Robotic Mobile Fulfillment Systems (RMFSs) are a recent type of automated warehouse deployed in e-commerce. In this parts-to-picker system, a fleet of small robots is tasked with retrieving and storing shelves of item...
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Robotic Mobile Fulfillment Systems (RMFSs) are a recent type of automated warehouse deployed in e-commerce. In this parts-to-picker system, a fleet of small robots is tasked with retrieving and storing shelves of items in the warehouse. Due to the nature of the e-commerce market, and the high flexibility of RMFSs, there are many opportunities to improve the productivity of the warehouse by optimising operational decisions. Online retailers promise extremely fast deliveries, which requires that new orders be included in the set of requests to fulfil as soon as they are revealed. For this reason, and because of the very dynamic nature of the robots' cycles, decision-making needs to be done in real time, in an uncertain environment. Because such a problem often lacks a formal description, we propose a mathematical framework that models the operational decisions taking place in an RMFS as a stochasticdynamic program. Our objective is to formalise optimisation opportunities, to allow researchers to develop more advanced methods in a well-defined environment. Embedded in a discrete event simulator, this model is illustrated by simulations to compare against standard storage decision rules.
The coordination of reservoir operation is critical for water systems' efficiency. Improved coordination requires sharing information, demanding a clear understanding of the potential gains and its distribution am...
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The coordination of reservoir operation is critical for water systems' efficiency. Improved coordination requires sharing information, demanding a clear understanding of the potential gains and its distribution among the users to motivate engagement in coordinated operations and bearing of transaction costs. In a multiuser, multireservoir system, the evaluation of the potential coordination gains is not trivial because it requires the simultaneous evaluation of numerous trade offs. This paper presents a methodology to identify the likely upper and lower bounds in multireservoir system benefits, providing a reference framework for analyzing the economic value of coordination. The methodology is applied to a large-scale multireservoir system in Brazil. The methods rely on the comparison between two management scenarios. The first one mimics typical system operation based on individually designed rule curves, which are likely to perform on the lower bound. This is compared with fullscale system-wide optimization through an stochastic Dual dynamicprogramming algorithm to represent fully coordinated reservoir operation (upper bound). For our case study, results indicate that better coordination reduced spills and improved releases timing according to reservoirs characteristics and location, allowing overall gains between 3% and 8% in energy and 7.9% in revenues, with revenues mostly improved by coordination in dry years. Larger reservoirs presented the highest gains in absolute terms, while the smaller ones presented the highest relative increases. By indicating individual gains at each reservoir, valuable information is produced to support future negotiations and benefit sharing among different agents, being water agencies or power companies.
The growth and spread of established Invasive Alien Species (IAS) cause significant ecological and economic damages. Minimising the costs of controlling, and the damages from, IAS depends on the spatial dynamics and u...
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The growth and spread of established Invasive Alien Species (IAS) cause significant ecological and economic damages. Minimising the costs of controlling, and the damages from, IAS depends on the spatial dynamics and uncertainty regarding IAS spread. This study expands on existing modelling approaches by allowing for varying stock sizes within patches and stochastic spread between patches. The objective of this study is to demonstrate the added value from this more detailed modelling approach. This is achieved in the context of coastal and riparian systems, which can be accurately modelled one-dimensional landscape, i.e., a series of patches connected in a line. The model allows for two types of intervention, namely (1) partial or complete removal of the population in within any patch;and (2) containment to reduce spread between patches. We analyse the general properties of the model using a two-patch setup to determine how the optimal policy depends on both the location and size of the invasion in patches. We find that allowing for varying stock sizes within patches facilitates optimal timing of the application of containment. We also identify two novel optimal policies: the combination of containment and removal to stop spread between patches and the application of up to four distinct policies for a single patch depending on the size of the invasion in that patch. (C) 2015 Elsevier B.V. All rights reserved.
This paper considers the problem of production planning of unreliable batch processing manufacturing systems. The finished goods are produced in lots, and are then transported to a storage area in order to continuousl...
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This paper considers the problem of production planning of unreliable batch processing manufacturing systems. The finished goods are produced in lots, and are then transported to a storage area in order to continuously meet a constant demand rate. The main objective of this work is to jointly determine the optimal lot sizing and optimal production control policy that minimise the total expected cost of inventory/backlog and transportation, over an infinite time horizon. The decision variables are the lot sizing and the production rate. The problem is formulated with a stochastic dynamic programming model and the impulse control theory is applied to establish the Hamilton-Jacobi-Bellman (HJB) equations. Based on a numerical resolution of the HJB equations, it is shown that the optimal control policy is governed by a base stock policy for production rate control and economic lot size for batch processing. A thorough analysis and practical issues are addressed with a simulation-based approach. Thus, a combined discrete-continuous simulation model is developed to determine the optimal parameters of the proposed policy when the failure and repair times follow general distributions. The results are illustrated with numerical examples and confirmed through sensitivity analysis.
We show the existence of average cost optimal stationary policies for Markov control processes with Borel state space and unbounded costs per stage, under a set of assumptions recently introduced by L.I. Sennott (1989...
