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Matching supply with demand remains a challenging task for many companies, especially when purchasing and production must be planned with sufficient lead time, demand is uncertain, overall supply may not suffice to fulfill all of the projected demands, and customers differ in their level of importance. The particular structure of sales organizations often adds another layer of complexity: These organizations often have multi-level hierarchical structures that include multiple geographic sales regions, distribution channels, customer groups, and individual customers (e.g., key accounts). In this paper, we address the problem of "allocation planning" in such sales hierarchies when customer demand is stochastic, supply is scarce, and the company's objective is to meet individual customer groups' service-level targets. Our first objective is to determine when conventional allocation rules lead to optimal (or at least acceptable) results and to characterize their optimality gap relative to the theoretical optimum. We find that these popular rules lead to optimal results only under very restrictive conditions and that the loss in optimality is often substantial. This result leads us to pursue our second objective: to find alternative (decentral) allocation approaches that generate acceptable performance under conditions in which the conventional allocation rules lead to poor results. We develop two alternative (decentral) allocation approaches and derive conditions under which they lead to optimal allocations. Based on numerical analyses, we show that these alternative approaches outperform the conventional allocation rules, independent of the conditions under which they are used. Our results suggest that they lead to near-optimal solutions under most conditions. [ABSTRACT FROM AUTHOR]

We study critical-level inventory-management policies as means to provide differentiated ( $$\alpha $$ and $$\beta $$ ) service levels to more than two classes of customers. First, we derive closed-form expressions for the service levels of a single-period critical-level policy with an arbitrary number of customer classes (with Poisson demand). Based on the service-level expressions, we derive additional structural insights and provide an efficient algorithm with which to compute the essential system parameters, that is, the minimum required starting inventory and the associated critical levels. Based on these results, we conduct numerical experiments and develop structural insights into the system's behavior. [ABSTRACT FROM AUTHOR]

We investigate the use of priority mechanisms when assigning service engineers to customers as a tool for service differentiation. To this end, we analyze a non-preemptive $$M/PH/c$$ priority queue with various customer classes. For this queue, we present various accurate and fast methods to estimate the first two moments of the waiting time per class given that all servers are occupied. These waiting time moments allow us to approximate the overall waiting time distribution per class. We subsequently apply these methods to real-life data in a case study. [ABSTRACT FROM AUTHOR]