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In this paper, we develop a Lagrangean relaxation-based heuristic procedure to generate near-optimal solutions to very-large-scale capacitated lot-sizing problems (CLSP) with setup times and limited overtime. Our computational results show that large problems involving several thousand products and several thousand 0/1 integer variables can be solved in a reasonable amount of computer time to within one percent of their optimal solution. The proposed procedure is general enough to be applied directly or with slight modification to real-life production problems.inventory/production, deterministic models, inventory/production, material requirements planning, programming, large scale systems

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Purpose This study aims to propose a framework for developing strategies for the supply chain of craft beer that can make the business efficient and profitable, and at the same time, generate sustainability benefits from reducing waste, conserving natural resources and reducing pollution. Design/methodology/approach Based on an extensive review of the literature of academic and industry publications, source material from craft brewers primarily situated in the USA and industry experience in craft brewing, the proposed framework describes strategies to establish sustainable craft beer supply chains. Findings The framework for craft beer supply chain consists of four categories that contribute to craft beer sustainability: ingredient procurement, recycling efforts, energy usage and distribution systems – some of these mimicking those used by macrobrewers. Each of the categories is further subdivided. Successful practices and examples are highlighted for each of the subcategories. Research limitations/implications This proposed framework was built upon current practices and available literature in the USA and focused on the environmental pillar of sustainability. Further, the proposed framework arises from the fact that current best practices in sustainability were available primarily from larger craft brewers, like Sierra Nevada and New Belgium. Practical implications By paying attention to operational changes in their supply chains, craft brewers can manage costs and improve their sustainability track record by reducing waste, conserving natural resources and improving upon their pollution footprint. Craft brewers can economize in the use of water, grains, hops and yeast by using practices discussed in this paper. Originality/value This is the first time that all aspects of supply chain and sustainability considerations in craft beer production are discussed in a comprehensive manner to propose a framework for analysis and enhancement of productivity and sustainability at the same time. The fact that the proposed framework can be used in future studies to empirically evaluate the utility of various sustainability strategies adds to the originality and value of this research.

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