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This paper addresses the multi-period two-echelon integrated competitive/uncompetitive facility location problem in a distribution system design that involves locating regional distribution centers (RDCs) and stores, and determining the best strategy for distributing the commodities from a central distribution center (CDC) to RDCs and from RDCs to stores. The goal is to determine the optimal numbers, locations and capacities of RDCs and stores so as to maximize the total profit of the distribution system. Unlike most of past research, our study allows for dynamic planning horizon, distribution of commodities, configuration of two-echelon facilities, availability of capital for investment, external market competition, customer choice behavior and storage limitation. This problem is formulated as a bi-level programming model and a mutually consistent programming mode, respectively. Since such a distribution system design problem belongs to a class of NP-hard problem, a genetic algorithm-based heuristic (GA) is presented and compared with random search solution and mutually consistent solution (MC) using numerical example. The computational results show that the GA approach is efficient and the values of the performance index were significantly improved relative to the MC.

As a basic part of organizations’ logistics management, purchasing function has supplier selection as one of its main responsibilities. One of the main objectives a buyer follows in supplier selection is to determine optimal quota to be allocated to each supplier. How to allocate orders to different suppliers is as important task as it may affect efficiency of the whole chain. Also, due to variations in real-world business environment, order allocation process is always associated with uncertainties that make it complicated. Therefore, a three-stage integrated framework with environmental uncertainties considered is proposed to allocate orders; this framework can determine qualified suppliers to whom it assigns optimal quota. Considering multi-period purchases and uncertainties, this framework presents a multi-objective nonlinear programming model to determine optimal quota to be allocated to each qualified supplier within each specified period. In order to have the order allocation process closer to real-world cases while increasing the reliability of the obtained solutions, time value of money, inflation, transportation modes, supplier’s profit, and pricing strategy are considered in this model. According to uncertain structure of the proposed model, a solution strategy is proposed to convert this model into a single-objective deterministic model. Then, the resulted single-objective deterministic model is solved by proposing three evolutionary metaheuristic algorithms based on cuckoo optimization algorithm and imperialist competitive algorithm. Finally, a sample problem is presented together with some statistical tests and sensitivity analyses to assess and examine the proposed framework.

A model is constructed for a type of multi-period inventory problem with deteriorating items, in which demands are assumed to be uncertain variables. The objective is to minimize the expected total cost including the ordering cost, inventory holding cost and deteriorating cost under constraints that demands should be satisfied with some service level in each period. To solve the model, two methods are proposed in different cases. When uncertain variables are linear, a crisp equivalent form of the model is provided. For the general cases, a hybrid algorithm integrating the 99-method and genetic algorithm is designed. Two examples are given to illustrate the effectiveness of the model and solving methods.

Multi-period risk functionals assign a risk value to discrete-time stochastic processes. While convexity and monotonicity extend in straightforward manner from the single-period case, the role of information is more problematic in the multi-period situation. In this paper, we define multi-period functionals in such a way that the development of available information over time (expressed as a filtration) enters explicitly the definition of the functional. This allows to define and study the property of information monotonicity, i.e. monotonicity w.r.t. increasing filtrations. On the other hand, time consistency of valuations is a favorable property and it is well-known that this requirement essentially leads to compositions of conditional mappings. We demonstrate that generally spoken the intersection of time consistent and information monotone valuation functionals is rather sparse, although both classes alone are quite rich. In particular, the paper gives a necessary and sufficient condition for information monotonicity of additive compositions of positively homogeneous risk/acceptability mappings. Within the class of distortion functionals only compositions of expectation or essential infima are information monotone. Furthermore, we give a sufficient condition and examples for compositions of nonhomogeneous mappings exhibiting information monotonicity.