arXiv subjects

Roberto Rossi

Publications and source records attributed to Roberto Rossi.

At least 19 recordsLinked to original sources

arXiv2026

The optimality of an (s, S) hiring policy on a workforce planning problem with fixed recruitment costs and binomial turnover

We study a finite-horizon workforce planning problem in which staff turnover in each period follows a binomial distribution whose parameters depend on the post-hiring workforce level. The model incorporates a fixed hiring cost that is incurred whenever recruitment occurs, regardless of the number of employees hired. The objective is to minimise the expected total cost, including recruitment, salary, and shortage costs, where deviations below period-specific staffing requirements are penalised. To analyse this stochastic dynamic programme with decision-dependent transition probabilities, we establish the discrete convexity of the variable single-period cost (the sum of expected salary and penalty costs) and the K-convexity of the expected total cost. Specifically, we introduce the concept of Binomial-K-convexity to facilitate the proof that K-convexity is preserved under Binomial propagation in the Bellman function. We then show that the optimal hiring policy exhibits an (s, S)-type structure: when the workforce level in a given period falls below a threshold s, staff are hired up to level S; otherwise, no hiring occurs. Furthermore, we develop a piecewise approximation approach that yields a mixed-integer linear programming (MILP) formulation for solving the problem and computing the (s, S) parameters for each period. Numerical results demonstrate that the proposed method achieves fast computation with small optimality gaps.

math.OC↗

arXiv2026

A Structural Interpretation of GELU and Threshold-Transmission Activations via the First-Order Loss Function

The Gaussian Error Linear Unit is usually motivated as the expected output of an input-dependent Bernoulli gate. This work gives an alternative interpretation: GELU is the expected output of a hard linear gate with a Gaussian random threshold. This view provides a generative interpretation for the Bernoulli gate: the gate opens once the input clears a latent Gaussian threshold. This interpretation stems from a decomposition based on well-known results in stochastic inventory theory and leads to a threshold-transmission family that includes ReLU, GELU, SiLU/Swish, and hard swish as special cases. By considering a latent uniform threshold, we recover a hard-swish-like piecewise-polynomial gate whose nonlinear transition is confined to a finite interval, yielding fixed- and learned-width variants. Controlled experiments on compact vision and language models show that calibrated or learned uniform-threshold gates are consistently competitive with GELU, ReLU, and SiLU/Swish, display architecture-dependent learned widths, and use the finite transition region nontrivially.

cs.LG↗

arXiv2026

Grammar-Aware Literate Generative Mathematical Programming with Compiler-in-the-Loop

Mathematical programming is widely employed across various sectors - such as logistics, energy, and workforce planning - to model and solve industrial optimisation problems, but its use requires substantial domain expertise. Large language models offer a promising way to translate natural-language problem descriptions into optimisation models, yet existing approaches are costly and generally produce models written in general-purpose computer code (e.g. Python), which can be difficult to inspect, validate, and reuse. In this work, we introduce SyntAGM, a system that generates optimisation models in a readable algebraic modelling language through an iterative generate-compile-assess-revise loop. SyntAGM leverages PyOPL, an OPL-like modelling language compiler designed to provide actionable feedback for iterative model repair. To obtain a valid PyOPL model that matches the problem description, SyntAGM mobilises compiler feedback and an LLM-based alignment judge. In addition, it combines in-context exposure to the target language grammar, and few-shot retrieval of modelling exemplars. Across multiple benchmarks, SyntAGM achieves a more favourable cost-quality trade-off compared to established prompting baselines.

cs.PL↗

arXiv2025

Mixed-Integer Linear Programming Approximations for the Stochastic Knapsack

We develop mathematical programming approximations to tackle the stochastic knapsack problem. In this problem, the decision maker considers items for which either weights or values, or both, are random. The aim is to select a subset of these items to be included into their knapsack. We study both static and dynamic variants of this problem: in the static setting, the decision about which items should be included in the knapsack is taken at the outset, before any random item value or weight is revealed; in the dynamic setting, items are received sequentially, and the decision about a particular item is made by taking into account previously observed values and weights. The knapsack has a given capacity, and if the total realised weight exceeds this capacity then a penalty cost is incurred for each unit of excess capacity utilised. The goal is to maximise the expected net profit. We tackle the case of normally distributed item weights and we show that our approach extends to the case in which item weights are correlated and follow a multivariate normal distribution. In addition, we show our approach represents an effective heuristic for the case in which item weights follow generic probability distributions. In an extensive computational study we demonstrate that our models are near-optimal and more scalable than other state-of-the-art approaches.

