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Hybrid Formulation of the Multi-Item Capacitated Dynamic lot Sizing Problem

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American Journal of Operations Research 2015年第6期5卷 503-513页

作者： Mayank Verma Renduchintala Raghavendra Kumar Sharma Department of Industrial and Management Engineering Indian Institute of Technology Kanpur Kanpur India

It is shown that when backorders, setup times and dynamic demand are included in capacitated lot sizing problem, the resulting classical formulation and one of the transportation formulations of the problem (referred to as CLSP_BS) are equivalent. And it is shown that both the formulations are “weak” formulations (as opposed to “strong” formulation). The other transportation version is a strong formulation of CLSP_BS. Extensive computational studies are presented for medium and large sized problems. In case of medium-sized problems, strong formulation produces better LP bounds, and takes lesser number of branch-and-bound (B&B) nodes and less CPU time to solve the problem optimally. However for large-sized problems strong formulation takes more time to solve the problem optimally, defeating the benefit of strength of bounds. This essentially is because of excessive increase in the number of constraints for the large sized problems. Hybrid formulations are proposed where only few most promising strong constraints are added to the weak formulation. Hybrid formulation emerges as the best performer against the strong and weak formulations. This concept of hybrid formulation can efficiently solve a variety of complex real life large-sized problems.

关键词： Capacitated lot Sizing Linear Relaxation Strong Formulation Hybrid Formulation Branch-and-Bound

Computationally Efficient Problem Reformulations for Capacitated lot Sizing Problem

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American Journal of Operations Research 2018年第4期8卷 312-322页

作者： Renduchintala Raghavendra Kumar Sharma Priyank Sinha Mananjay Kumar Verma Industrial and Management Engineering Department IIT Kanpur Kanpur India

In this article, we propose novel reformulations for capacitated lot sizing problem. These reformulations are the result of reducing the number of variables (by eliminating the backorder variable) or increasing the number of constraints (time capacity constraints) in the standard problem formulation. These reformulations are expected to reduce the computational time complexity of the problem. Their computational efficiency is evaluated later in this article through numerical analysis on randomly generated problems.

关键词： Capacitated lot Sizing Problem Efficient Problem Formulation Branch and Bound

Conditional lot Splitting to Avoid Setups While Reducing Flow Time

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American Journal of Operations Research 2012年第4期2卷 453-466页

作者： Jacob V. Simons Jr Mark E. Kraus Willis Mwangola Gerard Burke Department of Management Georgia Southern University Statesboro USA Department of Marketing and Logistics Georgia Southern University Statesboro USA U.S. Air Force Academy Colorado Springs USA

Previous research has clearly and consistently shown that flow time advantages accrue from splitting production lots into smaller transfer batches or sub-lots. Less extensively discussed, and certainly undesired, is the fact that lot splitting may dramatically increase the number of setups required, making it impractical in some settings. This paper describes and demonstrates a primary cause of these “extra” setups. It then proposes and evaluates decision rules which selectively invoke lot splitting in an attempt to avoid extra setups. For the closed job shop environment tested, our results indicate that conditional logic can achieve a substantial portion of lot splitting’s flow time improvement while avoiding the vast majority of the additional setups which would be caused by previously tested lot splitting schemes.

关键词： lot Splitting Scheduling Setups Shop Floor Control Simulation

The Quality of Medicines in Community Pharmacies in Riyadh, Saudi Arabia: A lot Quality Assurance Sampling (LQAS)-Based Survey

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Pharmacology & Pharmacy 2013年第7期4卷 511-519页

作者： Hani M. J. Khojah Henrik Pallos Naoko Yoshida Manabu Akazawa Hirohito Tsuboi Kazuko Kimura Department of Drug Management and Policy Graduate School of Natural Science and Technology Kanazawa University Kana-zawa Japan Department of Drug Management and Policy Graduate School of Natural Science and Technology Kanazawa University Kana-zawa Japan Department of Drug Management and Policy Graduate School of Natural Science and Technology Kanazawa University Kana-zawa Japan Department of Clinical and Hospital Pharmacy College of Pharmacy Taibah University Madinah KSA Department of International Pharmaceutical Sciences Graduate School of Natural Science and Technology Kanazawa University Kanazawa Japan Department of Public Health and Epidemiology Meiji Pharmaceutical University Kiyose Japan

Objectives: To classify community pharmacies (CPs) in Riyadh, Saudi Arabia, in terms of the quality of medicines sold by them, using?the lot quality assurance sampling (LQAS) technique with a predefined threshold. Methods: Riyadh CPs were divided into 2 categories (“lots” for the purpose of LQAS), i.e., chain and independent CPs. Upper and lower rate thresholds for CPs that sell low-quality medicines were predefined as 20% and 5%, respectively. Consumer and provider risks were predefined as 0.05 and 0.10, respectively. The calculated number of randomly selected CPs required in each lot was 36;then, sale of low-quality medicines in >3 CPs implies a prevalence of >20% of such CPs according to LQAS. A randomly selected brand of amoxicillin (selected as a quality indicator of medicines because it is both widely counterfeited and heat-sensitive) was purchased from each pharmacy by a “mystery shopper”, checked for authenticity, and analyzed for drug content and content uniformity using a validated HPLC method. Results: Substandard amoxicillin was purchased in 9 pharmacies (4 chains and 5 independent). Both lots were thus rejected as unacceptable, which may indicate that consumers in Riyadh are at risk of purchasing substandard medicines at CPs. Conclusions: The quality of medicines sold in CPs in Riyadh did not meet our acceptability criterion, and appropriate intervention by decision makers is recommended. LQAS proved to be a practical, economical, and statistically valid sampling method for surveying the quality of medicines. It should enable decision makers to allocate resources for improvement more efficiently.

关键词： Amoxicillin Antibiotic Quality of Medicines lot Quality Assurance Sampling Saudi Arabia Community Pharmacy

Reducing a lot Sizing Problem with Set up, Production, Shortage and Inventory Costs to lot Sizing Problem with Set up, Production and Inventory Costs

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American Journal of Operations Research 2017年第5期7卷 282-284页

作者： R. R. K. Sharma Syed Moize Ali Department of Industrial Engineering Indian Institute of Technology Kanpur India

We reduce lot sizing problem with (a) Set Up, Production, Shortage and Inventory Costs to lot sizing problem with (b) Set Up, Production, and Inventory Costs. For lot sizing problem (as in (b)), Pochet and Wolsey [1] have given already integral polyhedral with polynomial separation where a linear program yield “integer” solutions. Thus problem (b) which we have created can be more easily solved by methods available in literature. Also with the removal of shortage variables is an additional computational advantage.

关键词： lot Sizing Problem Wagner-Whitin Costs