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We show the existence of average cost optimal stationary policies for Markov control processes with Borel state space and unbounded costs per stage, under a set of assumptions recently introduced by L.I. Sennott (1989) for control processes with countable state space and finite control sets.
In this paper, we consider a problem of sequential resource allocation. Such a problem arises in a simplified intelligence, surveillance and reconnaissance scenario where a micro air vehicle (MAV) is tasked with class...
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In this paper, we consider a problem of sequential resource allocation. Such a problem arises in a simplified intelligence, surveillance and reconnaissance scenario where a micro air vehicle (MAV) is tasked with classification in an environment with false, that is, clutter, targets. The MAV visits the objects of interest in a specified sequence. A human operator is tasked with aiding the MAV's automatic target recognition system with the classification of objects, based on the images sent to him from the MAVs. If the images do not resolve the ambiguity concerning the status of the object being classified, the operator may request that the object be revisited. In this paper, for the sake of exposition of the employed methods and clarity of presentation, we assume that every object may be revisited at most once. Each object can be revisited and re-examined in L >= I ways. There is an information gain whose value is given by the running reward. The information gain depends on the way an object is re-examined, and the feedback from the operator but it is the same for all the objects. There is a random operator delay in communicating his findings to the MAV and the probability density function of the delay is assumed known. The MAV has a limited fuel reserve and upon getting feedback from the operator (and hence, knowing the delay associated with the object of interest only and not with those that it must revisit in the future), it must decide whether to revisit the object and if so, which of the L ways is optimal so as to maximize the total expected reward. In every revisit, fuel is expended from the reserve and is proportional to twice the delay plus a fixed cost, which is dependent on the way in which the object is re-examined. We employ a stochastic dynamic programming approach to solve this problem. Specifically, for the case when L = 1, we show that there is an optimal threshold for each object and it is optimal to revisit the object if the delay is at most the thr
We consider the optimal service control of a multiclass M/G/1 queueing system in which customers are served nonpreemptively and the system cost rate is additive across classes and increasing convex in the numbers pres...
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We consider the optimal service control of a multiclass M/G/1 queueing system in which customers are served nonpreemptively and the system cost rate is additive across classes and increasing convex in the numbers present in each class. Following Whittle's approach to a class of restless bandit problems, we develop a Langrangian relaxation of the service control problem which serves to motivate the development of a class of index heuristics. The index for a particular customer class is characterised as a fair charge for service of that class. The paper develops these indices and reports an extensive numerical investigation which exhibits strong performance of the index heuristics for both discounted and average costs.
The authors study a quality control problem in a two-stage system. They assume that at each stage units are processed in batches, and the rates are random variables with known distributions. Final products are supplie...
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The authors study a quality control problem in a two-stage system. They assume that at each stage units are processed in batches, and the rates are random variables with known distributions. Final products are supplied to customers under warranties or service contracts, with penalty costs associated with defective units. The focus is on coordinating the inspection procedures at the two stages. Using a stochastic dynamic programming approach, the authors show that the optimal policy at stage 1 is characterized by a sequence of thresholds, and at stage 2, by a priority structure, as well as a threshold structure. The key to optimality is a so-called K-submodularity property, which is a strengthening of the usual notion of submodularity.
Currently, most Renewable Energy Certificate (REC) markets are defined based on targets that create an artificial step demand function resembling a cliff. This target policy produces volatile prices that can make inve...
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Currently, most Renewable Energy Certificate (REC) markets are defined based on targets that create an artificial step demand function resembling a cliff. This target policy produces volatile prices that can make investing in renewables a risky proposition. In this paper, we propose an alternative policy called Adjustable dynamic Assignment of Penalties and Targets (ADAPT) that uses a sloped compliance penalty and a self-regulating requirement schedule, both designed to stabilize REC prices, helping to alleviate a common weakness of environmental markets. To capture market behavior, we model the market as a stochastic dynamic programming problem to understand how the market might balance the decision to use a REC now versus holding it for future periods (in the face of uncertain new supply). Then, we present and prove some of the properties of this market, and finally we show that this mechanism reduces the volatility of REC prices, which should stabilize the market and encourage long-term investment in renewables.
We formulate and analyze an optimal stopping problem concerning a terrorist who is attempting to drive a nuclear or radiological weapon toward a target in a city center. In our model, the terrorist needs to travel thr...
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We formulate and analyze an optimal stopping problem concerning a terrorist who is attempting to drive a nuclear or radiological weapon toward a target in a city center. In our model, the terrorist needs to travel through a two-dimensional lattice containing imperfect radiation sensors at some of the nodes, and decides at each node whether to detonate the bomb or proceed. We consider five different scenarios containing various informational structures and two different sensor array topologies: the sensors are placed randomly or they form an outer wall around the periphery of the city. We find that sensors can act as a deterrent in some cases, and that the government prefers the outer wall topology unless the sensors have a very low detection probability and the budget is tight (so that they are sparsely deployed).
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