arXiv subjects

Roberto Rossi

Publications and source records attributed to Roberto Rossi.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2019

A dynamic ordering policy for a stochastic inventory problem with cash constraints

This paper investigates a stochastic inventory management problem in which a cash-constrained small retailer periodically purchases a product from suppliers and sells it to a market while facing non-stationary demands. In each period, the retailer's available cash restricts the maximum quantity that can be ordered. There exists a fixed ordering cost for the retailer when purchasing. We partially characterize the optimal ordering policy by showing it has an $\bf s-C$ structure: for each period, when initial inventory is above the $\bf$s threshold, no product should be ordered no matter how much initial cash it has; when initial inventory is not large enough to be a $\bf s$ threshold, it is also better to not order when initial cash is below the threshold $C$. The values of $C$ may be state-dependent and related to each period's initial inventory. A heuristic policy $(s, C(x), S)$ is proposed: when initial inventory $x$ is less than $s$ and initial cash is greater than $C(x)$, order a quantity that brings inventory as close to $S$ as possible; otherwise, do not order. We first determine the values of the controlling parameters $s$, $C(x)$ and $S$ based on the results of stochastic dynamic programming and test their performance via an extensive computational study. The results show that the $(s, C(x), S)$ policy performs well with a maximum optimality gap of less than 1\% and an average gap of approximately 0.01\%. We then develop a simple and time-efficient heuristic method for computing policy $(s, C(x), S)$ by solving a mixed-integer linear programming problem and approximate newsvendor models: the average gap for this heuristic is approximately 2\% on our test bed.

math.OC↗

arXiv2019

An (R, S) Based Heuristic Model for the Stochastic Joint Replenishment Problem

This paper considers the periodic-review stochastic joint replenishment problem (JRP) under Bookbinder and Tan's static-dynamic uncertainty control policy. According to a static-dynamic uncertainty control rule, the decision maker fixes timing of replenishments once and for all at the beginning of the planning horizon, the inventory position is then raised to a predefined order-up-to-position at the beginning of each replenishment period. In this policy, freezing the replenishment times ameliorates the inherent difficulties pertinent to replenishment coordination of multiple products, whereas dynamic order quantities facilitate dealing with uncertain demands. We adapt and extend an earlier mixed integer linear programming (MILP) model for computing static-dynamic uncertainty policy parameters, and demonstrate that the same can be used to approximate the optimal control rule for the JRP, also known as $(σ, \vec{S})$ policy. An extensive computational study illustrates the effectiveness of our approach when compared to alternative approaches in the literature.

math.OC↗

arXiv2018

The Dynamic Bowser Routing Problem

We investigate opportunities offered by telematics and analytics to enable better informed, and more integrated, collaborative management decisions on construction sites. We focus on efficient refuelling of assets across construction sites. More specifically, we develop decision support models that, by leveraging data supplied by different assets, schedule refuelling operations by minimising the distance travelled by the bowser truck as well as fuel shortages. Motivated by a practical case study elicited in the context of a project we recently conducted at Crossrail, we introduce the Dynamic Bowser Routing Problem. In this problem the decision maker aims to dynamically refuel, by dispatching a bowser truck, a set of assets which consume fuel and whose location changes over time; the goal is to ensure that assets do not run out of fuel and that the bowser covers the minimum possible distance. We investigate deterministic and stochastic variants of this problem and introduce effective and scalable mathematical programming models to tackle these cases. We demonstrate the effectiveness of our approaches in the context of an extensive computational study designed around data collected on site as well as supplied by our project partners. Keywords: Routing; Dynamic Bowser Routing Problem; Stochastic Bowser Routing Problem; Mixed-Integer Linear Programming; Construction.

math.OC↗

arXiv2017

Declarative Statistics

In this work we introduce declarative statistics, a suite of declarative modelling tools for statistical analysis. Statistical constraints represent the key building block of declarative statistics. First, we introduce a range of relevant counting and matrix constraints and associated decompositions, some of which novel, that are instrumental in the design of statistical constraints. Second, we introduce a selection of novel statistical constraints and associated decompositions, which constitute a self-contained toolbox that can be used to tackle a wide range of problems typically encountered by statisticians. Finally, we deploy these statistical constraints to a wide range of application areas drawn from classical statistics and we contrast our framework against established practices.

cs.AI↗

arXiv2017

La Nova Scientia: Rewriting the History of Operational Research

The accepted lore is that Operational Research traces its roots back to the First and Second World Wars, when scientific research was used to improve military operations. In this essay we provide a different perspective on the origins of Operational Research by arguing that these are deeply intertwined with the impressive technological advances in Western Europe between the fifteenth and the sixteenth centuries.

