P re-positioning emergency inventory in selected facilities is commonly adopted to prepare for potential disaster threat. In this study, we simultaneously optimize the decisions of facility location, emergency inventory pre-positioning, and relief delivery operations within a single-commodity disaster relief network. A min-max robust model is proposed to capture the uncertainties in both the left-and right-hand-side parameters in the constraints. The former corresponds to the proportions of the pre-positioned inventories usable after a disaster attack, while the latter represents the demands of the inventories and the road capacities in the disaster-affected areas. We study how to solve the robust model efficiently and analyze a special case that minimizes the deprivation cost. The application of the model is illustrated by a case study of the 2010 earthquake attack at Yushu County in Qinghai Province of PR China. The advantage of the min-max robust model is demonstrated through comparison with the deterministic model and the two-stage stochastic model for the same problem. Experiment variants also show that the robust model outperforms the other two approaches for instances with significantly larger scales.
Given a discrete maximization problem with a linear objective function where the coefficients are chosen randomly from a distribution, we would like to evaluate the expected optimal value and the marginal distribution of the optimal solution. We call this the persistency problem for a discrete optimization problem under uncertain objective, and the marginal probability mass function of the optimal solution is named the persistence value. In general, this is a difficult problem to solve, even if the distribution of the objective coefficient is well specified. In this paper, we solve a subclass of this problem when the distribution is assumed to belong to the class of distributions defined by given marginal distributions, or given marginal moment conditions. Under this model, we show that the persistency problem maximizing the expected objective value over the set of distributions can be solved via a concave maximization model. The persistency model solved using this formulation can be used to obtain important qualitative insights to the behavior of stochastic discrete optimization problems. We demonstrate how the approach can be used to obtain insights to problems in discrete choice modeling. Using a set of survey data from a transport choice modeling study, we calibrate the random utility model with choice probabilities obtained from the persistency model. Numerical results suggest that our persistency model is capable of obtaining estimates that perform as well, if not better, than classical methods, such as logit and cross-nested logit models. We can also use the persistency model to obtain choice probability estimates for more complex choice problems. We illustrate this on a stochastic knapsack problem, which is essentially a discrete choice problem under budget constraint.probability distribution, integer programming, utility preference, choice functions
Traditional approaches in inventory control first estimate the demand distribution among a predefined family of distributions based on data fitting of historical demand observations, and then optimize the inventory control using the estimated distributions. These approaches often lead to fragile solutions whenever the preselected family of distributions was inadequate. In this work we propose a minimax robust model that integrates data fitting and inventory optimization for the single-item multi-period periodic review stochastic lot-sizing problem. In contrast with the standard assumption of given distributions, we assume that histograms are part of the input.The robust model generalizes the Bayesian model, and it can be interpreted as minimizing history dependent risk measures. We prove that the optimal inventory control policies of the robust model share the same structure as the traditional stochastic dynamic programming counterpart.In particular, we analyze the robust model based on the chi-square goodness-of-fit test. If demand samples are obtained from a known distribution, the robust model converges to the stochastic model with true distribution under generous conditions. Its effectiveness is also validated by numerical experiments. IntroductionThe stochastic lot-sizing model has been extensively studied in the inventory literature. Most of the research has focused on models with complete information about the distribution of customer demand. However, in most real-world situations, the demand distribution is not known; only historical data is available. A common approach is to hypothesize a family of demand distributions and then to estimate the parameters specifying the distribution using the historical data. Once the probability distribution has been identified, the inventory problem is solved following this estimated distribution. This implies that the inventory policy is determined under the assumption that the fitted distribution adequately characterizes the demand to be realized in the future.The estimated demand distribution may not be accurate and hence the approach of fitting the distribution and optimizing the inventory decisions sequentially may not work as expected. As shown in Liyanage and Shanthikumar (2005) for the newsvendor model, such an approach may generate suboptimal solutions. Besides, in distribution fitting, one needs to assume a parametric family of a demand distribution in the first place, and this hypothesis may also go awry. For instance, we may fit the historical data to a lognormal distribution while it actually follows a uniform distribution.The robust inventory models, without assuming a parametric family of distributions, provide an approach to address ambiguity in the demand distribution. A brief review of these robust models is provided in Section 1.1. These models adopt a minimax approach targeting to minimize the worst case expected cost maximized over the set of distributions. Without exception, the existing literature either considers a pre-specified set for ...
The accurate prediction of protein-ligand binding is of great importance for rational drug design. We present herein a novel docking algorithm called as FIPSDock, which implements a variant of the Fully Informed Particle Swarm (FIPS) optimization method and adopts the newly developed energy function of AutoDock 4.20 suite for solving flexible protein-ligand docking problems. The search ability and docking accuracy of FIPSDock were first evaluated by multiple cognate docking experiments. In a benchmarking test for 77 protein/ligand complex structures derived from GOLD benchmark set, FIPSDock has obtained a successful predicting rate of 93.5% and outperformed a few docking programs including particle swarm optimization (PSO)@AutoDock, SODOCK, AutoDock, DOCK, Glide, GOLD, FlexX, Surflex, and MolDock. More importantly, FIPSDock was evaluated against PSO@AutoDock, SODOCK, and AutoDock 4.20 suite by cross-docking experiments of 74 protein-ligand complexes among eight protein targets (CDK2, ESR1, F2, MAPK14, MMP8, MMP13, PDE4B, and PDE5A) derived from Sutherland-crossdock-set. Remarkably, FIPSDock is superior to PSO@AutoDock, SODOCK, and AutoDock in seven out of eight cross-docking experiments. The results reveal that FIPS algorithm might be more suitable than the conventional genetic algorithm-based algorithms in dealing with highly flexible docking problems.
In retailing operations, retailers face the challenge of incomplete demand information. We develop a new concept named K‐approximate convexity, which is shown to be a generalization of K‐convexity, to address this challenge. This idea is applied to obtain a base‐stock list‐price policy for the joint inventory and pricing control problem with incomplete demand information and even non‐concave revenue function. A worst‐case performance bound of the policy is established. In a numerical study where demand is driven from real sales data, we find that the average gap between the profits of our proposed policy and the optimal policy is 0.27%, and the maximum gap is 4.6%.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.