math.OC↗

arXiv2025

Dechanneling Population at Extreme Crystal Bending with 6.5 TeV Proton Beam

Beam measurements with bent crystals, installed in the Large Hadron Collider to assist multistage collimation system, provided information on hadron interactions with crystals in the multi-TeV energy range. In particular, the dechanneling population was observed through scans of deflected halo with collimators. Taking advantage of the fact that crystals with different values of curvature radii were present, the dependence of dechanneling on bending radius (R) was recorded. Dechanneling was found to be enhanced in crystals with smaller bending radius, because it is too close to the critical value R_c at the LHC energy of 6.5 TeV where channeling is lost. Data analysis and comparison to simulation results provided a better understanding of the phenomena and could be used to define specifications for more performing crystals in future upgrades of the crystal collimation system.

hep-ex↗

arXiv2025

Crystal Collimation Cleaning Measurements with 6.5 TeV protons in the LHC

Safe disposal of beam halo is a fundamental requirement of modern superconductive hadron colliders to reduce thermal load on magnets and background to experimental detectors. In the CERN Large Hadron Collider (LHC) a multistage system fully compliant with the needs of the baseline operation was build. At a later stage, two short bent crystals were interleaved to the devices for betatron collimation to investigate efficiency enhancement of the halo disposal when inserting them as primary stages of the collimation hierarchy. Each crystal was mounted on a high--accuracy angular actuator, called goniometer, and installed in the clockwise Beam 1, one for the horizontal and one for the vertical plane. In this paper, measurements of the cleaning performance at collision energy with and without inserting crystals in the standard collimation schemes are discussed; the results are compared to theoretical expectations.

physics.acc-ph↗

arXiv2025

Conformal Prediction for Electricity Price Forecasting in the Day-Ahead and Real-Time Balancing Market

The integration of renewable energy into electricity markets poses significant challenges to price stability and increases the complexity of market operations. Accurate and reliable electricity price forecasting is crucial for effective market participation, where price dynamics can be significantly more challenging to predict. Probabilistic forecasting, through prediction intervals, efficiently quantifies the inherent uncertainties in electricity prices, supporting better decision-making for market participants. This study explores the enhancement of probabilistic price prediction using Conformal Prediction (CP) techniques, specifically Ensemble Batch Prediction Intervals and Sequential Predictive Conformal Inference. These methods provide precise and reliable prediction intervals, outperforming traditional models in validity metrics. We propose an ensemble approach that combines the efficiency of quantile regression models with the robust coverage properties of time series adapted CP techniques. This ensemble delivers both narrow prediction intervals and high coverage, leading to more reliable and accurate forecasts. We further evaluate the practical implications of CP techniques through a simulated trading algorithm applied to a battery storage system. The ensemble approach demonstrates improved financial returns in energy trading in both the Day-Ahead and Balancing Markets, highlighting its practical benefits for market participants.

cs.LG↗

arXiv2024

The importance of visual modelling languages in generative software engineering

Multimodal GPTs represent a watershed in the interplay between Software Engineering and Generative Artificial Intelligence. GPT-4 accepts image and text inputs, rather than simply natural language. We investigate relevant use cases stemming from these enhanced capabilities of GPT-4. To the best of our knowledge, no other work has investigated similar use cases involving Software Engineering tasks carried out via multimodal GPTs prompted with a mix of diagrams and natural language.

cs.SE↗

arXiv2024

A graph-based heuristic for the non-stationary stochastic lot-sizing problem under penalty costs

