Institute for Systems Research
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Item Modeling Separations of Plant Layout Problems(2014-08) Herrmann, JeffreyThis paper describes the results of a simulation study that evaluated the performance of different separations of the plant layout problem solved by bounded rational decision-makers. Seven problem instances from the literature were studied. We simulated the solution of a problem by a bounded rational decision-maker as a random search over the solution space. The problem was separated by identifying “subsets” of adjacent locations. The subset assignment problem partitioned the departments into subsets corresponding to these subsets of locations. Then, the subset layout problem assigned the locations in the subset to the departments. We considered separations with 2, 3, and 4 subsets. We also considered separations that first aggregated the departments before assigning them to subsets of locations. The results showed that separating the problem can lead to better solutions than solving the problem all-at-once, but some separations lead to worse solutions. Maximizing the flow inside the subsets generated better solutions than maximizing the adjacency of the departments inside the subsets. When fewer subsets are used, minimizing the cost inside each subset generated better solutions than minimizing the total cost. These results show that the quality of the solutions created by a design process is influenced by the choice of subproblems that make up the design process.Item Predicting the Performance of Teams of Bounded Rational Decision-makers Using a Markov Chain Model(2013-08) Herrmann, JeffreyIn practice, when faced with a complex optimization problem, teams of human decision-makers often separate it into subproblems and then solve each subproblem instead of tackling the complete problem. It would be useful to know the conditions in which separating the problem is the superior approach and how the subproblems should be assigned to members of the teams. This paper describes a mathematical model of a search that represents a bounded rational decision-maker (“agent”) solving a generic optimization problem. The agent’s search can be modeled as a discrete-time Markov chain, which allows one to calculate the probability distribution of the value of the solution that the agent will find. We compared the distributions generated by the model to the distribution of results from searches of solutions to traveling salesman problems. Using this model, we evaluated the performance of two- and three-agent teams who used different solution approaches to solve generic optimization problems. In the “all-at-once” approach, the agents collaborate to search the entire set of solutions in a sequential manner: the next agent begins where the previous agent stopped. In the “separation” approach, the agents separate the problem into two subproblems: (1) find the best set of solutions, and (2) find the best solution in that set. The results show that teams found better solutions using separation when high-value solutions are less likely. Using the all-at-once approach yielded better results when the values were uniformly distributed. The optimal assignment of subproblems to teams also depended upon the distribution of values in the solution space.Item Separating the Searches of Bounded Rational Decision-Makers(2013-06) Herrmann, JeffreyIn practice, when faced with a complex optimization problem, human decision-makers often separate it into subproblems and then solve each subproblem instead of tackling the complete problem. This paper describes a study that simulated small teams of bounded rational decision-makers (“agents”) who try different approaches to solve optimization problems. In the “all-at-once” approaches, the agents collaborate to search the entire set of solutions in a sequential manner: each agent begins where the previous agent stopped. In other approaches, the agents separate the problem into subproblems, and each agent solves a different subproblem. Finally, in the hybrid approaches, the agents separate the problem but two agents will collaborate to solve one subproblem while another agent solves a different subproblem. In some cases, the subproblems are solved in parallel; in others, the subproblems are solved sequentially. The results show that the teams generally found better solutions when they separated the problem.