Design of Scheduling Algorithms Using Game Theoretic Ideas

Scheduling a set of jobs over a collection of machines to optimize a certain quality-of-service measure is one of the most important research topics in both computer science theory and practice. In this thesis, we design algorithms that optimize {\em flow-time} (or delay) of jobs for scheduling problems that arise in a wide range of applications. We consider the classical model of unrelated machine scheduling and resolve several long standing open problems; we introduce new models that capture the novel algorithmic challenges in scheduling jobs in data centers or large clusters; we study the effect of selfish behavior in distributed and decentralized environments; we design algorithms that strive to balance the energy consumption and performance.

The technically interesting aspect of our work is the surprising connections we establish between approximation and online algorithms, economics, game theory, and queuing theory. It is the interplay of ideas from these different areas that lies at the heart of most of the algorithms presented in this thesis.

The main contributions of the thesis can be placed in one of the following categories.

1. Classical Unrelated Machine Scheduling: We give the first polygorithmic approximation algorithms for minimizing the average flow-time and minimizing the maximum flow-time in the offline setting. In the online and non-clairvoyant setting, we design the first non-clairvoyant algorithm for minimizing the weighted flow-time in the resource augmentation model. Our work introduces iterated rounding technique for the offline flow-time optimization, and gives the first framework to analyze non-clairvoyant algorithms for unrelated machines.

2. Polytope Scheduling Problem: To capture the multidimensional nature of the scheduling problems that arise in practice, we introduce Polytope Scheduling Problem (\psp). The \psp problem generalizes almost all classical scheduling models, and also captures hitherto unstudied scheduling problems such as routing multi-commodity flows, routing multicast (video-on-demand) trees, and multi-dimensional resource allocation. We design several competitive algorithms for the \psp problem and its variants for the objectives of minimizing the flow-time and completion time. Our work establishes many interesting connections between scheduling and market equilibrium concepts, fairness and non-clairvoyant scheduling, and queuing theoretic notion of stability and resource augmentation analysis.

3. Energy Efficient Scheduling: We give the first non-clairvoyant algorithm for minimizing the total flow-time + energy in the online and resource augmentation model for the most general setting of unrelated machines.

4. Selfish Scheduling: We study the effect of selfish behavior in scheduling and routing problems. We define a fairness index for scheduling policies called {\em bounded stretch}, and show that for the objective of minimizing the average (weighted) completion time, policies with small stretch lead to equilibrium outcomes with small price of anarchy. Our work gives the first linear/ convex programming duality based framework to bound the price of anarchy for general equilibrium concepts such as coarse correlated equilibrium.

Public-Private Partnership Design for Inclusive Cocoa Global Value Chains in Ghana

Within 10 years, there could be a severe global shortage in the supply of cocoa, according to industry practitioners and other experts. Due to global population growth and the emergence of a growing global middle class, by 2025 the cocoa crop would need to increase by nearly 50 per cent to keep up with projected demand. A potential shortage of supply is a direct threat to the business model of lead firms – including cocoa grinders and processors, chocolate confectioners, and retail distributors. But these international firms – the ones that will suffer the most if there is a shortage of cocoa supply – are helping create the market failure that is stifling sustainability. Functioning as a two-tiered consolidated oligopoly with a combined market share of approximately 89%, these firms enjoy the largest portion of value capture in the cocoa-chocolate global value chain (GVC). The smallholder cocoa producers, conversely, are trapped in low value-add segments of the GVC. In fact, most smallholder farmers survive on less than $1.00 per day per capita, on average in many cocoa exporting countries. In Ghana - the second largest producer of cocoa in the world - the government has accomplished little to help these smallholders upgrade and make cocoa an attractive sector for the next generation to inherit. The result – both in Ghana and around the world – is a lack of sustainability of the supply of cocoa. Demand is already beginning to outstrip supply. As a result of these underlying circumstances, the United States Agency for International Development (USAID) has posed the following policy question: "Under what conditions could USAID, as a development agency, support and enhance potential public-private partnerships in order to improve the bargaining power (and financial wherewithal) of smallholder organizations and farmers in the context of the global value chain for cocoa in Ghana?"