Browsing by Author "Rossi, Roberto"

Now showing 1 - 14 of 14

Citation - WoS: 27
Citation - Scopus: 33
Computing the Non-Stationary Replenishment Cycle Inventory Policy Under Stochastic Supplier Lead-Times
(Elsevier, 2010) Rossi, Roberto; Tarim, S. Armagan; Hnich, Brahim; Prestwich, Steven
In this paper we address the general multi-period production/inventory problem with non-stationary stochastic demand and supplier lead-time under service level constraints. A replenishment cycle policy (RS) is modeled, where R is the nth replenishment cycle length and S is the respective order-up-to-level. We propose a stochastic constraint programming approach for computing the optimal policy parameters. In order to do so, a dedicated global chance-constraint and the respective filtering algorithm that enforce the required service level are presented. Our numerical examples show that a stochastic supplier lead-time significantly affects policy parameters with respect to the case in which the lead-time is assumed to be deterministic or absent. (C) 2010 Elsevier B.V. All rights reserved.
Citation - WoS: 30
Citation - Scopus: 36
Confidence-Based Optimisation for the Newsvendor Problem Under Binomial, Poisson and Exponential Demand
(Elsevier Science Bv, 2014) Rossi, Roberto; Prestwich, Steven; Tarim, S. Armagan; Hnich, Brahim
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 produces an upper and a lower bound for the associated cost. We apply this approach to three demand distributions 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. (C) 2014 Elsevier B.V. All rights reserved.
Citation - WoS: 10
Citation - Scopus: 11
Constraint Programming for Stochastic Inventory Systems Under Shortage Cost
(Springer, 2012) Rossi, Roberto; Tarim, S. Armagan; Hnich, Brahim; Prestwich, Steven
One of the most important policies adopted in inventory control is the replenishment cycle policy. Such a policy provides an effective means of damping planning instability and coping with demand uncertainty. In this paper we develop a constraint programming approach able to compute optimal replenishment cycle policy parameters under non-stationary stochastic demand, ordering, holding and shortage costs. We show how in our model it is possible to exploit the convexity of the cost-function during the search to dynamically compute bounds and perform cost-based filtering. Our computational experience show the effectiveness of our approach. Furthermore, we use the optimal solutions to analyze the quality of the solutions provided by an existing approximate mixed integer programming approach that exploits a piecewise linear approximation for the cost function.
Citation - WoS: 8
Citation - Scopus: 10
Cost-Based Filtering Techniques for Stochastic Inventory Control Under Service Level Constraints
(Springer, 2009) Tarim, S. Armagan; Hnich, Brahim; Rossi, Roberto; Prestwich, Steven
This paper(1) considers a single product and a single stocking location production/inventory control problem given a non-stationary stochastic demand. Under a widely-used control policy for this type of inventory system, the objective is to find the optimal number of replenishments, their timings and their respective order-up-to-levels that meet customer demands to a required service level. We extend a known CP approach for this problem using three cost-based filtering methods. Our approach can solve to optimality instances of realistic size much more efficiently than previous approaches, often with no search effort at all.
Citation - WoS: 12
Citation - Scopus: 13
Filtering Algorithms for Global Chance Constraints
(Elsevier Science Bv, 2012) Hnich, Brahim; Rossi, Roberto; Tarim, S. Armagan; Prestwich, Steven
Stochastic Constraint Satisfaction Problems (SCSPs) are a powerful modeling framework for problems under uncertainty. To solve them is a PSPACE task. The only complete solution approach to date - scenario-based stochastic constraint programming - compiles SCSPs clown into classical CSPs. This allows the reuse of classical constraint solvers to solve SCSPs, but at the cost of increased space requirements and weak constraint propagation. This paper tries to overcome these drawbacks by automatically synthesizing filtering algorithms for global chance constraints. These filtering algorithms are parameterized by propagators for the deterministic version of the chance constraints. This approach allows the reuse of existing propagators in current constraint solvers and it has the potential to enhance constraint propagation. Our results show that, for the test bed considered in this work, our approach is superior to scenario-based stochastic constraint programming. For these instances, our approach is more scalable, it produces more compact formulations, it is more efficient in terms of run time and more effective in terms of pruning for both stochastic constraint satisfaction and optimization problems. (C) 2012 Elsevier B.V. All rights reserved.
Citation - WoS: 6
Citation - Scopus: 6
Finding Reliable Solutions: Event-Driven Probabilistic Constraint Programming
(Springer, 2009) Tarim, S. Armagan; Hnich, Brahim; Prestwich, Steven; Rossi, Roberto
Real-life management decisions are usually made in uncertain environments, and decision support systems that ignore this uncertainty are unlikely to provide realistic guidance. We show that previous approaches fail to provide appropriate support for reasoning about reliability under uncertainty. We propose a new framework that addresses this issue by allowing logical dependencies between constraints. Reliability is then defined in terms of key constraints called events, which are related to other constraints via these dependencies. We illustrate our approach on three problems, contrast it with existing frameworks, and discuss future developments.
Citation - WoS: 25
Citation - Scopus: 32
A Global Chance-Constraint for Stochastic Inventory Systems Under Service Level Constraints
(Springer, 2008) Rossi, Roberto; Tarim, S. Armagan; Hnich, Brahim; Prestwich, Steven
We consider a class of production/inventory control problems that has a single product and a single stocking location, for which a stochastic demand with a known non-stationary probability distribution is given. Under the widely-known replenishment cycle policy the problem of computing policy parameters under service level constraints has been modeled using various techniques. Tarim and Kingsman introduced a modeling strategy that constitutes the state-of-the-art approach for solving this problem. In this paper we identify two sources of approximation in Tarim and Kingsman's model and we propose an exact stochastic constraint programming approach. We build our approach on a novel concept, global chance-constraints, which we introduce in this paper. Solutions provided by our exact approach are employed to analyze the accuracy of the model developed by Tarim and Kingsman.
