A Comprehensive Mathematical Model for a Location-routing-inventory Problem under Uncertain Demand: a Numerical Illustration in Cash-in-transit Sector

Document Type: Original Article

Authors

Department of Industrial Engineering, Yazd University, Yazd, Iran

Abstract

The purpose of this article is to model and solve an integrated location, routing and inventory problem (LRIP) in cash-in-transit (CIT) sector. In real operation of cash transportation, to decrease total cost and to reduce risk of robbery of such high-value commodity. There must be substantial variation, making problem difficult to formulate. In this paper, to better fit real life applications and to make the problem more practical, a bi-objective multiple periods, capacitated facilities with time windows under uncertain demand (BO-PCLRIP-TW-FD) in the LRIP, motivated by the replenishment of automated teller machines, is proposed. Then, using the chance constrained fuzzy programming to deal with uncertain parameters, the comprehensive model is formulated as a crisp mixed-integer linear programming. At last, to validate the mathematical formulation and to solve the problem, the latest version of ε-constraint method (i.e., AUGMECON2) is used. The proposed solution approach is tested on a realistic instance in CIT sector. Numerical results demonstrate the suitability of the model and the formulation. The ability of the model to be useful references for security carriers in real-world cases.

Keywords