Inventory rationing for a system with heterogeneous customer classes

Abstract

Many retailers find it useful to partition customers into multiple classes based on certain characteristics. We consider the case in which customers are primarily distinguished by whether they are willing to wait for backordered demand. A firm that faces demand from customers that are differentiated in this way may want to adopt an inventory management policy that takes advantage of this differentiation. We propose doing so by imposing a critical level (CL) policy: when inventory is at or below the critical level demand from those customers that are willing to wait is backordered, while demand from customers unwilling to wait will still be served as long as there is any inventory available. This policy reserves inventory for possible future demands from impatient customers by having other, patient, customers wait. We model a system that operates a continuous review replenishment policy, in which a base stock policy is used for replenishments. Demands as well as lead times are stochastic. We develop an exact and efficient procedure to determine the average infinite horizon performance of a given CL policy. Leveraging this procedure we develop an efficient algorithm to determine the optimal CL policy Serv Manuf J (2014) 26:344-386 DOI 10.1007 parameters. Then, in a numerical study we compare the cost of the optimal CL policy to the globally optimal state-dependent policy along with two alternative, more naïve, policies. The CL policy is slightly over 2 % from optimal, whereas the alternative policies are 7 and 27 % from optimal. We also study the sensitivity of our policy to the coefficient of variation of the lead time distribution, and find that the optimal CL policy is fairly insensitive, which is not the case for the globally optimal policy.

Optimal lateral transshipment policies for a two location inventory problem with multiple demand classes

“…The assumption of exponentially distributed service times is a common one when optimal policy structures are derived in a continuousreview setting; see also Zhao et al (2008). The system performance is known to be rather insensitive to this distribution, which has been shown by Alfredsson and Verrijdt (1999) and Enders et al (2014). The mean repair time is denoted by 1/µ (µ > 0), and is the same for both stockpoints.…”

System-oriented inventory models for spare parts

“…When on hand stock is higher than or equal to K i , demands from both classes of customers are fulfilled FCFS, but when on hand stock is lower than K i , demands of premium customers are fulfilled only, while the demands of the other customers are backordered (or lost, depending on the model assumptions). This policy has been applied to a spare parts inventory setting in several papers, see, e.g., Dekker et al (2002), Deshpande et al (2003, Kranenburg and Van Houtum (2008), Möllering and Thonemann (2010), and Enders et al (2013). In these studies, the cost performance of critical level policies is also compared numerically to the round-up and separate stock policies, see, e.g., Deshpande et al (2003) and Kranenburg and Van Houtum (2008).…”

The value of customization : on differentiation in service logistics

“…A few contributions consider single-item models with both backordering and lost sales, both in a continuous-review setting (e.g. Enders et al (2012), Benjaafar et al (2010, Van Wijk (2012)) and a periodic review setting (e.g. Tang et al (2007), Zhou and Zhao (2010a, 2010b)), see Van Wijk (2012) for details.…”

“…In certain papers, the shipment option used depends on the customer class (e.g. Enders et al (2012), where premium demand is lost, while non-premium demand is backordered), whereas other papers allow the choice of backordering versus lost sales to only depend on the system state (as in Benjaafar et al (2010)).…”