math.HO↗

arXiv2017

Design, fabrication and characterization of Computer Generated Holograms for anti-counterfeiting applications using OAM beams as light decoders

In this paper, we present the design, fabrication and optical characterization of computer-generated holograms (CGH) encoding information for light beams carrying orbital angular momentum (OAM). Through the use of a numerical code, based on an iterative Fourier transform algorithm, a phase-only diffractive optical element (PH-DOE) specifically designed for OAM illumination has been computed, fabricated and tested. In order to shape the incident beam into a helicoidal phase profile and generate light carrying phase singularities, a method based on transmission through high-order spiral phase plates (SPPs) has been used. The phase pattern of the designed holographic DOEs has been fabricated using high-resolution Electron-Beam Lithography (EBL) over glass substrates coated with a positive photoresist layer (polymethylmethacrylate). To the best of our knowledge, the present study is the first attempt, in a comprehensive work, to design, fabricate and characterize computer-generated holograms encoding information for structured light carrying OAM and phase singularities. These optical devices appear promising as high-security optical elements for anti-counterfeiting applications.

physics.optics↗

arXiv2017

Single item stochastic lot sizing problem considering capital flow and business overdraft

This paper introduces capital flow to the single item stochastic lot sizing problem. A retailer can leverage business overdraft to deal with unexpected capital shortage, but needs to pay interest if its available balance goes below zero. A stochastic dynamic programming model maximizing expected final capital increment is formulated to solve the problem to optimality. We then investigate the performance of four controlling policies: ($R, Q$), ($R, S$), ($s, S$) and ($s$, $\overline{Q}$, $S$); for these policies, we adopt simulation-genetic algorithm to obtain approximate values of the controlling parameters. Finally, a simulation-optimization heuristic is also employed to solve this problem. Computational comparisons among these approaches show that policy $(s, S)$ and policy $(s, \overline{Q}, S)$ provide performance close to that of optimal solutions obtained by stochastic dynamic programming, while simulation-optimization heuristic offers advantages in terms of computational efficiency. Our numerical tests also show that capital availability as well as business overdraft interest rate can substantially affect the retailer's optimal lot sizing decisions.

cs.CE↗

arXiv2017

Stochastic Constraint Programming as Reinforcement Learning

Stochastic Constraint Programming (SCP) is an extension of Constraint Programming (CP) used for modelling and solving problems involving constraints and uncertainty. SCP inherits excellent modelling abilities and filtering algorithms from CP, but so far it has not been applied to large problems. Reinforcement Learning (RL) extends Dynamic Programming to large stochastic problems, but is problem-specific and has no generic solvers. We propose a hybrid combining the scalability of RL with the modelling and constraint filtering methods of CP. We implement a prototype in a CP system and demonstrate its usefulness on SCP problems.

cs.AI↗

arXiv2017

Computing non-stationary $(s, S)$ policies using mixed integer linear programming

This paper addresses the single-item single-stocking location stochastic lot sizing problem under the $(s, S) $ policy. We first present a mixed integer non-linear programming (MINLP) formulation for determining near-optimal $(s, S)$ policy parameters. To tackle larger instances, we then combine the previously introduced MINLP model and a binary search approach. These models can be reformulated as mixed integer linear programming (MILP) models which can be easily implemented and solved by using off-the-shelf optimisation software. Computational experiments demonstrate that optimality gaps of these models are around $0.3\%$ of the optimal policy cost and computational times are reasonable.

math.OC↗

arXiv2016

The BIN_COUNTS Constraint: Filtering and Applications

We introduce the BIN_COUNTS constraint, which deals with the problem of counting the number of decision variables in a set which are assigned values that lie in given bins. We illustrate a decomposition and a filtering algorithm that achieves generalised arc consistency. We contrast the filtering power of these two approaches and we discuss a number of applications. We show that BIN_COUNTS can be employed to develop a decomposition for the $χ^2$ test constraint, a new statistical constraint that we introduce in this work. We also show how this new constraint can be employed in the context of the Balanced Academic Curriculum Problem and of the Balanced Nursing Workload Problem. For both these problems we carry out numerical studies involving our reformulations. Finally, we present a further application of the $χ^2$ test constraint in the context of confidence interval analysis.

cs.AI↗

arXiv2016

A comparison of non-stationary stochastic lot-sizing strategies

We consider the non-stationary stochastic lot sizing problem with backorder costs and make a cost comparison among different lot-sizing strategies. We initially provide an overview of the strategies and some corresponding solution approaches in the literature. We then compare the cost performances of the lot-sizing strategies on a common test bed while taking into account the added value of realized demand information. The results of this numerical experience enable us to derive novel insights about the cost performance of different stochastic lot-sizing strategies under re-planning with respect to demand realization.

