Optimal Pooling, Batching, and Pasteurizing of Donor Human Milk

Human breast milk provides nutritional and medicinal benefits that are important to infants, particularly those who are premature or ill. Donor human milk, collected, processed, and dispensed via milk banks, is the standard of care for infants in need whose mothers cannot provide an adequate supply of milk. In this paper, we focus on streamlining donor human milk processing at nonprofit milk banks. On days that milk is processed, milk banks thaw frozen deposits, pool together milk from multiple donors to meet nutritional specifications of predefined milk types, bottle and divide the pools into batches, and pasteurize the batches using equipment with various degrees of labor requirements. Limitations in staffing and equipment and the need to follow strict healthcare protocols require productive, expedient, and frugal pooling strategies. We formulate integer programs that optimize the batching-pasteurizing decisions and the integrated pooling-batching-pasteurizing decisions by minimizing labor and meeting target production goals. We further strengthen these formulations by establishing valid inequalities for the integrated model. Numerical results demonstrate a reduction in the optimality gap through the strengthened formulation versus the basic integer programming formulation. A case study at Mothers’ Milk Bank of North Texas demonstrates significant improvement in meeting milk type production targets and a modest reduction in labor compared with former practice. The model is in use at Mothers’ Milk Bank of North Texas and has effectively improved their production balance across different milk types.

New solution procedures for the order picker routing problem in U-shaped pick areas with a movable depot

This paper develops new solution procedures for the order picker routing problem in U-shaped order picking zones with a movable depot, which has so far only been solved using simple heuristics. The paper presents the first exact solution approach, based on combinatorial Benders decomposition, as well as a heuristic approach based on dynamic programming that extends the idea of the venerable sweep algorithm. In a computational study, we demonstrate that the exact approach can solve small instances well, while the heuristic dynamic programming approach is fast and exhibits an average optimality gap close to zero in all test instances. Moreover, we investigate the influence of various storage assignment policies from the literature and compare them to a newly derived policy that is shown to be advantageous under certain circumstances. Secondly, we investigate the effects of having a movable depot compared to a fixed one and the influence of the effort to move the depot.

Pricing and Optimization in Shared Vehicle Systems: An Approximation Framework

The optimal management of shared vehicle systems, such as bike-, scooter-, car-, or ride-sharing, is more challenging compared with traditional resource allocation settings because of the presence of spatial externalities—changes in the demand/supply at any location affect future supply throughout the system within short timescales. These externalities are well captured by steady-state Markovian models, which are therefore widely used to analyze such systems. However, using Markovian models to design pricing and other control policies is computationally difficult because the resulting optimization problems are high dimensional and nonconvex. In our work, we design a framework that provides near-optimal policies, for a range of possible controls, that are based on applying the possible controls to achieve spatial balance on average. The optimality gap of these policies improves as the ratio between supply and the number of locations increases and asymptotically goes to zero.

A Study of Learning Search Approximation in Mixed Integer Branch and Bound: Node Selection in SCIP

In line with the growing trend of using machine learning to help solve combinatorial optimisation problems, one promising idea is to improve node selection within a mixed integer programming (MIP) branch-and-bound tree by using a learned policy. Previous work using imitation learning indicates the feasibility of acquiring a node selection policy, by learning an adaptive node searching order. In contrast, our imitation learning policy is focused solely on learning which of a node’s children to select. We present an offline method to learn such a policy in two settings: one that comprises a heuristic by committing to pruning of nodes; one that is exact and backtracks from a leaf to guarantee finding the optimal integer solution. The former setting corresponds to a child selector during plunging, while the latter is akin to a diving heuristic. We apply the policy within the popular open-source solver SCIP, in both heuristic and exact settings. Empirical results on five MIP datasets indicate that our node selection policy leads to solutions significantly more quickly than the state-of-the-art precedent in the literature. While we do not beat the highly-optimised SCIP state-of-practice baseline node selector in terms of solving time on exact solutions, our heuristic policies have a consistently better optimality gap than all baselines, if the accuracy of the predictive model is sufficient. Further, the results also indicate that, when a time limit is applied, our heuristic method finds better solutions than all baselines in the majority of problems tested. We explain the results by showing that the learned policies have imitated the SCIP baseline, but without the latter’s early plunge abort. Our recommendation is that, despite the clear improvements over the literature, this kind of MIP child selector is better seen in a broader approach to using learning in MIP branch-and-bound tree decisions.

