Piecewise linear approximations for the static-dynamic uncertainty strategy in stochastic lot-sizing

In this paper, we develop mixed integer linear programming models to compute near-optimal policy parameters for the non-stationary stochastic lot sizing problem under Bookbinder and Tan's static-dynamic uncertainty strategy. Our models build on piecewise linear upper and lower bounds of the first order loss function. We discuss different formulations of the stochastic lot sizing problem, in which the quality of service is captured by means of backorder penalty costs, non-stockout probability, or fill rate constraints. These models can be easily adapted to operate in settings in which unmet demand is backordered or lost. The proposed approach has a number of advantages with respect to existing methods in the literature: it enables seamless modelling of different variants of the above problem, which have been previously tackled via ad-hoc solution methods; and it produces an accurate estimation of the expected total cost, expressed in terms of upper and lower bounds. Our computational study demonstrates the effectiveness and flexibility of our models.Comment: 38 pages, working draf

On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times

Several mixed integer programming formulations have been proposed for modeling capacitated multi-level lot sizing problems with setup times. These formulations include the so-called facility location formulation, the shortest route formulation, and the inventory and lot sizing formulation with (l,S) inequalities. In this paper, we demonstrate the equivalence of these formulations when the integrality requirement is relaxed for any subset of binary setup decision variables. This equivalence has significant implications for decomposition-based methods since same optimal solution values are obtained no matter which formulation is used. In particular, we discuss the relax-and-fix method, a decomposition-based heuristic used for the efficient solution of hard lot sizing problems. Computational tests allow us to compare the effectiveness of different formulations using benchmark problems. The choice of formulation directly affects the required computational effort, and our results therefore provide guidelines on choosing an effective formulation during the development of heuristic-based solution procedures

Mixed integer programming in production planning with backlogging and setup carryover : modeling and algorithms

This paper proposes a mixed integer programming formulation for modeling the capacitated multi-level lot sizing problem with both backlogging and setup carryover. Based on the model formulation, a progressive time-oriented decomposition heuristic framework is then proposed, where improvement and construction heuristics are effectively combined, therefore efficiently avoiding the weaknesses associated with the one-time decisions made by other classical time-oriented decomposition algorithms. Computational results show that the proposed optimization framework provides competitive solutions within a reasonable time

LuTHy: a double-readout bioluminescence-based two-hybrid technology for quantitative mapping of protein-protein interactions in mammalian cells

Information on protein-protein interactions (PPIs) is of critical importance for studying complex biological systems and developing therapeutic strategies. Here, we present a double-readout bioluminescence-based two-hybrid technology, termed LuTHy, which provides two quantitative scores in one experimental procedure when testing binary interactions. PPIs are first monitored in cells by quantification of bioluminescence resonance energy transfer (BRET) and, following cell lysis, are again quantitatively assessed by luminescence-based co-precipitation (LuC). The double-readout procedure detects interactions with higher sensitivity than traditional single-readout methods and is broadly applicable, for example, for detecting the effects of small molecules or disease-causing mutations on PPIs. Applying LuTHy in a focused screen, we identified 42 interactions for the presynaptic chaperone CSPα, causative to adult-onset neuronal ceroid lipofuscinosis (ANCL), a progressive neurodegenerative disease. Nearly 50% of PPIs were found to be affected when studying the effect of the disease-causing missense mutations L115R and ∆L116 in CSPα with LuTHy. Our study presents a robust, sensitive research tool with high utility for investigating the molecular mechanisms by which disease-associated mutations impair protein activity in biological systems

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