An attainable region approach for production planning of multiproduct processes

Abstract

in Wiley InterScience (www.interscience.wiley.com).A novel approach is presented for the solution of production planning problems for multiproduct processes. A mixed-integer programming (MIP) scheduling model is analyzed off-line to obtain a convex approximation of feasible production levels and a convex underestimation of total production cost as a function of production levels. The two approximating functions are expressed via linear inequalities that involve only planning variables yet provide all the relevant scheduling information necessary to solve the planning problem with high quality. A rolling horizon algorithm is also presented for generation (if necessary) of detailed schedules. Keywords: production planning, scheduling, attainable region IntroductionIn 2005, the US chemical industry contributed over 2.3%, $540 billion, 1 to the gross domestic product (GDP). It is the second largest manufacturing sector and one of the largest private sector investors in R&D, with chemical patents accounting for 21% of total awarded patents in 2004.2 At the same time, however, the chemical industry faces a number of major challenges such as migration of customer industries, saturation of markets, increased global competition, continued environmental regulation, and energy price and availability. 3,4 To remain healthy in today's competitive environment, chemical companies must operate efficiently by simultaneously optimizing multiple levels of operation. 5,6 To achieve this, advanced modeling methods and optimization tools for the integration and solution of large-scale supply chain optimization models are necessary.In this article, we are specifically interested in mediumterm production planning of multiproduct processes. Production planning seeks to determine optimal production targets and product inventories for a given demand forecast. To effectively solve this problem, we should also account for the capacity of manufacturing facilities and production costs, which is currently achieved via the integration of planning and scheduling models. However, integrated models are notoriously difficult to solve despite improvements in computer hardware and optimization software. Current state of the art methods are insufficient to meet industrial needs, while ad hoc approaches are not adequate due to the complexity of the chemical manufacturing facilities (e.g., batch splitting/mixing, recycle streams, coproduction, different storage policies, utility constraints, etc.). To address this problem, we propose developing a set of constraints to accurately define the space of feasible production levels (amounts) and associated production costs. The strength of this framework is being able to locate feasible production levels without needing to on-line obtain a detailed schedule for achieving each target.This article is organized as follows. We begin by reviewing the area of supply chain management (SCM), defining the production planning problem, discussing integration of planning and scheduling, and reviewing previously proposed me...

Advances in Integrated and Sustainable Supply Chain Planning

“…• Improved manners to include the impact of scheduling decisions into SC design may be further explored. One interesting approach to be examined is the use of attainable regions (Sung and Maravelias 2007) for modeling feasible aggregated production rates. • More research efforts are required to address decentralized SCs problems.…”

Data-driven construction of Convex Region Surrogate models

“…To evaluate the feasibility of nonconvex processes, Goyal and Ierapetritou (2003) develop an approach in which the feasible region is approximated by subtracting outer polytopes around the infeasible regions from an expanded convex hull obtained by simplicial approximation (Goyal and Ierapetritou 2002). Sung and Maravelias (2007) propose an attainable region approach that determines the feasible production levels of the underlying MILP production scheduling model and an underestimation of the production cost in an integrated planning and scheduling framework. In a subsequent work (Sung and Maravelias 2009), the same authors develop an extension of the attainable region approach that takes nonconvexities into account by combining multiple polytopes.…”

A projection‐based method for production planning of multiproduct facilities

“…Sung and Maravelias4 proposed conveying feasibility and cost information using a surrogate model to provide a convex approximation of the scheduling feasible region and an underestimation of production cost. That work is extended here to models capable of capturing and representing nonconvex regions.…”