The demand in the healthcare industry is increasing exponentially due to aging population of the world and this is leading to a rapid increase in the cost of healthcare. The emergency departments of the hospitals are the frontline of health care systems and play an additional critical role in providing an efficient and high-quality response for patients. The overcrowding at the emergency departments due to growing demand results in a situation where the demand for ED services exceeds the ability to provide care in a reasonable amount of time. This has led countries to reconsider their health policies in a way to increase their efficiency in their healthcare systems in general and in emergency departments, in particular. As in many countries, there has been a steady and significant increase in the number of patients that seek health services at the emergency departments of state hospitals of Turkey, due to the significant structural reforms in health services since 2003. While meeting this increasing demand, it is ever more important to provide these critical health services efficiently. Therefore, the efficiency of the emergency departments of seven general hospitals run by Istanbul's Beyoglu State Hospitals Association have been analyzed using categorical Data Envelopment Analysis (DEA) models. The analysis of DEA results is supported by a set of statistical methods to make it easier for the hospital administrators to interpret the analysis and draw conclusions. The analysis shows that less-equipped EDs are supported by better equipped, larger EDs, resulting in a hub-and-spoke type of structure among the EDs where "satellite" EDs serve an important referral function and thus evaluating their efficiency without taking the interoperability among these units into account would not be an accurate assessment of their performance.
The use of Automated Teller Machines (ATMs) has become increasingly popular throughout the world due to the widespread adoption of electronic financial transactions and better access to financial services in many countries. As the network of ATMs is becoming denser while the users are accessing them at a greater rate, the current financial institutions are faced with addressing inventory and replenishment optimal policies when managing a large number of ATMs. An excessive ATM replenishment will result in a large holding cost whereas an inadequate cash inventory will increase the frequency of the replenishments and the probability of stockouts along with customer dissatisfaction. To facilitate informed decisions in ATM cash management, in this paper, we introduce an approach for optimal replenishment amounts to minimize the total costs of money holding and customer dissatisfaction by taking the replenishment costs into account including stock-outs. An important aspect of the replenishment strategy is that the future cash demands are not available at the time of planning. To account for uncertainties in unobserved future cash demands, we use prediction intervals instead of point predictions and solve the cash replenishment-planning problem using robust optimization with linear programming. We illustrate the application of the optimal ATM replenishment policy under future demand uncertainties using data consisting of daily cash withdrawals of 98 ATMs of a bank in Istanbul. We find that the optimization approach introduced in this paper results in significant reductions in costs as compared to common practice strategies.
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