Duality and Existence of Optimal Policies in Generalized Joint Replenishment

Adelman, Daniel; Klabjan, Diego
February 2005
Mathematics of Operations Research;Feb2005, Vol. 30 Issue 1, p28
Academic Journal
We establish a duality theory for a broad class of deterministic inventory control problems on continuous spaces that includes the classical joint replenishment problem and inventory routing. Using this theory, we establish the existence of an optimal policy, which has been an open question. We show how a primal-dual pair of infinite dimensional linear programs encode both cyclic and noncyclic schedules, and provide various results regarding cyclic schedules, including an example showing that they need not be optimal.


Related Articles

  • COLUMN GENERATION.  // Encyclopedia of Operations Research & Management Science;2001, p94 

    A definition of the term "column generation" is presented. It refers to a technique that permits solution of very large linear-programming problems by generating the columns of the constraint matrix only when they are needed. It is used when the constraint matrix is too large to be stored and to...

  • Compact integer-programming models for extracting subsets of stimuli from confusion matrices. BRUSCO, MICHAEL J.; STAHL, STEPHANIE // Psychometrika;Sep2001, Vol. 66 Issue 3, p405 

    This paper presents an integer linear programming formulation for the problem of extracting a subset of stimuli from a confusion matrix. The objective is to select stimuli such that total confusion among the stimuli is minimized for a particular subset size. This formulation provides a drastic...

  • The Problem of Estimation of Importance Factors as a Symmetric-Lexicographic Problem of Optimization. Podinovskii, V. V. // Automation & Remote Control;Mar2003, Vol. 64 Issue 3, p480 

    It is shown that the problem of calculating the importance factors of objects on the basis of their interval paired comparisons, which is set up as a multicriteria problem of the minimization of equally important criteria that manifest themselves as multiplicative residuals of the system of...

  • Gains and costs of information in stochastic programming. Zvi Artstein // Annals of Operations Research;1999, Vol. 85 Issue 1-4, p129 

    The paper reviews the role of sensors as a variable depicting information in a stochastic program. Through examples, and with mathematical analysis of random measures, it is shown how policy variables affect the sensors in a given problem. Sensors are amenable to mathematical derivations. It is...

  • An Algorithm for the Solution of Multiparametric Mixed Integer Linear Programming Problems. Dua, Vivek; Pistikopoulos, Efstratios N. // Annals of Operations Research;2000, Vol. 99 Issue 1-4, p123 

    In this paper, we present an algorithm for the solution of multiparametric mixed integer linear programming (mp-MILP) problems involving (i) 0–1 integer variables, and, (ii) more than one parameter, bounded between lower and upper bounds, present on the right hand side (RHS) of...

  • Efficient reformulation and solution of a nonlinear PDE-controlled flow network model. F�genschuh, A.; G�ttlich, S.; Herty, M.; Kirchner, C.; Martin, A. // Computing;Sep2009, Vol. 85 Issue 3, p245 

    We consider a flow network where the flow of parts can be controlled at the vertices of the network. Based on a modified coarse grid discretization presented in F�genschuh et al. (SIAM J Scientific Comput 30(3):1490�1507, 2008) we derive a mixed-integer program (MIP). Under suitable...

  • Implicit solution function of P and Z matrix linear complementarity constraints. Xiaojun Chen; Shuhuang Xiang // Mathematical Programming;May2011, Vol. 128 Issue 1/2, p1 

    Using the least element solution of the P and Z matrix linear complementarity problem (LCP), we define an implicit solution function for linear complementarity constraints (LCC). We show that the sequence of solution functions defined by the unique solution of the regularized LCP is...

  • On the two-stage problem of linear stochastic programming with quantile criterion and discrete distribution of the random parameters. Naumov, A.; Bobylev, I. // Automation & Remote Control;Feb2012, Vol. 73 Issue 2, p265 

    Consideration was given to the two-stage problem of stochastic linear programming with a discrete distribution of the random parameter vector. The property of continuity of the quantile function in strategy was proved, the sufficient conditions for existence of solution were formulated, and an...

  • Sufficient Optimality Criterion for Linearly Constrained, Separable Concave Minimization Problems. Illés, T.; Nagy, Á B. // Journal of Optimization Theory & Applications;Jun2005, Vol. 125 Issue 3, p559 

    A sufficient optimality criterion for linearly-constrained concave minimization problems is given in this paper. Our optimally criterion is based on the sensitivity analysis of the relaxed linear programming Problem. The main result is similar to that of Phillips and Rosen (Ref. 1); however, our...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics