Conference Agenda

This study explores the sales force deployment problem, focusing on profit-maximizing through four main areas: setting the optimal salesforce size, assigning salesperson locations, designing sales territories, and managing resource allocation. We employ a concave sales response function based on the premise that sales efficiency decreases as more resources are expended, specifically referencing the critical resource of salesperson time devoted to accounts. Our model incorporates an infinite number of binary variables to represent a point of selling time in a continuous time interval. Extending upon Haase & Müller (2014) branch-and-price algorithm by allowing sales territories to be handled by sales teams instead of only one sales representative.

We analyze the fixed costs associated with various sales team sizes within specific sales coverage units, investigating how the sales function effectiveness changes with sales team size due to time elasticity. The objective is to maximize overall profit from all sales representatives across their territories. This approach enhances our understanding of sales coverage by examining the impact of sales force composition and the strategic distribution of sales territories. We present preliminary numerical results that light the relationship between sales team size and revenue fluctuations, guided by different parameters for time elasticity.

We examine the Hazmat Transport Network Design Problem (HNDP), a well-researched bilevel problem in network design featuring linking interdiction constraints, where the first level of decision-making is governed by authorities and the second level by truck drivers transporting hazardous goods. The authorities can forbid certain streets for hazmat transport, and the truck drivers react by selecting the shortest path that adheres to these restrictions. The objective for the authorities is to forbid roads such that the drivers are guided towards less risky roads. We propose a novel extension by incorporating electric vehicles at the second level, which transforms the second level problem into a non-convex one. To solve the resulting bilevel problem, we develop a novel cutting plane procedure that merges Dantzig-Wolfe with Benders decomposition. Analogous to the well-known results for the case with a convex follower, we show that the underlying Benders subproblem can be decomposed into two subproblems, where the first represents the leader's problem conditional on the follower's reaction, and the second corresponds to the follower problem with a penalty term. We introduce additional speed-up techniques, such as partial decomposition and Pareto-optimal cuts, enhancing the efficacy of our methodology. In a preliminary computational analyses, we compare our approach with the standard Benders-like technique from the literature.

Airline passengers usually have their seats selected or assigned before arriving at the gate in the airport. We investigate the impact of the passenger-seat assignment on the boarding completion time, especially when considering a central decision-making process that takes place when passengers are already in line. Different seat assignments may result in different boarding completion times, which directly influence the turn-around time of an airplane. Identifying seat assignments that minimize boarding time can therefore provide airlines with significant cost savings. We introduce the problem of assigning passengers to seats while minimizing boarding time in the context of combinatorial optimization, study the computational complexity of the problem and develop exact, approximation, and heuristic algorithms. In addition to a theoretical analysis, we compare these algorithms in a computational study. Furthermore, we investigate an online variant of assigning passengers to seats—proposed in Jaehn and Neumann’s section on future research—and present results on the competitive ratio.

Flowty is a network optimisation solver that exploits the network structure in a column generation algorithm. This talk is about the resource constrained shortest path (RCSPP) algorithm at the core of this algorithm.

The RCSPP algorithm is a bidirectional labeling algorithm parallelised on a bucket level, that is pulling (as opposed to pushing) labels into buckets. The sizes of the buckets are small enough to avoid cycles within the bucket.

Pulling into buckets is done in parallel for independent buckets. The dependency graph between buckets is handled implicitly, and the bidirectional midpoint/stopping criteria is dynamic, meaning that buckets are extended until the opposite direction is encountered.

As is always the case for pull-based labeling algorithms; carefully choosing the order of which labels are created, it is possible to guarantee that only labels not dominated are ever stored. This not only limits the memory footprint, it also allows labels to be stored as immutable ‘object of arrays’ (as opposed to ‘array of objects’) thereby enabling the use of vectorised instructions for dominance checks and thus exploiting a second level of parallelisation.

The Vehicle Routing Problem with Time Windows (VPRTW) is used as an illustrative case.