Aiming at the large group decision-making problem in which every decision maker compares pairwise alternatives with fuzzy preference relations, this paper proposes a fuzzy preference relation decision-making method of large group based on conflicts. Firstly, priority should be given to the preference difference under complex large group environment, so we define the conflict degree of two fuzzy preference relations, which contributes to cluster analysis on preferences of the decision maker and thus forms several different clusters. Based on this, we simulate and analyze the threshold of conflict degree. Then we develop the entropy weight method to get the relevant weight of each cluster, and use the weight to aggregate the cluster preferences in order to attain the large group preference based on fuzzy preference relation. Next, an iteration algorithm is introduced to find a solution which could acquire the group alternatives fuzzy preference relation of a certain conflict level and obtain the ranking result of alternatives. Finally, a case analysis is given to illustrate the effectiveness of the method proposed.
We consider the classical appointment scheduling problem that does not have a session length constraint. The decision is to determine job allowances to minimize total expected weighted costs of waiting times of jobs and idle times of the service provider. In particular, we study a simple yet effective scheduling policy—the so‐called “constant" policy, which allocates a constant job allowance for each appointment. Prior studies on appointment scheduling suggest a “dome”‐shaped structure for the optimal job allowance over the planning horizon. This implies that job allowance does not vary significantly in the middle of the schedule sequence, but varies at the beginning as well as the end of the optimal schedule. We show that an even simple scheduling policy—the constant policy, is asymptotically optimal thus provide theoretical justification for such a widely used policy. Using a dynamic programming formulation, we express each job's waiting time as the maximum of a random walk, which allows us to bound the performance gap between the constant policy and the optimal schedule based on classical results on D/G/1 queues. We derive an explicit upper bound for the performance gap when either of the following conditions holds: (i) the server idling cost is relatively small compared to the job waiting cost, and (ii) the number of appointments is sufficiently large. We also extend this result to a more general setting with multiple service types. Numerical experiments show that the constant policy is near optimal even when the number of appointments is small or when the server idling cost is moderately large, which complements our theoretical results. Our result provides a justification and strong support for the constant policy under certain mild conditions. Moreover, with minor modifications, the constant policy can be adapted to more general scenarios with patient no‐shows, or with heterogeneous appointment types.
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