Allocation planning in sales hierarchies with stochastic demand and service-level targets

• Published in: OR Spectrum 2019-12, Vol.41 (4), p.981-1024
• Main Authors: Kloos, Konstantin, Pibernik, Richard, Schulte, Benedikt
• Format: Article
• Language: English
• Subjects: Allocations; Business and Management; Calculus of Variations and Optimal Control; Optimization; Customer services; Customers; Demand; Geographical distribution; Hierarchies; Lead time; Operations Research/Decision Theory; Optimization; Organizations; Regular Article; Sales; Structural hierarchy
• ISSN: 0171-6468; 1436-6304
• DOI: 10.1007/s00291-018-0531-5

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.