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 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.