Abstract The Triangle Scheduling (TS) Problem, defined by Dürr et al. (J Sched 21:305–312, 2018. https://doi.org/10.1007/s10951-017-0533-1 ), is a geometric model for non-preemptive scheduling of jobs with different criticality levels on a single machine. The jobs have a criticality equal to the worst-case execution time and are scheduled off-line. In this article, we describe, implement and analyze the Bintree algorithm on TS, which is an algorithm based on a binary tree construction. It has $$O(n\log (n))$$ runtime and its approximation ratio is between 1.35 and $$2\ln (2) \approx 1.386$$ . Bintree is, therefore, the first polynomial-time approximation algorithm for TS with an approximation ratio below 1.5. We also explore Bintree’s relation to a previously defined algorithm, Greedy, and a potential hybrid algorithm that runs both and chooses the shorter schedule, which we suspect to be better than either algorithm by itself. We analyze the behavior of Bintree on small values of input sizes formalizing its quadratic integer programming model.

Production routing problems (PRPs) are integrated planning problems that combine vehicle routing and lot-sizing decisions. Given a discrete finite time horizon and a set of customers, the basic PRP consists of deciding for each period if and how much to produce, the inventories at the supplier and the customers, and the vehicle routes. The latter include the decisions on which customers to serve and the quantities delivered. The objective is to minimize the total cost over the planning horizon consisting of production, inventory, and routing cost. In this paper, we consider the PRP with time windows (PRPTW) and propose a branch-price-and-cut (BPC) algorithm for its solution. The BPC relies on a path-based formulation that explicitly specifies which demands are satisfied by which deliveries and employs several families of valid inequalities. The performance of the BPC is assessed in an extensive computational study on existing benchmark instances for the related inventory routing problem with time windows (IRPTW) and newly created instances for the PRPTW. Our BPC outperforms the current state-of-the-art BPC for the IRPTW, closing 62 previously open instances. Finally, we derive managerial insights from our PRPTW instances.

Abstract The drone routing problem with energy replenishment (DRP-E) describes a general class of routing problems with intermediate stops and synchronization constraints. In DRP-E, the drone has to visit a set of nodes and routinely requires battery swaps, energy- or payload replenishment from mobile or stationary replenishment stations. Thereby, the drone may visit several destinations between two replenishments, and mutual waiting at the rendezvous locations may occur. In this paper, we propose a very large-scale neighborhood that synergistically leverages two large-sized polynomially solvable DRP-E subproblems (SP1 and SP2). The number of feasible solutions in the resulting neighborhood is a multiple of those in SP1 and SP2, and, thus, exponential in the input size of the problem. We develop a non-trivial search procedure, VLNS, which examines this neighborhood entirely , in a computational time that remains polynomial in the problem size. The desired trade-off between accuracy and runtime of the proposed two-stage dynamic programming approach can be flexibly adjusted with just a single parameter. For large parameter values, it converts to an exact approach. VLNS is a flexible improvement procedure , which is easy to implement. It can be straightforwardly adapted to many DRP-E variants and may be embedded in any algorithmic scheme, meta- or math-heuristic. In computational tests, we demonstrate that a lean local-search-based implementation of VLNS already outperforms state-of-the-art heuristics for several DRP-E variants by a significant margin. We furthermore propose a well-performing exact approach for DRP-E.

Abstract We study the tactical time slot management problem under mixed logit demand for attended home delivery in subscription settings. We propose a static mixed-integer linear programming model that integrates delivery slot assortment, price discount decisions, and routing optimization while capturing customer heterogeneity through the mixed logit model. To overcome the computational challenges posed by simulation-based choice probabilities, we develop a simulation-based Adaptive Large Neighborhood Search method aligned with a Sample Average Approximation reformulation. Computational experiments on large-scale instances demonstrate the effectiveness of our approach in capturing stochastic customer behavior and preference heterogeneity, providing a scalable and flexible method for optimizing time slot management under complex demand structures.

Abstract Ocean shipping is integral to today’s global and interconnected supply chain networks. To supply products to the hinterland, inland waterway transport is vital due to its economic advantages wherever possible. However, major inland waterways are prone to recurring disruptions caused. These disruptions lead carriers to impose surcharges, which can severely affect firm performance. To mitigate these disruptions, different resilience strategies, which potentially influence each other, need to be evaluated for each product within the product portfolio. In this paper, we decide on the resilience strategies and transportation flows for a two-echelon inbound supply chain with multiple products that are needed to produce a single finished good under transportation cost and lead time uncertainty to minimize total expected costs. The problem is formulated as a two-stage stochastic mixed-integer linear program. To solve large instances, we propose model enhancements that strengthen the formulation and a heuristic approach to particularly solve large problem instances. We present a case study based on a chemical company at the border of the Rhine River. Considering disruptions, the cost-efficient mix of resilience strategies significantly depends on the specific product characteristics. Considering multiple products jointly reduces resilience costs by up to 79% compared with solving the problem separately for each product. Moreover, historical shifts in disruption probabilities and impacts over the past four decades require an adjustment of the resilience mix. Our findings demonstrate that multi-product considerations are essential for resilient supply chain network design and that resilience strategies must be tailored to product characteristics and evolving disruption risks.

2004).These models capture, in full generality, the trade-offs among capacity, uncertainty, and customer choice that define RM.Yet, as already noted by Talluri and van Ryzin (1998), the resulting problems are often simply too large to solve exactly.The enduring challenge, therefore, lies not in formulating the "perfect" model but in extracting useful, implementable decision policies from systems that defy exact optimization.This Special Issue on Revenue Management for Complex Systems brings together five contributions that embody precisely this philosophy.Each paper begins with a theoretically sound model that captures the richness of real-world complexity (multidimensional heterogeneity, dynamic decisions under uncertainty, coupled subsystems, and data-driven learning) but then forges a computational path that makes the model tractable and actionable.Although they operate across diverse domains from pricing consumer products to managing transportation, logistics, and mobility networks, they share a unifying spirit: to turn complexity into structure, and structure into insight. Dynamic Nonlinear Pricing under Multiunit DemandWhen customers differ not only in their willingness to pay but also in the quantity they demand, even the simplest dynamic pricing problems become analytically