A Generic Mathematical Model to Optimize the Integrted Production, Inventory and Distribution Decisions in Supply Chains

Noha A Mostafa, Amr B Eltawil

Abstract


Integration of decisions in supply chain management has received increasing
consideration recently. The Production-Inventory-Distribution-Routing Problem
(PIDRP) is a recent and complex problem that integrates decisions on lot-sizing,
inventory management, distribution planning, and vehicle routing problems.  In this
paper, a generic problem description is given and a Mixed-Integer Programming
model (MIP) is proposed to solve the PIDRP, the objective is to minimize the total
cost of the combined functions while satisfying the required service levels. The
proposed model contributes to the existing literature since it deals with multiple
products, split deliveries, a heterogeneous fleet of vehicles, and puts a limit on the
duration of the route performed by each vehicle. The proposed model was
successfully validated and tested by using small-sized instances from literature.
Also, a sensitivity analysis was performed to investigate the effect of estimated
parameters on the model results.

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