Online Demand Scheduling with Failovers

Motivated by cloud computing applications, we study the problem of how to optimally deploy new hardware subject to both power and robustness constraints. To model the situation observed in large-scale data centers, we introduce the Online Demand Scheduling with Failover problem. There are m identical devices with capacity constraints. Demands come one-by-one and, to be robust against a device failure, need to be assigned to a pair of devices. When a device fails (in a failover scenario), each demand assigned to it is rerouted to its paired device (which may now run at increased capacity). The goal is to assign demands to the devices to maximize the total utilization subject to both the normal capacity constraints as well as these novel failover constraints. These latter constraints introduce new decision tradeoffs not present in classic assignment problems such as the Multiple Knapsack problem and AdWords. In the worst-case model, we design a deterministic ? 1/2-competitive algorithm, and show this is essentially tight. To circumvent this constant-factor loss, which represents substantial capital losses for big cloud providers, we consider the stochastic arrival model, where all demands come i.i.d. from an unknown distribution. In this model we design an algorithm that achieves sub-linear additive regret (i.e. as OPT or m increases, the multiplicative competitive ratio goes to 1). This requires a combination of different techniques, including a configuration LP with a non-trivial post-processing step and an online monotone matching procedure introduced by Rhee and Talagrand

Large Language Models for Supply Chain Optimization

Supply chain operations traditionally involve a variety of complex decision making problems. Over the last few decades, supply chains greatly benefited from advances in computation, which allowed the transition from manual processing to automation and cost-effective optimization. Nonetheless, business operators still need to spend substantial efforts in \emph{explaining} and interpreting the optimization outcomes to stakeholders. Motivated by the recent advances in Large Language Models (LLMs), we study how this disruptive technology can help bridge the gap between supply chain automation and human comprehension and trust thereof. We design \name{} -- a framework that accepts as input queries in plain text, and outputs insights about the underlying optimization outcomes. Our framework does not forgo the state-of-the-art combinatorial optimization technology, but rather leverages it to quantitatively answer what-if scenarios (e.g., how would the cost change if we used supplier B instead of supplier A for a given demand?). Importantly, our design does not require sending proprietary data over to LLMs, which can be a privacy concern in some circumstances. We demonstrate the effectiveness of our framework on a real server placement scenario within Microsoft's cloud supply chain. Along the way, we develop a general evaluation benchmark, which can be used to evaluate the accuracy of the LLM output in other scenarios

Resource scheduling and optimization in dynamic and complex transportation settings

This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2019Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 145-151).Resource optimization has always been a challenge both in traditional fields, such as logistics, and particularly so in most emerging systems in the sharing economy. These systems are by definition founded on the sharing of resources among users, which naturally creates many coordination needs as well as challenges to ensure enough resource supply to cover customer demand. This thesis addresses these challenges in the application of vehicle sharing systems, as well as in the context of multi-operation companies that provide a wide range of services to their users. More specifically, the first part of this thesis focuses on models and algorithms for the optimization of bike sharing systems. Shortage of bikes and docks is a common issue in bike sharing systems, and, to tackle this problem, operators use a fleet of vehicles to redistribute bikes across the network.We study multiple aspects of these operations, and develop models that can capture all user trips that are performed successfully in the system, as well as algorithms that generate complete redistribution plans for the operators to maximize the served demand, in running times that are fast enough to allow real-time information to be taken into account. Furthermore, we propose an approach for the estimation of the actual user demand which takes into account both the lost demand (users that left the system due to lack of bikes or docks) and shifted demand (users that had to walk to nearby stations to find available resources). More accurate demand representations can then be used to inform better decisions for the daily operations, as well as the long-term planning of the system. The second part of this thesis is focused on schedule generation for resources of large companies that must support a complex set of operations.Different operation types come with a variety of constraints and requirements that need to be taken into account. Moreover, specialized employees with a variety of skills and experience levels are required, along with an heterogeneous fleet of vehicles with various properties (e.g., refrigerator vehicles). We introduce the Complex Event Scheduling Problem (CESP), which captures known problems such as pickup-and-delivery and technician scheduling as special cases. We then develop a unified optimization framework for CESP, which relies on a combination of metaheuristics (ALNS) and Linear Programming. Our experiments show that our framework scales to large problem instances, and may help companies and organizations improve operation efficiency (e.g., reduce fleet size).by Konstantina Mellou.Ph. D.Ph.D. Massachusetts Institute of Technology, Sloan School of Management, Operations Research Cente

