Wolfram Wiesemann

The Robust Capacitated Vehicle Routing Problem Under Demand Uncertainty

The robust capacitated vehicle routing problem (CVRP) under demand uncertainty is studied to address the minimum cost delivery of a product to geographically dispersed customers using capacity-constrained vehicles. Contrary to the deterministic CVRP, which postulates that the customer demands for the product are deterministic and known, the robust CVRP models the customer demands as random variables, and it determines a minimum cost delivery plan that is feasible for all anticipated demand realizations. Robust optimization counterparts of several deterministic CVRP formulations are derived and compared numerically. Robust rounded capacity inequalities are developed, and it is shown how they can be separated efficiently for two broad classes of demand supports. Finally, it is analyzed how the robust CVRP relates to the chance-constrained CVRP, which allows a controlled degree of supply shortfall to decrease delivery costs.

A Stochastic Programming Approach for QoS-Aware Service Composition

We formulate the service composition problem as a multi-objective stochastic program which simultaneously optimizes the following quality of service (QoS) parameters: workflow duration, service invocation costs, availability, and reliability. All of these quality measures are modelled as decision-dependent random variables. Our model minimizes the average value-at- risk (AVaR) of the workflow duration and costs while imposing constraints on the workflow availability and reliability. AVaR is a popular risk measure in decision theory which quantifies the expected shortfall below some percentile of a loss distribution. By replacing the random durations and costs with their expected values, our risk-aware model reduces to the nominal problem formulation prevalent in literature. We argue that this nominal model can lead to overly risky decisions. Finally, we report on the scalability properties of our model.

Maximizing the net present value of a project under uncertainty

We address the maximization of a projects expected net present value when the activity durations and cash flows are described by a discrete set of alternative scenarios with associated occurrence probabilities. In this setting, the choice of scenario-independent activity start times frequently leads to infeasible schedules or severe losses in revenues. We suggest to determine an optimal target processing time policy for the project activities instead. Such a policy prescribes an activity to be started as early as possible in the realized scenario, but never before its (scenario-independent) target processing time. We formulate the resulting model as a global optimization problem and present a branch-and-bound algorithm for its solution. Extensive numerical results illustrate the suitability of the proposed policy class and the runtime behavior of the algorithm.

SQPR: Stream query planning with reuse

When users submit new queries to a distributed stream processing system (DSPS), a query planner must allocate physical resources, such as CPU cores, memory and network bandwidth, from a set of hosts to queries. Allocation decisions must provide the correct mix of resources required by queries, while achieving an efficient overall allocation to scale in the number of admitted queries. By exploiting overlap between queries and reusing partial results, a query planner can conserve resources but has to carry out more complex planning decisions. In this paper, we describe SQPR, a query planner that targets DSPSs in data centre environments with heterogeneous resources. SQPR models query admission, allocation and reuse as a single constrained optimisation problem and solves an approximate version to achieve scalability. It prevents individual resources from becoming bottlenecks by re-planning past allocation decisions and supports different allocation objectives. As our experimental evaluation in comparison with a state-of-the-art planner shows SQPR makes efficient resource allocation decisions, even with a high utilisation of resources, with acceptable overheads.

Pessimistic Bilevel Optimization

We study a variant of the pessimistic bilevel optimization problem, which comprises constraints that must be satisfied for any optimal solution of a subordinate (lower-level) optimization problem. We present conditions that guarantee the existence of optimal solutions in such a problem, and we characterize the computational complexity of various subclasses of the problem. We then focus on problem instances that may lack convexity, but that satisfy a certain independence property. We develop convergent approximations for these instances, and we derive an iterative solution scheme that is reminiscent of the discretization techniques used in semi-infinite programming. We also present a computational study that illustrates the numerical behavior of our algorithm on standard benchmark instances.

K-Adaptability in Two-Stage Robust Binary Programming

Over the last two decades, robust optimization has emerged as a computationally attractive approach to formulate and solve single-stage decision problems affected by uncertainty. More recently, robust optimization has been successfully applied to multistage problems with continuous recourse. This paper takes a step toward extending the robust optimization methodology to problems with integer recourse, which have largely resisted solution so far. To this end, we approximate two-stage robust binary programs by their corresponding K -adaptability problems, in which the decision maker precommits to K second-stage policies, here -and-now, and implements the best of these policies once the uncertain parameters are observed. We study the approximation quality and the computational complexity of the K -adaptability problem, and we propose two mixed-integer linear programming reformulations that can be solved with off-the-shelf software. We demonstrate the effectiveness of our reformulations for stylized instances of supply chain design, route planning, and capital budgeting problems.

Robust Resource Allocations in Temporal Networks

Temporal networks describe workflows of time-consuming tasks whose processing order is constrained by precedence relations. In many cases, the durations of the network tasks can be influenced by the assignment of resources. This leads to the problem of selecting an ‘optimal’ resource allocation, where optimality is measured by network characteristics such as the makespan (i.e., the time required to complete all tasks). In this paper we study a robust resource allocation problem where the task durations are uncertain, and the goal is to minimise the worst-case makespan. We show that this problem is generically

A comment on computational complexity of stochastic programming problems

{\mathcal{NP}}