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

Lu, Laura; Song, Jing-Sheng; Zhang, Hanqin

doi:10.1002/nav.21671

Cited by 32 publications

(10 citation statements)

References 46 publications

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“…Lu et al (2010) also extend this optimality result to N -systems and generalized W -systems. Lu et al (2012) prove the optimality of coordinated base-stock policies and no-holdback rules for N -systems with backordering and symmetric costs and extend this result to the case with high demand volume and asymmetric costs. The optimal allocation rules in all of these papers have the following property: a component is allocated to a demand only if it enables immediate fulfillment of that demand.…”

Section: Introductionmentioning

confidence: 74%

“…Different but more restricted versions of the N -system have been studied in the literature: Lu et al (2010) prove that no-holdback rules are optimal among all allocation rules for N -systems with backordering, a base-stock replenishment policy, and a symmetric cost structure. In a recent paper, Lu et al (2012) establish the optimality of coordinated base-stock policies and no-holdback rules for N -systems with backordering and symmetric costs. Lu et al (2012) also extend this result to the case with high demand volume and asymmetric costs.…”

Section: Generalized N-systemsmentioning

confidence: 99%

“…In a recent paper, Lu et al (2012) establish the optimality of coordinated base-stock policies and no-holdback rules for N -systems with backordering and symmetric costs. Lu et al (2012) also extend this result to the case with high demand volume and asymmetric costs. Last, in a lost sales environment, ElHafsi et al (2008) consider a nested product structure with unitary component usage rates and unitary replenishment quantities.…”

Section: Generalized N-systemsmentioning

confidence: 99%

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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: Introductionmentioning

confidence: 74%

Section: Generalized N-systemsmentioning

confidence: 99%

Section: Generalized N-systemsmentioning

confidence: 99%

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

Nadar

Akan

Scheller‐Wolf

2014

Operations Research

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“…Previous work has only established the optimal policy structure for very specific ATO systems -such as the W -system and the M -system; see Dogru et al (2010), Lu et al (2014), and for example. As a result, simple heuristic control policies for general ATO systems are attracting widespread interest in practice (Lu et al 2010).…”

Section: Introductionmentioning

confidence: 99%

Experimental Results Indicating Lattice-Dependent Policies May Be Optimal for General Assemble-to-Order Systems

Nadar¹,

Akan²,

Scheller‐Wolf³

2015

SSRN Journal

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We consider an assemble-to-order (ATO) system with multiple products, multiple components which may be demanded in different quantities by different products, possible batch ordering of components, random lead times, and lost sales. We model the system as an infinite-horizon Markov decision process under the average cost criterion. A control policy specifies when a batch of components should be produced, and whether an arriving demand for each product should be satisfied. Previous work has shown that a lattice-dependent base-stock and lattice-dependent rationing (LBLR) policy is an optimal stationary policy for a special case of the ATO model presented here (the generalized M -system).In this paper, we conduct numerical experiments to evaluate the use of an LBLR policy for our general ATO model as a heuristic, comparing it to two other heuristics from the literature: a state-dependent basestock and state-dependent rationing (SBSR) policy, and a fixed base-stock and fixed rationing (FBFR) policy. Remarkably, LBLR yields the globally optimal cost in each of more than 22,500 instances of the general problem, outperforming SBSR and FBFR with respect to both objective value (by up to 2.6% and 4.8%, respectively) and computation time (by up to three orders and one order of magnitude, respectively) in 350 of these instances (those on which we compare the heuristics). LBLR and SBSR perform significantly better than FBFR when replenishment batch sizes imperfectly match the component requirements of the most valuable or most highly demanded product. In addition, LBLR substantially outperforms SBSR if it is crucial to hold a significant amount of inventory that must be rationed.

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“…(Kapuscinski et al, 2004, Xu et al, 2009, and Lu et al, 2014, provide specific examples from these industries.) ATO production holds inventory at the component level so that a product may be assembled from its components -if sufficient inventory exists -immediately after a customer demand for this product occurs.…”

Section: Introductionmentioning

confidence: 99%

Replenishment and Fulfillment Based Aggregation for General Assemble-to-Order Systems

et al. 2015

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We consider an assemble-to-order system with multiple products, multiple components which may be demanded in different quantities by different products, batch ordering of components, random lead times, and lost sales. We model the system as an infinite-horizon Markov decision process under the discounted cost criterion. A control policy 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). As optimal solutions for such problems are computationally intractable for even moderate sized systems, we approximate the optimal cost function by reducing the state space of the original problem via a novel aggregation technique that uses knowledge of products' component requirements and components' replenishment batch sizes.We establish that a lattice-dependent base-stock and lattice-dependent rationing policy is the optimal inventory replenishment and allocation policy for the aggregate problem under a disaggregation rule that disaggregates each aggregate state into its two extreme original states. This rule drastically reduces the per iteration computational complexity of the value iteration algorithm for the aggregate problem (without sacrificing much accuracy, according to our numerical experiments). We further alleviate the value iteration computational burden by eliminating suboptimal actions based on our optimal policy structure.For systems in which there is a product that has fulfillment priority over all other products at optimality, we are able to derive finite error bound for the cost function of the aggregate problem. With these bounds we show that the value iteration algorithm in the original problem that starts with the aggregate solution converges to the optimal cost function. Numerical experiments indicate that such an algorithm has distinct computational advantage over the standard value iteration method in the original problem.

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

Cited by 32 publications

References 46 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

Experimental Results Indicating Lattice-Dependent Policies May Be Optimal for General Assemble-to-Order Systems

Replenishment and Fulfillment Based Aggregation for General Assemble-to-Order Systems

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