A polyhedral study of multiechelon lot sizing with intermediate demands

In this paper, we study a multiechelon uncapacitated lot-sizing problem in series (m-ULS), where the output of the intermediate echelons has its own external demand and is also an input to the next echelon. We propose a polynomial-time dynamic programming algorithm, which gives a tight, compact extended formulation for the two-echelon case (2-ULS). Next, we present a family of valid inequalities for m-ULS, show its strength, and give a polynomial-time separation algorithm. We establish a hierarchy between the alternative formulations for 2-ULS. In particular, we show that our valid inequalities can be obtained from the projection of the multicommodity formulation. Our computational results show that this extended formulation is very effective in solving our uncapacitated multi-item two-echelon test problems. In addition, for capacitated multi-item, multiechelon problems, we demonstrate the effectiveness of a branch-and-cut algorithm using the proposed inequalities. © 2012 INFORMS

A computational analysis of lower bounds for big bucket production planning problems

In this paper, we analyze a variety of approaches to obtain lower bounds for multi-level production planning problems with big bucket capacities, i.e., problems in which multiple items compete for the same resources. We give an extensive survey of both known and new methods, and also establish relationships between some of these methods that, to our knowledge, have not been presented before. As will be highlighted, understanding the substructures of difficult problems provide crucial insights on why these problems are hard to solve, and this is addressed by a thorough analysis in the paper. We conclude with computational results on a variety of widely used test sets, and a discussion of future research

Conformational transition in poly(p-tert-butylstyrene)

Publisher's Versio

Radiation-induced solid-state copolymerization in binary acrylamide-maleic anhydride systems

γ-Ray-initiated copolymerization of acrylamide and maleic anhydride was studied in the solid state at 25°C. The polymeric product was found to be free of the homopolymers. The mole fraction of acrylamide in the monomer mixture was varied from 0.33 to 0.91. The copolymerization reached a ‘limiting conversion’ the value of which was dependent on the composition of the monomer feed. The mole fraction of maleic anhydride in the copolymers did not exceed 0.50 and the compositions of copolymers obtained from acrylamide-rich mixtures were virtually the same as those from the monomer feed compositions. The alternating tendency of maleic anhydride was evidenced by the variation of the copolymer compositions and the consumption rates of the individual monomers