one must decide whether and how much to order, and how much demand of the lower class should be satisfied. We show that the optimal ordering policy can be characterized as a state dependent (s, S) policy, and the rationing structure is partially obtained based on the subconvexity of the cost function. We then propose a simple heuristic rationing policy, which is easy to implement and close to optimal for intensive numerical examples. We further study the case when the first demand class is deterministic and must be satisfied immediately. We show the optimality of the state dependent (s, S) ordering policy, and obtain additional rationing structural properties. Based on these properties, the optimal ordering and rationing policy for any state can be generated by finding the optimal policy of only a finite set of states, and for each state in this set, the optimal policy is obtained simply by choosing a policy from at most two alternatives. An efficient algorithm is then proposed.

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Production and Inventory Control of a Single Product Assemble-to-Order System with Multiple Customer Classes

Cited by 163 publications

References 22 publications

Technical Note—Optimal Structural Results for Assemble-to-Order Generalized M-Systems

Technical Note—Optimal Structural Results for Assemble-to-Order Generalized M-Systems

Optimal control of a production‐inventory system with both backorders and lost sales

A partial characterization of the optimal ordering/rationing policy for a periodic review system with two demand classes and backordering

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