Optimal lot-sizing/vehicle-dispatching policies under stochastic lead times and stepwise fixed costs

Alp, O
Erkip, NK
Gullu, R
We characterize optimal policies of a dynamic lot-sizing/vehicle-dispatching problem under dynamic deterministic demands and stochastic lead times. An essential feature of the problem is the structure of the ordering cost, where a fixed cost is incurred every time a batch is initiated (or a vehicle is hired) regardless of the portion of the batch (or vehicle) utilized. Moreover, for every unit of demand not satisfied on time, holding and backorder costs are incurred. Under mild assumptions we show that the demand of a period is satisfied from at most three distinct production (dispatching) epochs. We devise a dynamic programming algorithm to compute the production/dispatching quantities and times.


Neural network calibrated stochastic processes: forecasting financial assets
Giebel, Stefan; Rainer, Martin (Springer Science and Business Media LLC, 2013-03-01)
If a given dynamical process contains an inherently unpredictable component, it may be modeled as a stochastic process. Typical examples from financial markets are the dynamics of prices (e.g. prices of stocks or commodities) or fundamental rates (exchange rates etc.). The unknown future value of the corresponding stochastic process is usually estimated as the expected value under a suitable measure, which may be determined from distribution of past (historical) values. The predictive power of this estimati...
Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market
Savku, E.; Weber, Gerhard Wilhelm (Springer Science and Business Media LLC, 2020-08-01)
We apply dynamic programming principle to discuss two optimal investment problems by using zero-sum and nonzero-sum stochastic game approaches in a continuous-time Markov regime-switching environment within the frame work of behavioral finance. We represent different states of an economy and, consequently, investors' floating levels of psychological reactions by aD-state Markov chain. The first application is a zero-sum game between an investor and the market, and the second one formulates a nonzero-sum sto...
Effective optimization with weighted automata on decomposable trees
Ravve, E. V.; Volkovich, Z.; Weber, Gerhard Wilhelm (Informa UK Limited, 2014-01-02)
In this paper, we consider quantitative optimization problems on decomposable discrete systems. We restrict ourselves to labeled trees as the description of the systems and we use weighted automata on them as our computational model. We introduce a new kind of labeled decomposable trees, sum-like weighted labeled trees, and propose a method, which allows us to reduce the solution of an optimization problem, defined in a fragment of Weighted Monadic Second Order Logic, on such a tree to the solution of effec...
Multi-objective integer programming: A general approach for generating all non-dominated solutions
Oezlen, Melih; Azizoğlu, Meral (Elsevier BV, 2009-11-16)
In this paper we develop a general approach to generate all non-dominated solutions of the multi-objective integer programming (MOIP) Problem. Our approach, which is based on the identification of objective efficiency ranges, is an improvement over classical epsilon-constraint method. Objective efficiency ranges are identified by solving simpler MOIP problems with fewer objectives. We first provide the classical epsilon-constraint method on the bi-objective integer programming problem for the sake of comple...
Markov decision processes under observability constraints
Serin, Yaşar Yasemin (Springer Science and Business Media LLC, 2005-06-01)
We develop an algorithm to compute optimal policies for Markov decision processes subject to constraints that result from some observability restrictions on the process. We assume that the state of the Markov process is unobservable. There is an observable process related to the unobservable state. So, we want to find a decision rule depending only on this observable process. The objective is to minimize the expected average cost over an infinite horizon. We also analyze the possibility of performing observ...
Citation Formats
O. Alp, N. Erkip, and R. Gullu, “Optimal lot-sizing/vehicle-dispatching policies under stochastic lead times and stepwise fixed costs,” OPERATIONS RESEARCH, pp. 160–166, 2003, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/66870.