Models and algorithms for integrated production and distribution problems.

Article published in Computers & Industrial Engineering 154 (2021)


Vincenzo Bo (a), Marco Bortolini (b), Enrico Malaguti (c), Michele Monaci (c), Cristina Mora (b), Paolo Paronuzzi (c).

(a) Plannet S.r.l., Via Pier Carlo Cadoppi 4/6, I-42124 Reggio nell’Emilia, Italy

(b) DIN, Università di Bologna, Viale Risorgimento 2, I-40136 Bologna, Italy

(c) DEI, Università di Bologna, Viale Risorgimento 2, I-40136 Bologna, Italy



Motivated by real-world applications from the non-perishable food and beverage industry, we consider a general optimization problem that involves production, distribution and warehouse logistics. The problem deals with the logistic network design and material flow management to supply the multi-product and multi- period customer demand. Decisions on production site use, including lot-sizing, setup and minimum batches are taken from a cost saving perspective together with warehouse management decisions, including shipments to external warehouses. We present a mathematical formulation of the problem that is based on a Mixed Integer Linear Programming (MILP) model and takes into account all the nasty constraints that are present in the real problem. We show that such a model is computationally hard even using a state-of-the-art commercial solver, and introduce a metaheuristic algorithm that we use to compute approximate solutions. We test the proposed algorithms on two realworld test-cases and on a large set of realistic problems. The results show that, in all cases, the algorithm is very fast and produces solutions whose quality is very close to those that can be obtained by running a state-of-the-art commercial solver on the mathematical model for a very long time, thus providing for an efficient method for evaluating effective policies to be used under different scenarios. The models and the solving algorithms are of help to the industrial practitioners for the mid-term tactical management of their logistic networks.

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The research has been partially supported by Regione Emilia- Romagna, under the POR-FESR 2014-20 project “PreLeveling & Plan Cost Optimization (PCO)”. The project was the basis for the development of the Plan Cost Optimiser, a new software solution of Plannet's Compass10 Suite.



  • Production planning

  • Mixed Integer Linear Programming

  • Heuristic algorithms

  • Lot-sizing

  • Multiple plants

  • Computational experiments


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