A Service System with Packing Constraints: Greedy Randomized Algorithm Achieving Sublinear in Scale Optimality Gap

A service system with multiple types of arriving customers is considered. There is an infinite number of homogeneous servers. Multiple customers can be placed for simultaneous service into one server, subject to general packing constraints. The service times of different customers are independent even if they are served simultaneously by the same server; the service time distribution depends on the customer type. Each new arriving customer is placed for service immediately into either an occupied server, that is, one already serving other customers, as long as packing constraints are not violated or into an empty server. After service completion, each customer leaves its server and the system. The basic objective is to minimize the number of occupied servers in steady state. We study a greedy random (GRAND) placement (packing) algorithm, introduced in our previous work. This is a simple online algorithm that places each arriving customer uniformly at random into either one of the already occupied servers that can still fit the customer or one of the so-called zero servers, which are empty servers designated to be available to new arrivals. In our previous work, a version of the algorithm, labeled GRAND(aZ), is considered, in which the number of zero servers is aZ with Z being the current total number of customers in the system and positive a being an algorithm parameter. GRAND(aZ) is shown in our previous work to be asymptotically optimal in the following sense: (a) the steady-state optimality gap grows linearly in the system scale r (the mean total number of customers in service), that is, as c(a)r for some positive c(a), and (b) c(a) vanishes as a goes to zero. In this paper, we consider the GRAND(Zp) algorithm, in which the number of zero servers is Zp, where p < 1 is a fixed parameter, sufficiently close to 1. We prove the asymptotic optimality of GRAND(Zp) in the sense that the steady-state optimality gap is sublinear in the system scale r. This is a stronger form of asymptotic optimality than that of GRAND(aZ).

Optimal versus approximate channel selection methods for EEG decoding with application to topology-constrained neuro-sensor networks

Channel selection or electrode placement for neural decoding is a commonly encountered problem in electroencephalography (EEG). Since evaluating all possible channel combinations is usually infeasible, one usually has to settle for heuristic methods or convex approximations without optimality guarantees. To date, it remains unclear how large the gap is between the selection made by these approximate methods and the truly optimal selection. The goal of this paper is to quantify this optimality gap for several state-of-the-art channel selection methods in the context of least-squares based neural decoding. To this end, we reformulate the channel selection problem as a mixed-integer quadratic program (MIQP), which allows the use of efficient MIQP solvers to find the optimal channel combination in a feasible computation time for up to 100 candidate channels. As this reveals the exact solution to the combinatorial problem, it allows to quantify the performance losses when using state-of-the-art sub-optimal (yet faster) channel selection methods. In a context of auditory attention decoding, we find that a greedy channel selection based on the utility metric does not show a significant optimality gap compared to optimal channel selection, whereas other state-of-the-art greedy or l1-norm penalized methods do show a significant loss in performance. Furthermore, we demonstrate that the MIQP formulation also provides a natural way to incorporate topology constraints in the selection, e.g., for electrode placement in neuro-sensor networks with galvanic separation constraints. Furthermore, a combination of this utility-based greedy selection with an MIQP solver allows to perform a topology constrained electrode placement, even in large scale problems with more than 100 candidate positions.

Token-Weighted Crowdsourcing

Blockchain-based platforms often rely on token-weighted voting (“τ-weighting”) to efficiently crowdsource information from their users for a wide range of applications, including content curation and on-chain governance. We examine the effectiveness of such decentralized platforms for harnessing the wisdom and effort of the crowd. We find that τ-weighting generally discourages truthful voting and erodes the platform’s predictive power unless users are “strategic enough” to unravel the underlying aggregation mechanism. Platform accuracy decreases with the number of truthful users and the dispersion in their token holdings, and in many cases, platforms would be better off with a “flat” 1/n mechanism. When, prior to voting, strategic users can exert effort to endogenously improve their signals, users with more tokens generally exert more effort—a feature often touted in marketing materials as a core advantage of τ-weighting—however, this feature is not attributable to the mechanism itself, and more importantly, the ensuing equilibrium fails to achieve the first-best accuracy of a centralized platform. The optimality gap decreases as the distribution of tokens across users approaches a theoretical optimum, which we derive, but tends to increase with the dispersion in users’ token holdings. This paper was accepted by Gabriel Weintraub, revenue management and market analytics.

Drone-Based Parcel Delivery Using the Rooftops of City Buildings: Model and Solution

In general, the demand for delivery cannot be fulfilled efficiently due to the excessive traffic in dense urban areas. Therefore, many innovative concepts for intelligent transportation of freight have recently been developed. One of these concepts relies on drone-based parcel delivery using rooftops of city buildings. To apply drone logistics system in cities, the operation design should be adequately prepared. In this regard, a mixed integer programming model for drone operation planning and a heuristic based on block stacking are newly proposed to provide solutions. Additionally, numerical experiments with three different problem sizes are conducted to check the feasibility of the proposed model and to assess the performance of the proposed heuristic. The experimental results show that the proposed model seems to be viable and that the developed heuristic provides very good operation plans in terms of the optimality gap and the computation time.