This paper introduces a graph-based algorithm for solving single-item, single-location inventory lot-sizing problems under non-stationary stochastic demand using the $(R_t, S_t)$ policy and a penalty cost scheme. The proposed method relaxes the original mixed-integer linear programming (MILP) model by eliminating non-negative order quantity constraints and formulating it as a shortest-path problem on a weighted directed acyclic graph. A repetitive augmentation procedure is proposed to resolve any infeasibility in the solution. This procedure consists of three stages: (1) filtration, (2) repeated augmentation by redirecting, reconnecting, and duplicating between newly introduced and existing nodes to adjust the graph and eliminate negative replenishment orders, and (3) re-optimising. The effectiveness and computational efficiency of the proposed approach are assessed through extensive experiments on 1,620 test instances across various demand patterns and parameter settings. The results show that 195 instances required augmentation, mainly those with high penalty costs, low fixed ordering costs, large demand variability, and extended planning horizons. The efficiency of the algorithm for instances with extended planning horizon scenarios demonstrates its suitability for use in real-world scenarios.

math.OC↗

arXiv2023

On the stochastic inventory problem under order capacity constraints

We consider the single-item single-stocking location stochastic inventory system under a fixed ordering cost component. A long-standing problem is that of determining the structure of the optimal control policy when this system is subject to order quantity capacity constraints; to date, only partial characterisations of the optimal policy have been discussed. An open question is whether a policy with a single continuous interval over which ordering is prescribed is optimal for this problem. Under the so-called "continuous order property" conjecture, we show that the optimal policy takes the modified multi-$(s,S)$ form. Moreover, we provide a numerical counterexample in which the continuous order property is violated, and hence show that a modified multi-$(s,S)$ policy is not optimal in general. However, in an extensive computational study, we show that instances violating the continuous order property are extremely rare in practice, and that the plans generated by a modified multi-$(s,S)$ policy can therefore be considered, for all practical purposes, optimal. Finally, we show that a modified $(s,S)$ policy also performs well in practice.

math.OC↗

arXiv2022

jsdp: a Java Stochastic DP Library

Stochastic Programming is a framework for modelling and solving problems of decision making under uncertainty. Stochastic Dynamic Programming is a branch of Stochastic Programming that takes a "functional equation" approach to the discovery of optimal policies. By leveraging constructs - lambda expressions, functional interfaces, collections and aggregate operators - implemented in Java to operationalise the MapReduce framework, jsdp provides a general purpose library for modelling and solving Stochastic Dynamic Programs.

cs.AI↗

arXiv2022

A hybrid inventory policy for non-stationary lot-sizing problem with lateral transshipment

This paper addresses the two-stocking locations single item non-stationary stochastic lot-sizing problem. The inventory level at each location is reviewed periodically. Items can be reordered and received from a common central warehouse and can also be transshipped laterally from the other location. Lateral transshipment is assumed to be proactive to re-distribute the stock between two stocking locations. Therefore, the order of action in each period is: transshipping (if necessary), reordering (if necessary) and satisfying the demand at each location and each installation. The costs are imposed on transshipping, ordering, holding, and back-ordering. The key issue in such systems is to determine the quantity of the lateral transshipment between depots and the order quantities from the warehouse to both locations. We formulate the problem via stochastic dynamic programming to minimise the expected total cost. Since the number of actions increases exponentially as the feasible quantities of transshipment and replenishment grow, we develop two-stage dynamic programming to improve the computation efficiency. A near-optimal policy against this two-stage formulation is introduced based on a mixed integer linear programming and receding-horizon approach. numerical experiments are implemented to demonstrate the performance of the two-stage model and the heuristic algorithm

math.OC↗

arXiv2022

Stochastic Dynamic Programming Heuristic for the (R, s, S) Policy Parameters Computation

