We consider controlling ticket resale by introducing a centralized exchange (CE) system and explore the resultant impacts on the benefits to the event organizer as well as social welfare. The CE system allows customers who cannot attend the event to transfer their tickets directly to other customers at face value. We formulate a profit maximization model for an event ticket market where scalpers exist and the event organizer implements a CE system. The model also incorporates customers’ purchase-postponement behavior, which means that customers who may not be able to attend the event in the primary market will consider purchasing through the CE system. As a result, the following findings are presented. First, we show that the introduction of a CE system will increase the total demand in terms of customers purchasing in the primary market and the CE system. This is because the introduction of the CE system provides customers with an environment in which they can transfer at face value, so even customers with uncertain schedules can purchase tickets in the primary market. Second, in the special case where customers do not postpone their purchases and the willingness to pay for the ticket follows a standard uniform distribution, the introduction of CE increases price in the primary market. Although this is a negative factor from the perspective of consumer surplus, higher prices increase organizer’s profits, resulting in an increase in social welfare (i.e. the sum of consumer surplus and organizer’s profits). Moreover, numerical experiments reveal that the introduction of a CE system will lower the resale price and improve social welfare.

Data Envelopment Analysis (DEA) is a linear programming (LP)-based technique used to evaluate the performance of homogeneous Decision-Making Units (DMUs) with multiple inputs and outputs. However, applying DEA to large-scale datasets with a high number of DMUs poses significant computational challenges. A practical solution to this problem is to solve the LPs of DEA with only decision variables associated with efficient DMUs. Building on this idea, we propose an arithmetic approach to identify a subset of efficient DMUs. Using this subset, we can effectively classify DMUs and rapidly identify the complete set of efficient units. To validate our approach, we conducted experiments on both real-world and simulated datasets, varying the cardinalities (number of DMUs), dimensions (number of inputs and outputs), and densities (proportion of efficient DMUs). The results demonstrate the effectiveness and robustness of our method, highlighting its potential for improving existing DEA methodologies.

This study considers an active set algorithm for solving large-scale bound constrained optimization problems. We propose an active set block Barzilai-Borwein method and demonstrate its global convergence property. This method aims to separate decision variables from blocks. In numerous applications, such as model predictive control (MPC), problem variables often have a block structure. This studyformulated the application of active set methods to MPC using the penalty method. In our numerical experiments, we evaluated the proposed method’s effectiveness and showed its practical applicability to problems characterized by a block-structured variable configuration.