design of a logistics network in proper way provides a proper platform for efficient and effective supply chain management. this paper studies a multi-period, multi echelon and multi-product integrated forward-reverse logistics network under uncertainty. first, an efficient complex mixed-integer linear programming (milp) model by considering some real-world assumptions is developed for the inte...

This article examines a new approach which solves Linear Programming (LP) problems with stochastic parameters as a generalized model of the fuzzy mathematical model analyzed by Verdegay. An expectation model is provided for solving the problem. A multi-parametric programming is applied to access to a solution with different desired degrees as well as problem constraints. Additionally, we presen...

This paper proposes a compromise model, based on a new method, to solve the multi-objective large-scale linear programming (MOLSLP) problems with block angular structure involving fuzzy parameters. The problem involves fuzzy parameters in the objective functions and constraints. In this compromise programming method, two concepts are considered simultaneously. First of them is that the optimal ...

This study proposes a new multi-item inventory model with hybrid cost parameters under a fuzzy-stochastic constraint and permissible delay in payment. The price and marketing expenditure dependent stochastic demand and the demand dependent the unit production cost are considered. Shortages are allowed and partially backordered. The main objective of this paper is to determine selling price, mar...

During the last decade, reverse logistics networks received a considerable attention due to economic importance and environmental regulations and customer awareness. Integration of leading and reverse logistics networks during logistical network design is one of the most important factors in supply chain. In this research, an Integer Linear Programming model is presented to design a multi-layer...

Abstract: Bi-level programming, a tool for modeling decentralized decisions, consists of the objective(s) of the leader at its first level and that is of the follower at the second level. Three level programming results when second level is itself a bi-level programming. By extending this idea it is possible to define multi-level programs with any number of levels. Supply chain planning problem...

Probabilistic predicate transformers provide a semantics for imperative programs containing both demonic and probabilistic nondeterminism. Like the (standard) predicate transformers popularised by Dijkstra, they model programs as functions from final results to the initial conditions sufficient to achieve them. This paper presents practical proof rules, using the probabilistic transformers, for...