A Heuristic Algorithm for the Capacitated Inventory Grouping Problem

This paper presents and solves a model for the multiple supplier inventory grouping problem, which involves the minimization of logistics costs for a firm that has multiple suppliers with capacity limitations. The costs included in the model are purchasing, transportation, ordering, and inventory holding, while the firm\u27s objective is to determine the optimal flows and groups of commodities from each supplier. We present an algorithm, which combines subgradient optimization and a primal heuristic, to quickly solve the multiple supplier inventory grouping problem. Our algorithm is tested extensively on problems of various sizes and structures, and its performance is compared to that of OSL, a state-of-the-art integer programming code. The computational results indicate that our approach is extremely efficient for solving the multiple supplier inventory grouping problem

Stochastic binary problems with simple penalties for capacity constraints violations

This paper studies stochastic programs with first-stage binary variables and capacity constraints, using simple penalties for capacities violations. In particular, we take a closer look at the knapsack problem with weights and capacity following independent random variables and prove that the problem is weakly NP -hard in general. We provide pseudo-polynomial algorithms for three special cases of the problem: constant weights and capacity uniformly distributed, subset sum with Gaussian weights and strictly positively distributed random capacity, and subset sum with constant weights and arbitrary random capacity. We then turn to a branch-and-cut algorithm based on the outer approximation of the objective function. We provide computational results for the stochastic knapsack problem (i) with Gaussian weights and constant capacity and (ii) with constant weights and capacity uniformly distributed, on randomly generated instances inspired by computational results for the knapsack problem.SCOPUS: ar.jinfo:eu-repo/semantics/publishe