Appointment scheduling at a multidisciplinary outpatient clinic using stochastic programming

The purpose of this paper is to investigate the problem of constructing an appointment template for scheduling patients at a specific type of multidisciplinary outpatient clinic called an integrated practice unit (IPU). The focus is on developing and solving a stochastic optimization model for a back pain IPU in the face of random arrivals, an uncertain patient mix, and variable service times. The deterministic version of the problem is modeled as a mixed integer program with the objective of minimizing a weighted combination of clinic closing time (duration) and total patient waiting time (length of stay). A two‐stage stochastic program is then derived to account for the randomness and the sequential nature of the decisions. Although it was not possible to solve the two‐stage problem for even a limited number of scenarios, the wait‐and‐see (WS) problem was sufficiently tractable to provide a lower bound on the stochastic solution. The introduction of valid inequalities, limiting indices, and the use of special ordered sets helped to speed up the computations. A greedy heuristic was also developed to obtain solutions much more quickly. Out of practical considerations, it was necessary to develop appointment templates with time slots at fixed intervals, which are not available from the WS solution. The first to be derived was the expected value (EV) template that is used to find the expected value of the EV solution (EEV). This solution provides an upper bound on the objective function value of the two‐stage stochastic program. The average gap between the EEV and WS solutions was 18%. Results from extensive computational testing are presented for the EV template and for our adaptation of three other templates found in the literature. Depending on the relative importance of the two objective function metrics, the results demonstrate the trade‐off that exists between them. For the templates investigated, the “closing time” ranged from an average of 235 to 275 minutes for a 300‐minute session, while the corresponding “total patient time in clinic” ranged from 80 to 71 minutes.     

The campaign of the lost footsteps: the pacification of Burma, 1885-95

ABSTRACT

What Rudyard Kipling called the ‘campaign of lost footsteps’ was the longest campaign fought by the Victorian army. The conquest of Upper Burma, an area of 140,000 sq. miles with a population of four million, took only three weeks in November 1885 and was accomplished with minimum cost. However, the removal and deportation of the Burmese King and dismantling of all traditional authority dismantled led to growing resistance to British rule leading to an increasingly difficult guerrilla war. Though the Burmese guerrillas were characterised by the British as mere bandits or dacoits, many were former soldiers along with Buddhist monks. The extremely difficult nature of campaigning in the terrain and climate of Burma was not sufficiently appreciated by the War Office, who viewed the conflict as a ‘subaltern’s war’ and ‘police’ work. Intended regime change was also not accompanied by any consideration of the likely implications. Prolonged insurgency necessitated deploying a force far larger than originally intended; though order was finally secured by 1895, the campaign proved destructive of Burmese society while British recruitment of hill tribes into the police and armed forces sowed the seeds for future divisions.