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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.

Abstract:In this paper, a two-stage stochastic programming modelling is proposed, to design a multi-period, multistage, and single-commodity integrated forward/reverse logistics network design problem under uncertainty. The problem involved both strategic and tactical decision levels. The first stage dealt with strategic decisions, which are the number, capacity, and location of forward and reverse facilities. In the second stage, tactical decisions, such as base stock level as an inventory policy, were determined. The generic introduced model consisted of suppliers, manufactures, and distribution centers in forward logistic and collection centers, remanufactures, redistribution, and disposal centers in reverse logistic. The strength of the proposed model is its applicability to various industries. The problem was formulated as a mixed-integer linear programming model and was solved by using Benders' Decomposition (BD) approach. In order to accelerate the Benders' decomposition, a number of valid inequalities were added to the master problem. The proposed accelerated BD was evaluated through small-, medium-, and large-sized test problems. Numerical results confirmed that the proposed solution algorithm improved the convergence of BD lower bound and the upper bound, enabling to reach an acceptable optimality gap in a convenient time.

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