An assemble-to-order system with product and components demand with lost sales

Abstract

This paper studies a single end product assemble-to-order system serving both the demand of the end product and the individual components. Demands are assumed to form independent Poisson streams with different rates. Unsatisfied demand, both for the end product and for components, is assumed lost and thus incurs a per unit lost sale penalty. The end product is assembled from K distinct components each produced on a different production facility (or procured from independent suppliers). Production lead times are non-identical and are assumed to be independent and exponentially distributed. Produced components are held in stock in anticipation of future demands. The goal is to determine the optimal component production and inventory allocation policy. The optimal policy is characterised using a Markov Decision Process model. It is shown that, in addition to the state-dependent threshold type, the optimal policy exhibits counterintuitive features which have not been observed in systems without components demand. In particular, for certain combinations of system parameters, the optimal inventory allocation policy switches priority as the inventory level of components changes. Furthermore, for a particular component k, as the inventory level of other components increases, the desirability of satisfying Component k demand decreases. Finally, because in general the optimal policy is fairly complicated and is difficult to obtain numerically, due to the curse of dimensionality of dynamic programming, three heuristic policies are proposed. Extensive numerical experiments indicate that the three heuristics perform very well compared to the optimal policy.

A complete algebraic solution to the optimal dynamic rationing policy in the stock-rationing queue with two demand classes

“…( 2009 ); an assemble-to-order production system by Elhafsi et al. ( 2015 ); ElHafsi et al. ( 2018 ) and Nadar et al.…”

A Complete Algebraic Solution to the Optimal Dynamic Rationing Policy in the Stock-Rationing Queue with Two Demand Classes

“…Since the seminal work of Ha [36], it has been interesting to extend and generalize how to apply the MDPs to deal with rationing inventory systems. Important examples include the Erlang production times by Ha [38] and Gayon et al [34]; the backorders with two demand classes by Ha [37] and with multiple demand classes by de Véricourt [16,17]; the parallel production channels by Bulut and Fadiloglu [6]; the batch ordering by Huang and Iravani [42], and the batch production by Pang et al [67]; the utilization of information by Gayon et al [33] and ElHafsi et al [26]; an assemble-to-order production system by Benjaafar and ElHafsi [3], ElHafsi [24], ElHafsi et al [25,27], Benjaafar et al [4] and Nadar et al [64]; a two-stage tandem production system by Xu [90], supply chain by Huang and Iravani [41] and van Wijk et al [80]; periodic review by Frank et al [32] and Chen et al [12]; dynamic price by Ding et al [21,22], Schulte and Pibernik [72] and so forth.…”

Survey and classification of operational control problems in discrete event logistics systems (DELS)

“…Capacitated processing networks model multi-resource allocation decisions, where resource capacity, such as machines or inventory, is allocated to fulfill demands (Van Mieghem and Rudi 2002). In assemble-to-order systems, inventory of common components are allocated to satisfy demands for several finished goods (Elhafsi et al 2015). The complexity of resource assignment problems can be characterized by the degree of coordination required between types of resources (Powell et al 2001).…”