10:30-12:00 - 2104B Simulation, stochastic programming and modeling Stream: Simulation, stochastic programming and model- ing (contributed) Contributed session Chair: Benjamin Legros Chair: Dinesh Sharma 1 - Mathematical analysis of machine repair problems with common cause failure, hot spares and multiple repair- men Dinesh Sharma We study the machine repairable system comprising M operating ma- chines, H spares and more than one repairman where "the partial server vacation" is applied on some of the repairmen. In this system, the ﬁrst repairman never takes vacation and always available for servicing of failed machines while other repairmen goes to random length vacation whenever the number of failed machines are less than N, N +1 respec- tively. Machines may breakdown individually or due to common cause according to Poisson process. Vacation time and service time of repair- men follows the exponential distribution. Recursive approach is used to obtain the steady state probabilities. A cost model is developed to determine the optimum value of failed machine maintaining the sys- tem availability and other performance measures. Sensitivity analysis is investigated for optimal conditions and also analyzes the reliability characteristics of the system. 2 - Unintended consequences of optimizing a queue disci- pline for a service level deﬁned by a percentile of the waiting time Benjamin Legros 4 - Single-period newsvendor problem under random end- of-season demand Subrata Mitra Newsvendor problems, which have attracted the attention of re- searchers since 1950’s, have wide applications in various indus- tries. There have been many extensions to the standard single-period newsvendor problem. In this paper, we consider the single-period, single-item and single-stage newsvendor problem under random end- of-season demand, and develop a model to determine the optimal order quantity and expected proﬁt. We prove that the optimal order quantity and expected proﬁt thus obtained are lower than their respective values obtained from the standard newsvendor formulation. We also provide numerical examples and perform sensitivity analyses to compute the extent of deviations of the ’true’ optimal solutions from the newsven- dor solutions. We observe that the deviations are most sensitive to the ratio of the means of the demand distributions. The deviations are also found sensitive to the contribution margin, salvage price, coe cients of variation of the demand distributions and correlation between sea- sonal and end-of-season demands. We provide broad guidelines for managers as to when the model developed in this paper should be used and when the standard newsvendor formulation would su ce to deter- mine the order quantity. Finally, we present the concluding remarks and directions for future research. ⌅ TB-23 Tuesday, 10:30-12:00 - 2105 MADM principles 2 Stream: Multiple criteria decision analysis Invited session Chair: Jung-Ho Lu 1 - A hybrid multiple attributes decision-making model for of the waiting time. This may create an incentive for managers to mod- ify the traditional ﬁrst-come-ﬁrst-served discipline of service. For this purpose, we consider the analysis of the M/M/s queue under the queue- ing discipline which minimizes a given percentile of the waiting time. We prove that a strict non-preemptive priority should be given to the oldest customer who has waited less than the acceptable waiting time. We derive closed-form expressions of the performance measures un- der this discipline, and evaluate the unintended consequences that this discipline may have on service levels and on sta ng decisions. In par- ticular, we show that although this discipline may reduce sta ng costs, it leads to excessive wait for non-prioritized customers. 3 - Morphing M/M/m: A new view of an old queue Neil Gunther 2017 is the centenary of A.K. Erlang’s paper on waiting times in an M/D/m queue. M/M/m queues are used to model call centers, multi- cores & the Internet. Unfortunately, those who should be using M/M/m models often don’t know applied probability theory. Our remedy de- ﬁnes a morphing approximation to M/M/m that’s accurate within 10% for typical applications+. The morphing residence-time formula is both simpler and more intuitive than the exact solution involving the Erlang-C function. We have also developed an animation of this mor- phing process. An outstanding challenge, however, has been to eluci- date the nature of the corrections that transform the approximate mor- phing solution to the exact Erlang solution. In this presentation, we show: 1) the morphing solutions correspond to the m-roots of unity in the complex z-plane; 2) the exact solutions can be expressed as a rational function with poles; 3) these poles lie inside the unit disk and converge around the Szego curve with increasing m-servers; 4) the correction factor for the morphing model is deﬁned by the deﬂated polynomial; 5) the pattern of poles in the z-plane provides a conve- nient visualization of how the morphing solutions di↵er from the exact solutions. 2 88 c 2018 Performance Dynamics Morphing M/M/m July 3, 2018 2 / 24