@article { author = {Fallah-tafti, Alireza and Vahdatzad, Mohammad Ali and Sadeghieh, Ahmad}, title = {A Comprehensive Mathematical Model for a Location-routing-inventory Problem under Uncertain Demand: a Numerical Illustration in Cash-in-transit Sector}, journal = {International Journal of Engineering}, volume = {32}, number = {11}, pages = {1634-1642}, year = {2019}, publisher = {Materials and Energy Research Center}, issn = {1025-2495}, eissn = {1735-9244}, doi = {10.5829/ije.2019.32.11b.15}, 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 = {Location-routing-inventory Problem,Cash in Transit,Multiple objectives optimization,Chance Constrained Fuzzy Programming,Augmented ε-constraint}, url = {https://www.ije.ir/article_96219.html}, eprint = {https://www.ije.ir/article_96219_87995a2925b5d76c7fd4b7081734ce69.pdf} }