Single-period stochastic demand fulfillment in customer hierarchies

Highlights

• Formalization of the stochastic allocation planning problem in customer hierarchies.

• Introduction of information aggregation and allocation functions.

• Develop robust and near-optimal decentralized allocation methods.

• Numerical comparison of the proposed methods with practically relevant benchmarks.

• Identify crucial information for good decentralized allocation decisions.

Abstract

To maximize profits, given limited resources, companies commonly divide their overall customer base into different segments and use allocation policies to prioritize the most important segments. Determining the optimal allocations is challenging due to supply lead times and uncertain demand. Another challenge is the multilevel hierarchical structure of the customer segments. In general, available quotas are not determined by a central planner with full visibility of all individual customer segments but rather result from a sequence of allocation steps with an increasing level of granularity. In this paper, we investigate this sequential allocation process. Specifically, we identify crucial information for making allocation decisions in customer hierarchies and propose decentralized methods that lead to near-optimal allocations while respecting the requirements for information aggregation. We evaluate the methods by comparing their information requirements and reflect on the role of information sharing in hierarchical allocation decisions.

Introduction

This paper addresses the problem of allocating scarce supply to hierarchically structured customer segments so as to maximize profitability. The problem connects the supply chain planning task of profit-oriented demand fulfillment (DF) to the business reality of multilevel customer hierarchies.

DF aims to optimally match customer orders with available resources. In make-to-stock production systems, DF comprises fulfilling customer orders from inventory. Since acceptable customer response times are shorter than production lead times, in this setting, supply is essentially fixed when demand materializes (Fleischmann & Meyr, 2004). Therefore, firms face the risk of short-term supply shortages, especially when demand is uncertain. Under a first-come-first-served (FCFS) fulfillment approach, any customer may suffer from such shortages. However, customers commonly differ in their importance and profitability. FCFS demand fulfillment ignores these differences and therefore performs poorly under heterogeneous demand (Barut, Sridharan, 2005, Ketikidis, Lenny Koh, Gunasekaran, Pibernik, 2006, Meyr, 2009).

Revenue management (RM) approaches to demand fulfillment address this deficiency (Quante, Meyr, & Fleischmann, 2009b). Such approaches divide the overall customer base into different segments based on profitability or strategic importance. The DF problem is then solved in a two-stage process. First, in the allocation planning stage, available-to-promise quantities (ATP) are determined and allocated as quotas to different customer segments. Second, in the order promising stage, these quotas are consumed by fulfilling realized orders from the corresponding customer segments (Ball, Chen, Zhao, 2004, Kilger, Meyr, 2008). Orders exceeding the corresponding quota are lost or deferred to less constrained periods. This process prioritizes more profitable orders and avoids depleting scarce supply by fulfilling less profitable orders.

Available RM approaches to demand fulfillment rely on a one-dimensional ranking of the customer segments. In reality, however, customer segments commonly have a multilevel hierarchical structure that reflects the structure of the sales organization. A typical customer hierarchy includes different geographies, different distribution channels, and different customer groups, similar to that shown in Fig. 1. Roitsch and Meyr (2015) study an example of such a hierarchy in the downstream business of the European oil industry. The industry faces long lead times, and after deciding about the crude oil supply, quantities cannot easily be changed. The available supply is then iteratively allocated to different business units in 14 different countries, producing different products for different customers and yielding different profits.

In such hierarchies, there is no direct ranking of individual customer segments. Instead, allocation planning is an iterative and decentralized process in which higher-level sales quotas are disaggregated one level at a time by multiple local planners. This hierarchical problem, although practically relevant, has barely been studied in the academic literature. Vogel and Meyr (2015) are the first to address the problem while assuming deterministic demand. In practice, simplistic rules of thumb are applied to determine sales quotas, which leads to suboptimal results (Vogel, 2014).

This paper investigates the hierarchical DF problem. Specifically, the study addresses the question of what information is required at the individual levels of the hierarchy to allow for an effective allocation. Mathematically, the optimal decision in each allocation step depends on the projected demand distributions of all individual customer segments. While technically feasible, sharing this fine-grained information across the levels of the decision-making hierarchy is undesirable from a managerial perspective because it overloads higher-level decision makers with potentially insignificant details and makes the resulting allocation decisions difficult to communicate. Therefore, companies commonly aggregate the demand information propagated along the levels of the hierarchy. While aggregation simplifies the decision process, overly coarse information may result in ineffective allocation decisions. To strike the right balance, it is crucial to identify those pieces of information that yield the greatest benefits in terms of steering the consecutive allocation steps towards an overall optimum.

Our paper is meant to provide insight into this information-performance trade-off. In contrast to Vogel and Meyr (2015), we assume stochastic demand. Therefore, potentially relevant information about customer segments can be broadly divided into information on expected demand, demand uncertainty, and unit profits. We investigate the role of each of these dimensions in hierarchical allocation planning for demand fulfillment.

In summary, our paper makes the following contributions:

• We formalize the allocation planning problem in customer hierarchies by defining information aggregation and allocation functions;

• We characterize the optimal centralized solution to the stochastic allocation problem;

• We develop robust and near-optimal decentralized allocation methods for the hierarchical stochastic DF problem;

• We compare the numerical performance of the proposed methods with benchmarks commonly applied in APS and investigate the parameters driving the respective gaps;

• We reflect on the role of information sharing in hierarchical demand fulfillment and identify crucial information for good decentralized allocation decisions.

The paper proceeds as follows. In Section 2, we review the related literature and position our contribution. In Section 3, we formalize the hierarchical DF problem. In Section 4, we explain the best-case and worst-case benchmarks for the problem, including the optimal centralized solution. We present our new decentralized heuristics in Section 5 and evaluate their performance in extensive numerical experiments in Section 6. In Section 7, we provide our conclusions and managerial insights.