math.OC↗

arXiv2015

Confidence-based Reasoning in Stochastic Constraint Programming

In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the original problem being analysed; by solving this reduced problem, with a given confidence probability, we obtain assignments that satisfy the chance constraints in the original model within prescribed error tolerance thresholds. To achieve this, we blend concepts from stochastic constraint programming and statistics. We discuss both exact and approximate variants of our method. The framework we introduce can be immediately employed in concert with existing approaches for solving stochastic constraint programs. A thorough computational study on a number of stochastic combinatorial optimisation problems demonstrates the effectiveness of our approach.

math.OC↗

arXiv2014

Intermittency and Obsolescence: a Croston Method With Linear Decay

Only two Croston-style forecasting methods are currently known for handling stochastic intermittent demand with possible demand obsolescence: TSB and HES, both shown to be unbiased. When an item becomes obsolescent then TSB's forecasts decay exponentially, while HES's decay hyperbolically. We describe a third variant called Linear-Exponential Smoothing that is also unbiased, decays linearly to zero in a finite time, is asymptotically the best variant for handling obsolescence, and performs well in experiments.

stat.AP↗

arXiv2014

Statistical Constraints

We introduce statistical constraints, a declarative modelling tool that links statistics and constraint programming. We discuss two statistical constraints and some associated filtering algorithms. Finally, we illustrate applications to standard problems encountered in statistics and to a novel inspection scheduling problem in which the aim is to find inspection plans with desirable statistical properties.

cs.AI↗

arXiv2014

A unified modeling approach for the static-dynamic uncertainty strategy in stochastic lot-sizing

In this paper, we develop mixed integer linear programming models to compute near-optimal policy parameters for the non-stationary stochastic lot sizing problem under Bookbinder and Tan's static-dynamic uncertainty strategy. Our models build on piecewise linear upper and lower bounds of the first order loss function. We discuss different formulations of the stochastic lot sizing problem, in which the quality of service is captured by means of backorder penalty costs, non-stockout probability, or fill rate constraints. These models can be easily adapted to operate in settings in which unmet demand is backordered or lost. The proposed approach has a number of advantages with respect to existing methods in the literature: it enables seamless modelling of different variants of the above problem, which have been previously tackled via ad-hoc solution methods; and it produces an accurate estimation of the expected total cost, expressed in terms of upper and lower bounds. Our computational study demonstrates the effectiveness and flexibility of our models.

math.OC↗

arXiv2013

Confidence-based Optimization for the Newsvendor Problem

We introduce a novel strategy to address the issue of demand estimation in single-item single-period stochastic inventory optimisation problems. Our strategy analytically combines confidence interval analysis and inventory optimisation. We assume that the decision maker is given a set of past demand samples and we employ confidence interval analysis in order to identify a range of candidate order quantities that, with prescribed confidence probability, includes the real optimal order quantity for the underlying stochastic demand process with unknown stationary parameter(s). In addition, for each candidate order quantity that is identified, our approach can produce an upper and a lower bound for the associated cost. We apply our novel approach to three demand distribution in the exponential family: binomial, Poisson, and exponential. For two of these distributions we also discuss the extension to the case of unobserved lost sales. Numerical examples are presented in which we show how our approach complements existing frequentist - e.g. based on maximum likelihood estimators - or Bayesian strategies.

math.OC↗

arXiv2013

Piecewise linear approximations of the standard normal first order loss function

The first order loss function and its complementary function are extensively used in practical settings. When the random variable of interest is normally distributed, the first order loss function can be easily expressed in terms of the standard normal cumulative distribution and probability density function. However, the standard normal cumulative distribution does not admit a closed form solution and cannot be easily linearised. Several works in the literature discuss approximations for either the standard normal cumulative distribution or the first order loss function and their inverse. However, a comprehensive study on piecewise linear upper and lower bounds for the first order loss function is still missing. In this work, we initially summarise a number of distribution independent results for the first order loss function and its complementary function. We then extend this discussion by focusing first on random variable featuring a symmetric distribution, and then on normally distributed random variables. For the latter, we develop effective piecewise linear upper and lower bounds that can be immediately embedded in MILP models. These linearisations rely on constant parameters that are independent of the mean and standard deviation of the normal distribution of interest. We finally discuss how to compute optimal linearisation parameters that minimise the maximum approximation error.

math.OC↗