Strong Products of Hypergraphs: Unique Prime Factorization Theorems and Algorithms

It is well-known that all finite connected graphs have a unique prime factor decomposition (PFD) with respect to the strong graph product which can be computed in polynomial time. Essential for the PFD computation is the construction of the so-called Cartesian skeleton of the graphs under investigation. In this contribution, we show that every connected thin hypergraph H has a unique prime factorization with respect to the normal and strong (hypergraph) product. Both products coincide with the usual strong graph product whenever H is a graph. We introduce the notion of the Cartesian skeleton of hypergraphs as a natural generalization of the Cartesian skeleton of graphs and prove that it is uniquely defined for thin hypergraphs. Moreover, we show that the Cartesian skeleton of hypergraphs can be determined in O(|E|^2) time and that the PFD can be computed in O(|V|^2|E|) time, for hypergraphs H = (V,E) with bounded degree and bounded rank

Proactive food waste prevention in grocery retail supply chains – an exploratory study

Purpose Regarding the retail internal supply chain (SC), both retailers and research are currently focused on reactive food waste reduction options in stores (e.g. discounting or donations). These options reduce waste after a surplus has emerged but do not prevent an emerging surplus in the first place. This paper aims to reveal how retailers can proactively prevent waste along the SC and why the options identified are impactful but, at the same time, often complex to implement. Design/methodology/approach The authors follow an exploratory approach for a nascent topic to obtain insights into measures taken in practice. Interviews with experts from retail build the main data source. Findings The authors identify and analyze 21 inbound, warehousing, distribution and store-related options applied in grocery retail. Despite the expected high overall impact on waste, prevention measures in inbound logistics and distribution and warehousing have not been intensively applied to date. Practical implications The authors provide a structured approach to mitigate waste within retailers' operations and categorize the types of barriers that need to be addressed. Originality/value This research provides a better understanding of prevention options in retail operations, which has not yet been empirically explored. Furthermore, this study conceptualizes prevention and reduction options and reveals implementation patterns

Winning the race to customers with micro-fulfillment centers: an approach for network planning in quick commerce

In 2020, the first quick commerce businesses in grocery retail emerged in the European market. Customers can order online and receive their groceries within 15 min in the best case. The ability to provide short lead times is, therefore, essential. However, the ambitious service promises of quick deliveries further complicate order fulfillment, and many retailers are struggling to achieve profitability. Quick commerce retailers need to establish an efficient network of micro-fulfillment centers (MFCs) in customer proximity, i.e., urban areas, to master these challenges. We address this strategic network problem and formulate it as a location routing problem. This enables us to define the number, location, type, and size of MFCs based on setup, replenishment, order processing, and transportation costs. We solve the problem using a cluster-first-route-second heuristic based on agglomerative clustering to approximate transportation costs. Our numerical experiments show that our heuristic solves the problem effectively and provides efficient decision support for quick commerce retailing. We generate managerial insights by analyzing key aspects of a quick commerce business, such as lead times and problem-specific cost factors. We show, for example, that allowing slightly higher delivery flexibility (e.g., offering extended lead times) enables bundling effects and results in cost savings of 50% or more of fulfillment costs. Furthermore, using multiple small MFCs is more efficient than larger, automated MFCs from a lead time and cost perspective

Integrated zone picking and vehicle routing operations with restricted intermediate storage

The competitiveness of a retailer is highly dependent on an efficient distribution system. This is especially true for the supply of stores from distribution centers. Stores ask for high flexibility when it comes to their supply. This means that fast order processing is essential. Order processing affects different subsystems at the distribution center: Orders are picked in multiple picking zones, transferred to intermediate storage, and delivered via dedicated tours. These processing steps are highly interdependent. The schedule for picking needs to be synchronized with the routing decisions to ensure availability of the delivery orders at the DC’s loading docks when their associated tours are scheduled. Concurrently, intermediate storage represents a bottleneck as capacities for order storage are limited. The simultaneous planning of picking and routing operations with restricted intermediate storage is therefore relevant for retail practice but has not so far been considered within an integrated planning approach. Our work addresses this task and discusses an integrated zone picking and vehicle routing problem with restricted intermediate storage. We present a comprehensive model formulation and introduce a general variable neighborhood search for simultaneous consideration of the given planning stages. We also present two alternative sequential approaches that are motivated by the prevailing planning situation in industry. Numerical experiments that we have conducted show the need for an integrated planning approach to obtain practicable results. Further, we identify the impact of the main problem characteristics on the overall planning problem and provide valuable insights for the application of this approach in industry