Elsevier

Computers & Chemical Engineering

Volume 32, Issue 11, 24 November 2008, Pages 2606-2625
Computers & Chemical Engineering

Planning and scheduling of industrial supply chains with reverse flows: A real pharmaceutical case study

https://doi.org/10.1016/j.compchemeng.2008.03.006Get rights and content

Abstract

This paper presents a modeling approach for the sequential planning and scheduling of supply chain (SC) structures with reverse flows. At the planning level an aggregated description is proposed to represent the supply chain operational problem. A master representation is defined to support supply chain resources, operational occurrences (events), involved materials and associated markets. Based on this master representation a mathematical formulation is proposed for the optimal supply chain planning. The planning solution is then processed at the scheduling level, where an increased level of detail is considered, through the solution of a scheduling mathematical formulation. The link between the planning and the scheduling levels is performed sequentially by setting up common time domain bounds. At each operational level both supply chain structural and dynamic characteristics are accounted for where different topological, operational and marketing characteristics (market supplies, demands and price levels) are considered. Furthermore, the presence of reverse flows is also modeled allowing for the analysis of the closed supply chain. As final solution the models provide two levels of information: (1) the optimal aggregated plan for a given planning time domain (e.g. 6 months) and (2) its concretization at the scheduling level (e.g. 1 week) where detailed information on supply, production, inventory, transportation and recovery of products is optimized based on a pre-defined economical performance criterion. The models developed and the associated planning/scheduling methodologies are validated through the solution of a real industrial pharmaceutical case study.

Introduction

The growth in globalization and the associated management challenges have motivated the interest of practitioners and academics into global supply chains (Grossmann, 2004; Maxwell & Gargeya, 2005). Traditionally, a supply chain has been seen as an operational structure that produces and distributes a set of products to a set of market places geographically disperse, using internal resources (production, storage and transportation facilities) and some external resources (raw-materials, utilities, etc.). However, the increased society awareness towards environment aspects has created the need of extending this traditional supply chain into a more generalized structure where the incorporation of reverse flows with product returns is considered (Fleischmann, Beullens, Bloemhof-Ruwaard, & van Wassenhove, 2001; Shah, 2005). The introduction of these aspects creates an increased level of complexity in the management of such structures. The sharing of information amongst supply partners, at all decision levels, as well as the need of optimized management procedures exists. The operational procedures are not an exception and both planning and scheduling processes need to be performed in an optimized way.

As referred by Varma, Rekalitis, Blau, and Pekny (2007) the supply chain research communities tend to focus on sub-sets of the management decision instead of looking in a cross-functional and co-coordinated way to the different levels of decisions. In this paper the integration of the planning and scheduling decisions is addressed.

Berning, Brandenburg, Gursoy, Mehta, and Tolle (2002) describe a multi-site planning scheduling application where genetic algorithms are used. Timpe and Kallrath (2000) presented a mixed integer optimization for a multi-site structure where batch production is assumed. Bok, Grossmann, and Park (2000) considered the short term operation of continuous flexible process were a multiperiod problem was formulated. Gupta and Maranas (2000) also looked to the mid-term planning where uncertainty on demand was considered. A heard and known methodology was applied to the production while at the distribution level a wait-and-see procedure was used. Ryu and Pistikopoulus (2003) looked into hierarchical decisions structures with interdependence and uncertainty in data. All the above works considered the traditional supply chains representation where no reverse flows are modeled. Also, the planning and scheduling decisions do not account for a high level of detail and transportation networks as well as production sharing amongst partners have not yet been addressed.

As referred by Dogan and Grossmann (2006), that studied the simultaneous planning and scheduling for single-stage multiproduct plants, the simplest alternative for solving planning and scheduling problems is to consider a single level formulation that spans the entire planning horizon. This however will often lead to intractable problems, case that within supply chain networks is even harder to address. Most part of the research work presented so far, deals with two-level decomposition strategies where an aggregate upper level is used to represent the planning and a detailed lower level is considered to the associated scheduling problems (Basset, Pekny, & Reklaitis, 1996; Birewar, Grossmann, & Park, 1990; Dogan & Grossmann, 2006; Subrahmanyam, Pekny, & Reklaitis, 1996; Zhu & Majozi, 2001). Following a different approach, Sung and Maravelias (2007) presented recently some computational techniques that intended to identify a lower dimensional space, convex hull, in the scheduling model. All the above contributions focus only on single plants modeling with no systematic replica on the planning and scheduling of supply chain (SC) structures. As referred by Grossmann (2004) there is still a need to develop methods and approaches that can integrate efficiently planning and scheduling decision levels in supply chain structures.

In this paper a generalized supply chain structure, closed loop supply chain, is explored where planning and scheduling decisions are accounted for. Two integrated models that run sequentially are developed each one being described as a Mixed Integer Linear Programming formulation (MILP). The first model considers the planning decisions and establishes the role of each SC partner in terms of production, customization, distribution, transportation and recovery requirements resulting from the optimization of a master operational plan. Market issues such as products customization or operational criteria imposed by recycling or remanufacturing operations are explicitly accounted for. The integration of the reverse material flows is judged based on the economical and operational improvements achieved on the global supply chain performance. The recovery products, if in an adequate form, are integrated into the forward chain after being subject to the required processing steps. From the planning level different scheduling problems are generated. The time horizon of each one of these scheduling problems is equal to the duration of the considered planning period (e.g. 1 week). The optimal planning results such as materials to supply/produce/transfer/recycle are taken as boundary constraints at the scheduling problem and the operational details of each partner in terms of production, distribution, recycling and recovery are calculated. The SC scheduling is optimized by exploiting the details of resource sharing policies, capacities, equipment/tasks suitability's and the operational conditions.

The developed formulations were tested in the solution of a real pharmaceutical SC in order to help decisions related namely with the handling of non-confirming medicines.

The paper is organized as follows. In Section 2, the problems definition and the modeling details are presented. Section 3 resumes the mathematical formulations developed. A real case study is solved, in Section 4, showing the applicability of the models and methodologies developed. Finally, the paper concludes with a summary of the work presented and a discussion of some ideas for further research.

Section snippets

Problems definition and modeling details

In this paper we look into a generalized industrial supply chain structure where reverse flows are accounted for (see Fig. 1). This structure, independently of the market dimension and complexity, is characterized by a set of SC partners (entities) such as suppliers, industrial facilities, distribution centres, customers and disposal centres.

All the facilities are connected through a network of transportation resources where a high number of products and flows are considered. These, combined

Mathematical formulations

The supply chain, SC, operation is characterized, as previously discussed (Section 2), by a geographically disperse network of operations, resources and market places. The bridge between the industrial problem and its formal description is carried out through the development of an adequate representation model. This is based on a set of events, resources and material states that represent the SC operational problem. The problem details accounted within the representation are usually dependent

Industrial example—a pharmaceutical case study

In this section a real case study is solved. This although representing a real industrial problem and showing clearly the model applicability to the solution of real industrial problems does not explores fully the generalized model characteristics.

Conclusions

This paper presents an integrated approach for the planning and scheduling of generalized supply chains. The supply chain is described not only by the traditional forward flow, that links suppliers to customers through factories, warehouses and distribution centres, but also considers the existence of reverse flows where recycling or non-conforming products are returned to factories, for extra processing, or sent to disposal. A complex transportation network structure is modeled where different

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