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

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 e-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.