Collaborative Proposal: A Framework for Integrating Production Planning with Inventory Control

这个项目关注的是一个具有调度功能和库存功能的新模型框架。提出的框架包含了一大类模型，在已经建立的库存模型和调度模型之间有许多新的模型。这些新模型似乎具有实际意义。一个模型通常假定许多不同的产品类型。对于每种类型的产品，都有一个给定的需求流，用于若干具有给定交付截止日期的单元。给定产品类型的每个单元必须在特定的截止日期前交付。预产期可能是规律的，也可能是不规律的。生产某一种产品的时间是固定的。每种产品类型都有早期成本和延迟成本。如果一台机器（或设备）正在被设置为生产一组（或一批）给定类型的产品，则产生了设置成本。目标是最小化所有生产成本，包括提前成本、延迟成本和安装成本。要考虑的机器（或设施）环境包括：(i)单台机器，（ii）并联机器，（iii）串联机器，（iv）灵活流程车间。拟议的工作有各种目标。首先，重要的是要确定所提出的类中的哪些模型可以在多项式时间内解决，以及在多项式时间内可解决的问题和np困难问题之间的界限在哪里。其次，为np困难的问题设计和测试启发式是很有趣的。第三，我们打算将开发的启发式方法应用于工业界同事提供给我们的真实世界数据。所提出的活动的智力价值是基于这样一个事实，即模型是对现有的、已建立的模型的有意义的概括，并且许多新模型似乎具有允许多项式时间解的有趣的新特性。多项式时间算法以及np困难情况下的启发式算法有望呈现出有趣的新结构。所提议的活动的广泛影响是基于这样一个事实，即研究团队与真正对模型和解决方案感兴趣的各种公司有着牢固的联系。涉及的公司包括与项目团队关系密切的Dash Optimization。此外，这项研究将在主要研究人员各机构举行的会议上传播；在过去，这些会议通常由学术界人士和工业界人士参加。

This project focuses on a new framework of models that have scheduling features as well as inventory features. The framework proposed contains a large class of models with a number of new models lying in between already well established inventory models and scheduling models. The new models appear to be of real practical significance. A model typically assumes a number of different product types. Of each product type there is a given demand stream for a number of units with given delivery due dates. Each unit of a given product type must be delivered by a specific due date. The due dates may be regular or irregular. The time to produce any unit of a given type is fixed. Each product type has an earliness cost and atardiness cost. If a machine (or facility) is being set up to produce a run (or batch) of products of a given type a setup cost is incurred. The objective is to minimize all production costs including earliness costs, tardiness costs and setup costs. The machine (or facility) environments to be considered include: (i) the single machine, (ii) parallel machines, (iii) machines in series,(iv) flexible flow shops.The proposed work has various objectives. First, it is important to determine which models in the proposed class can be solved in polynomial time and where the borderline lies between the problems that are solvable in polynomial time and the problems that are NP-hard. Second, it is of interest to design and test heuristics for the problems that are NP-hard. Third, we intend to apply the heuristics developed to real world data that will be provided to us by colleagues in industry. The intellectual merit of the proposed activity is based on the fact that the models are meaningful generalizations of existing, well-established models and that a number of the new models appear to have interesting new properties that allow for polynomial time solutions. The polynomial time algorithms as well as the heuristics for the NP-hard cases are expected to exhibit interesting new structures. The broader impact of the proposed activity is based on the fact that the research team has strong ties with various companies that are genuinely interested in the models and in the solutions. The companies involved include Dash Optimization with which the project team has very close ties. Furthermore, the research will be disseminated at conferences to be held at the various institutions of the Principal Investigators; these conferences have, in the past, typically been attended by academicians as well as by people from industry.