Integrated scheduling of a multi-site mining supply chain with blending, alternative routings and co-production

Abstract

This paper proposes a multi-site global optimisation model of blending operations, alternative routings and order scheduling with a co-production flow. It is performed in a phosphoric supply chain owning three open-pit mines of different geological structures and chemical compositions, each having a dry blending plant. One main challenge of the phosphate industries is to produce merchantable ores (MO) that verify a quality charter (chemical composition) with chemical heterogeneous source ores (SO). Thus, a process of SO blending followed by a treatment is mostly necessary to obtain the required MO. Six alternative routings exist to produce an MO; one of them involving a calcination plant generates a co-product. The model objective is to determine the least costly production programme of a set of MO orders to be delivered within precise time windows, in given quantities and compliance with a specific quality charter, by assigning for each MO its blending plant, routing, blend of SOs and production schedule; it also defines the feeding of the blending plants. A real case study illustrates the proposed model.

KEYWORDS:

• Integrated scheduling
• multi-site
• blending
• alternative routings
• co-production
• mining supply chain

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article and its supplementary materials. Data Set and Results are included in the Mendeley data (https://data.mendeley.com/datasets/mz2f7gxb9w/draft?a=683bb4cc-48bf-4b62-bd19-f1b7152644f3)

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 http://aeep.eu/data-and-statistics/phosphoric-acid/

2 The Office Chérifien des Phosphates (OCP) founded in Morocco in 1920, became in 2008, the OCP Group S.A. owned by the Moroccan Government and the Banque Populaire du Maroc (https://www.ocpgroup.ma/history).

3 The passage of SOs through one or more treatment units linked to a routing $\left(h>1\right)$ induces both a reduction weight of the set of SOs processed in the dry blending plant, and a modification of the composition in chemical components (BPL, CO₂, MgO, S_iO₂, Cd) of each SO of that set: after using routing h, the initial weight of input i is decreased by the reduction factor ${\eta }_{ch}$ and the initial percentage ${\alpha }_{ci}$ of component c in the weight of input i must be multiplied by a distortion rate ${\gamma }_{cih}$(which can be greater or lower than 1).

4 M can be replaced by $\text{2}\text{.}{\text{D}}_k$, as the used routing h is not already known and because 0.5 is slightly above the lowest possible value ${\eta }_{ih}$).

5 The product of a binary and a real is linearised using the following property (see Sioshansi and Conejo 2017, p. 149). Consider the real variable x $(0<x<{\text{X}}_{max})$ with ${\text{X}}_{max}$ a preset real parameter, and y a binary variable. The non-linear equation $z=x\cdot y$. is then equivalent to the following four linear equations:$z\ge 0$, $z\le y.{\text{X}}_{max}$, $z\le x$ et $z\ge x-(1-y)\cdot {\text{X}}_{max}$.

6 (https://data.mendeley.com/datasets/mz2f7gxb9w/draft?a=683bb4cc-48bf-4b62-bd19-f1b7152644f3).

Additional information

Notes on contributors

Hajar Hilali

Hajar Hilali (https://www.linkedin.com/in/hajar-hilali-698a75a1/) is a Doctor in management sciences from Rennes 1 University and EMINES-UM6P on 2020. She is a temporary research and teaching assistants, at the Industrial Engineering Research Department of CentraleSupélec (http://www.lgi.centralesupelec.fr/), Paris-Saclay University. She has participated in various international conferences and has published one article in the International Journal of Production Research.

Vincent Hovelaque

Vincent Hovelaque (https://www.igr.univ-rennes1.fr/enseignant/hovelaque/; https://www.linkedin.com/in/vincent-hovelaque/) is a full Professor at IGR-IAE of Rennes (University of Rennes 1), member of the CREM, UMR CNRS 6211 (http://crem.univ-rennes1.fr) and currently affiliate Professor at EMINES School of Industrial Management (http://www.emines-ingenieur.org) of Mohammed VI Polytechnic University. His current research focuses on stakeholders coordination in supply chain, sustainable location and supply chain finance. It has notably published papers dealing with supply chain finance, carbon issues in both problems of inventory management and location. His research contributions have been published in several articles in academic journals and collective books.

Vincent Giard

Vincent Giard (http://www.lamsade.dauphine.fr/∼giard/; https://www.linkedin.com/in/vincent-giard-2251b914/) is a Emeritus Professor at Paris Dauphine University, PSL (http://www.dauphine.fr) and affiliate Professor at EMINES School of Industrial Management (http://www.emines-ingenieur.org) of Mohammed VI Polytechnic University. He is a specialist in industrial management and project management. He has done several research contributions in these two fields as well as in mathematical modelling, simulation modelling, information systems and management accounting. He is the author of four books, co-edited four books and published about 100 articles in academic journals and collective books. He has overseen more than 20 large industrial contracts.