The (R, s, S) is a stochastic inventory control policy widely used by practitioners. In an inventory system managed according to this policy, the inventory is reviewed at instant R; if the observed inventory position is lower than the reorder level s an order is placed. The order's quantity is set to raise the inventory position to the order-up-to-level S. This paper introduces a new stochastic dynamic program (SDP) based heuristic to compute the (R, s, S) policy parameters for the non-stationary stochastic lot-sizing problem with backlogging of the excessive demand, fixed order and review costs, and linear holding and penalty costs. In a recent work, Visentin et al. (2021) present an approach to compute optimal policy parameters under these assumptions. Our model combines a greedy relaxation of the problem with a modified version of Scarf's (s, S) SDP. A simple implementation of the model requires a prohibitive computational effort to compute the parameters. However, we can speed up the computations by using K-convexity property and memorisation techniques. The resulting algorithm is considerably faster than the state-of-the-art, extending its adoptability by practitioners. An extensive computational study compares our approach with the algorithms available in the literature.

math.OC↗

arXiv2022

Controlling inventory on electric roads

Electric road systems (ERS) are roads that allow compatible vehicles to be powered by grid electricity while in transit, reducing the need for stopping to recharge electric batteries. We investigate how this technology can affect routing and delivery decisions for hybrid heavy good vehicles (HGVs) travelling on a ERS network to support the demand of a single product faced by a set of retailers in the network. We introduce the Electric Roads Routing Problem, which accounts for the costs of electricity and fuel on a ERS network, consumption that are affected by the battery level of the vehicle in each step of the journey, the routing decisions and the variable weight of the vehicle, which depends on vehicle load and delivery decisions. In particular, we study a stochastic demand version of the problem, formulating a mathematical programming heuristic and proving its effectiveness. We use our model on a realistic instance of the problem, showcasing the different strategies that a vehicle may follow depending on fuel costs in relation to the costs of electricity.

math.OC↗

arXiv2022

Curatio et Innovatio

The Middle Ages focused obsessively on the old; our era is totally absorbed with the new. In medio stat virtus. In this short note, I advocate a strategy that blends copyright and copyleft for disseminating research results in the sciences. I argue that such a blend may be beneficial in fields such as mathematics and computer science, that it may facilitate the evolution and emergence of improved problem descriptions, whilst at the same time preserving author's rights, and easing researchers' work.

cs.DL↗

arXiv2020

Computing Optimal (R, s, S) Policy Parameters by a Hybrid of Branch-and-Bound and Stochastic Dynamic Programming

A well-know control policy in stochastic inventory control is the (R, s, S) policy, in which inventory is raised to an order-up-to-level S at a review instant R whenever it falls below reorder-level s. To date, little or no work has been devoted to developing approaches for computing (R, s, S) policy parameters. In this work, we introduce a hybrid approach that exploits tree search to compute optimal replenishment cycles, and stochastic dynamic programming to compute (s, S) levels for a given cycle. Up to 99.8% of the search tree is pruned by a branch-and-bound technique with bounds generated by dynamic programming. A numerical study shows that the method can solve instances of realistic size in a reasonable time.

math.OC↗

arXiv2020

MILP Approximations for non-stationary stochastic lot-sizing under (s,Q)-type policy

This paper addresses the single-item single-stocking location non-stationary stochastic lot-sizing problem under a reorder point -- order quantity control strategy. The reorder points and order quantities are chosen at the beginning of the planning horizon. The reorder points are allowed to vary with time and we consider order quantities either to be a series of time-dependent constants or a fixed value; this leads to two variants of the policy: the (st,Qt) and the (st,Q) policies, respectively. For both policies, we present stochastic dynamic programs (SDP) to determine optimal policy parameters and introduce mixed integer non-linear programming (MINLP) heuristics that leverage piecewise-linear approximations of the cost function. Numerical experiments demonstrate that our solution method efficiently computes near-optimal parameters for a broad class of problem instances.

math.OC↗

arXiv2020

A computational study for the inventory routing problem

In this work we compare several new computational approaches to an inventory routing problem, in which a single product is shipped from a warehouse to retailers via an uncapacitated vehicle. We survey exact algorithms for the Traveling Salesman Problem (TSP) and its relaxations in the literature for the routing component. For the inventory control component we survey classical mixed integer linear programming and shortest path formulations for inventory models. We present a numerical study comparing combinations of the two empirically in terms of cost and solution time.

math.OC↗