Citation - WoS: 43
Citation - Scopus: 50
Mean-Based Error Measures for Intermittent Demand Forecasting
(Taylor & Francis Ltd, 2014) Prestwich, Steven; Rossi, Roberto; Tarim, S. Armagan; Hnich B.
To compare different forecasting methods on demand series, we require an error measure. Many error measures have been proposed, but when demand is intermittent some become inapplicable because of infinities, some give counter-intuitive results, and there is no agreement on which is best. We argue that almost all known measures rank forecasters incorrectly on intermittent demand series. We propose several new error measures with almost no infinities, and with correct forecaster ranking on several intermittent demand patterns. We call these mean-based' error measures because they evaluate forecasts against the (possibly time-dependent) mean of the underlying stochastic process instead of point demands.
Citation - WoS: 3
Citation - Scopus: 4
A Note on Liu-iwamura's Dependent-Chance Programming
(Elsevier Science Bv, 2009) Rossi, Roberto; Tarim, S. Armagan; Hnich, Brahim; Prestwich, Steven; Guran, Cahit
Sometimes a complex stochastic decision system undertakes multiple tasks called events, and the decision-maker wishes to maximize the chance functions which are defined as the probabilities of satisfying these events. Originally introduced by Liu and Iwamura [B. Liu, K. Iwarnura, Modelling stochastic decision systems using dependent-chance programming, European journal of Operational Research 101 (1997) 193-203], dependent-chance programming is aimed at maximizing some chance functions of events in an uncertain environment. In this work. we show that the original dependent chance-programming framework needs to be extended in order to capture an exact reliability measure for a given plan. (C) 2008 Elsevier B.V. All rights reserved.
Citation - WoS: 4
Citation - Scopus: 6
Partial Symmetry Breaking by Local Search in the Group
(Springer, 2012) Prestwich, Steve D.; Hnich, Brahim; Simonis, Helmut; Rossi, Roberto; Tarim, S. Armagan
The presence of symmetry in constraint satisfaction problems can cause a great deal of wasted search effort, and several methods for breaking symmetries have been reported. In this paper we describe a new method called Symmetry Breaking by Nonstationary Optimisation, which interleaves local search in the symmetry group with backtrack search on the constraint problem. It can be tuned to break each symmetry with an arbitrarily high probability with high runtime overhead, or as a lightweight but still powerful method with low runtime overhead. It has negligible memory requirement, it combines well with static lex-leader constraints, and its benefit increases with problem hardness.
Citation - WoS: 24
Citation - Scopus: 27
Piecewise Linear Lower and Upper Bounds for the Standard Normal First Order Loss Function
(Elsevier Science Inc, 2014) Rossi, Roberto; Tarim, S. Armagan; Prestwich, Steven; Hnich, Brahim
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 variables 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. (C) 2014 Elsevier Inc. All rights reserved.
Citation - WoS: 3
Citation - Scopus: 4
Scheduling Internal Audit Activities: a Stochastic Combinatorial Optimization Problem
(Springer, 2010) Rossi, Roberto; Tarim, S. Armagan; Hnich, Brahim; Prestwich, Steven; Karacaer, Semra
The problem of finding the optimal timing of audit activities within an organisation has been addressed by many researchers. We propose a stochastic programming formulation with Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) certainty-equivalent models. In experiments neither approach dominates the other. However, the CP approach is orders of magnitude faster for large audit times, and almost as fast as the MILP approach for small audit times. This work generalises a previous approach by relaxing the assumption of instantaneous audits, and by prohibiting concurrent auditing.
Citation - WoS: 12
Citation - Scopus: 13
A State Space Augmentation Algorithm for the Replenishment Cycle Inventory Policy
(Elsevier, 2011) Rossi, Roberto; Tarim, S. Armagan; Hnich, Brahim; Prestwich, Steven
In this work we propose an efficient dynamic programming approach for computing replenishment cycle policy parameters under non-stationary stochastic demand and service level constraints. The replenishment cycle policy is a popular inventory control policy typically employed for dampening planning instability. The approach proposed in this work achieves a significant computational efficiency and it can solve any relevant size instance in trivial time. Our method exploits the well known concept of state space relaxation. A filtering procedure and an augmenting procedure for the state space graph are proposed. Starting from a relaxed state space graph our method tries to remove provably suboptimal arcs and states (filtering) and then it tries to efficiently build up (augmenting) a reduced state space graph representing the original problem. Our experimental results show that the filtering procedure and the augmenting procedure often generate a small filtered state space graph, which can be easily processed using dynamic programming in order to produce a solution for the original problem. (C) 2010 Elsevier B.V. All rights reserved.
Citation - WoS: 11
Citation - Scopus: 12
A Survey on Cp-Ai Hybrids for Decision Making Under Uncertainty
(Springer, 2011) Hnich, Brahim; Rossi, Roberto; Tarim, S. Armagan; Prestwich, Steven
In this survey, we focus on problems of decision making under uncertainty. First, we clarify the meaning of the word uncertainty and we describe the general structure of problems that fall into this class. Second, we provide a list of problems from the Constraint Programming, Artificial Intelligence, and Operations Research literatures in which uncertainty plays a role. Third, we survey existing modeling frameworks that provide facilities for handling uncertainty. A number of general purpose and specialized hybrid solution methods are surveyed, which deal with the problems in the list provided. These approaches are categorized into three main classes: stochastic reasoning-based, reformulation-based, and sample-based. Finally, we provide a classification for other related approaches and frameworks in the literature.