Efficient Algorithms For Finding The Largest Empty Cube In Spaces With Obstacles

94 σ.Η υπολογιστική γεωμετρία είναι ένας κλάδος της επιστήμης υπολογιστών, συγκεκριμένα του σχεδιασμού αλγορίθμων, που μελετάει προβλήματα γεωμετρικής φύσης. Αυτή η περιοχή έχει προσελκύσει το ενδιαφέρον στο πέρασμα των χρόνων λόγω των ποικίλων εφαρμογών της στη γραφική υπολογιστών, τη ρομποτική και άλλους τομείς. Η εφαρμογή που ενέπνευσε τη μελέτη αυτής της εργασίας αφορά την περιοχή της σχεδίασης ηλεκτρονικών κυκλωμάτων. Προκειμένου να επιτευχθεί μια ακριβής προσομοίωση ενός ολοκληρωμένου κυκλώματος, κάποιες παρασιτικές συνιστώσες του πρέπει να μοντελοποιηθούν. Ένα σημαντικό βήμα της διαδικασίας αυτής περιλαμβάνει τον υπολογισμό του μέγιστου άδειου κύβου με δεδομένο κέντρο που μπορεί να τοποθετηθεί ανάμεσα στους αγωγούς. Αυτός ο υπολογισμός πρέπει να επαναληφθεί πολλές φορές και, επομένως, ένας αποδοτικός αλγόριθμος είναι απαραίτητος. Αυτό το πρόβλημα είναι στενά συνδεδεμένο με θεμελιώδη προβλήματα της υπολογιστικής γεωμετρίας, όπως η αναζήτηση του μέγιστου άδειου ορθογωνίου ανάμεσα σε σημεία και το πρόβλημα του πλησιέστερου γείτονα, τα οποία βρίσκουν εφαρμογή σε πολλούς τομείς, όπως η αναγνώριση προτύπων, η εξόρυξη δεδομένων και η κατασκευή υλικών. Σε αυτήν την εργασία, περιγράφουμε αυτά και άλλα σχετικά προβλήματα και σκιαγραφούμε κάποιες από τις προτεινόμενες λύσεις τους. Στη συνέχεια, παρουσιάζεται το κυρίως μέρος της εργασίας. Αρχικά, επικεντρωνόμαστε στις γεωμετρίες Manhattan, όπου ο ζητούμενος κύβος και όλα τα εμπόδια είναι ευθυγραμμισμένα με τους άξονες. Η δομή δεδομένων που χρησιμοποιείται ονομάζεται octree. Ο αλγόριθμος στηρίζεται στην εισαγωγή των εμποδίων στους κατάλληλους κόμβους του δέντρου, έτσι ώστε κάθε αναζήτηση να εξετάζει μόνο τα γειτονικά εμπόδια του δοσμένου κέντρου. Όταν το πλησιέστερο εμπόδιο εντοπιστεί, υπολογίζεται ο μέγιστος άδειος κύβος που εφάπτεται σε αυτό. Έπειτα, ο αλγόριθμος γενικεύεται για non-Manhattan γεωμετρίες. Τα εμπόδια μπορεί να είναι πολυγωνικά ή περιστραμμένα ορθογώνια παραλληλεπίπεδα γύρω από τον άξονα z κατά γωνία φ, όπου φ ο προσανατολισμός της ακμής κάποιου εμποδίου. Τέλος, προτείνονται κάποιες τεχνικές βελτιστοποίησης και ακολουθεί μια πειραματική μελέτη για την αξιολόγηση της επίδοσης του αλγορίθμου. Συγκεκριμένα, υλοποιούμε τον αλγόριθμο σε C++ και χρησιμοποιούμε διάφορα σετ εισόδου για να αξιολογήσουμε τη χρονική επίδοση και τη χρήση της μνήμης κατά την κατασκευή του δέντρου και την πραγματοποίηση των αναζητήσεων.Computational geometry is a branch of computer science, in particular algorithms design, that studies problems of geometric nature. This area has gained enormous attention over the years due to its various applications in computer graphics, robotics, geographic information systems and other important fields. The application that motivated the study of this thesis lies in the field of electronic design automation. In order to achieve an accurate simulation of an integrated circuit, some parasitic components of the circuit need to be modeled. An important step of this procedure involves the calculation of the largest empty cube that can be placed among the conductors considering a given center. This calculation must be repeated numerous times and, therefore, an efficient algorithm is required. This problem is closely related to fundamental problems of computational geometry, such as the search of the largest empty rectangle among a set of points or the nearest neighbor problem, both of which apply in many areas, like pattern recognition, data mining and material manufacturing. In this thesis, we describe these and other related problems and outline some of their proposed solutions. After a general overview is provided to the reader, the main subject of this thesis is introduced. The first part focuses on Manhattan geometries, where all obstacles as well as the requested cube are axis aligned. The data structure that is used for their representation is called octree. The algorithm focuses on inserting the obstacles in the proper tree nodes, such that each search query examines only the obstacles that are located in the neighborhood of the query point. When the nearest obstacle to the query point is identified, the largest empty cube that abuts this obstacle is calculated. Afterwards, this algorithm is generalized for the case of non-Manhattan geometries. Now, the obstacles can be polygonal or rotated rectangular cuboids and the requested cube is no more axis aligned. It can be rotated by an angle φ around the z axis, where φ is the direction of one of the obstacles’ edges. Finally, some accelerating techniques are proposed and an experimental study is conducted in order to evaluate the performance of the algorithm. More specifically, the algorithm is implemented in C++ and various input sets are used to assess the time performance and the memory usage of the program during the creation of the octree and the execution of the queries.Κωνσταντίνα Κ. Μέλλο

Optimizing Onsite Food Services at Scale

© 2020 ACM. Large food-service companies typically support a wide range of operations (catering, vending machines, repairs), each with different operational characteristics (manpower, vehicles, tools, timing constraints, etc.). While the advances in Internet-based technologies facilitate the adoption of automated scheduling systems, the complexity and heterogeneity of the different operations hinders the design of comprehensive optimization solutions. Indeed, our collaboration with Compass Group, one of the largest food-service companies in the world, reveals that many of its workforce assignments are done manually due to the lack of scheduling solutions that can accommodate the complexity of operational constraints. Further, the diversity in the nature of operations prevents collaboration and sharing of resources among various services such as catering and beverage distribution, leading to an inflated fleet size. To address these challenges, we design a unified optimization framework, which can be applied to various food-service operations. Our design combines neighborhood search methods and Linear Programming techniques. We test our framework on real food-service request data from a large Compass Group customer, the Puget-Sound Microsoft Campus. Our results show that our approach scales well while yielding fleet size reductions of around 2x. Further, using our unified framework to simultaneously schedule the operations of two different divisions (catering, water distribution) yields 20% additional savings