Kai Helge Becker

An outlook on behavioural OR – Three tasks, three pitfalls, one definition

In their recent paper, Hamalainen, Luoma, and Saarinen (2013) have made a strong case for the importance of Behavioural OR. With the motivation to contribute to a broad academic outlook in this emerging discipline, this rather programmatic paper intends to further the discussion by describing three types of research tasks that should play an important role in Behavioural OR, namely a descriptive, a methodological and a technological task. Moreover, by relating Behavioural OR to similar academic endeavours, three potential pitfalls are presented that Behavioural OR should avoid: (1) a too narrow understanding of what “behavioural” means, (2) ignorance of interdisciplinary links, and (3) a development without close connection with the core disciplines of OR. The paper concludes by suggesting a definition of Behavioural OR that sums up all points addressed.

A heuristic for the Minimum Score Separation Problem, a combinatorial problem associated with the cutting stock problem

The Minimum Score Separation Problem (MSSP) is a combinatorial problem that was introduced in JORS 55 as an open problem in the paper industry arising in conjunction with the cutting stock problem. During the process of producing boxes, flat papers are prepared for folding by being scored with knives. The problem is to determine whether and how a given production pattern of boxes can be arranged such that a certain minimum distance between the knives can be kept. Introducing the concept of matching-based alternating Hamiltonian paths, this paper models the MSSP as the problem of finding an alternating Hamiltonian path on a graph that is the union of a matching and a type of graph known as a ‘threshold graph’. On this basis, we find a heuristic that can quickly recognize a large percentage of feasible and infeasible instances of the MSSP. Detailed computational experiments demonstrate the efficiency of our approach.

Selecting simultaneous actions of different durations to optimally manage an ecological network

1.Species management requires decision-making under uncertainty. Given a management objective and limited budget, managers need to decide what to do, and where and when to do it. A schedule of management actions that achieves the best performance is an optimal policy. A popular optimisation technique used to find optimal policies in ecology and conservation is stochastic dynamic programming (SDP). Most SDP approaches can only accommodate actions of equal durations. However, in many situations, actions take time to implement or cannot change rapidly. Calculating the optimal policy of such problems is computationally demanding and becomes intractable for large problems. Here, we address the problem of implementing several actions of different durations simultaneously. 2.We demonstrate analytically that synchronising actions and their durations provide upper and lower bounds of the optimal performance. These bounds provide a simple way to evaluate the performance of any policy, including rules of thumb. We apply this approach to the management of a dynamic ecological network of Aedes albopictus, an invasive mosquito that vectors human diseases. The objective is to prevent mosquitoes from colonising mainland Australia from the nearby Torres Straits Islands where managers must decide between management actions that differ in duration and effectiveness. 3.We were unable to compute an optimal policy for more than eight islands out of 17, but obtained upper and lower bounds for up to 13 islands. These bounds are within 16% of an optimal policy. We used the bounds to recommend managing highly populated islands as a priority. 4.Our approach calculates upper and lower bounds for the optimal policy by solving simpler problems that are guaranteed to perform better and worse than the optimal policy, respectively. By providing bounds on the optimal solution, the performance of policies can be evaluated even if the optimal policy cannot be calculated. Our general approach can be replicated for problems where simultaneous actions of different durations need to be implemented.

Two Approximate Dynamic Programming Algorithms for Managing Complete SIS Networks

Inspired by the problem of best managing the invasive mosquito Aedes albopictus across the 17 Torres Straits islands of Australia, we aim at solving a Markov decision process on large Susceptible-Infected-Susceptible (SIS) networks that are highly connected. While dynamic programming approaches can solve sequential decision-making problems on sparsely connected networks, these approaches are intractable for highly connected networks. Inspired by our case study, we focus on problems where the probability of nodes changing state is low and propose two approximate dynamic programming approaches. The first approach is a modified version of value iteration where only those future states that are similar to the current state are accounted for. The second approach models the state space as continuous instead of binary, with an on-line algorithm that takes advantage of Bellmans adapted equation. We evaluate the resulting policies through simulations and provide a priority order to manage the 17 infested Torres Strait islands. Both algorithms show promise, with the continuous state approach being able to scale up to high dimensionality (50 nodes). This work provides a successful example of how AI algorithms can be designed to tackle challenging computational sustainability problems.