Three-partition flow cover inequalities for constant capacity fixed-charge network flow problems
نویسندگان
چکیده
Flow cover inequalities are among the most effective valid inequalities for capacitated fixed-charge network flow problems. These valid inequalities are based on implications for the flow quantity on the cut arcs of a two-partitioning of the network, depending on whether some of the cut arcs are open or closed. As the implications are only on the cut arcs, flow cover inequalities can be obtained by collapsing a subset of nodes into a single node. In this paper we derive new valid inequalities for the capacitated fixed-charge network flow problem by exploiting additional information from the network. In particular, the new inequalities are based on a three-partitioning of the nodes. The new three-partition flow cover inequalities include the flow cover inequalities as a special case. We discuss the constant capacity case and give a polynomial separation algorithm for the inequalities. Finally, we report computational results with the new inequalities for networks with different characteristics.
منابع مشابه
Three-partition Inequalities for Constant Capacity Capacitated Fixed-charge Network Flow Problems
Flow cover inequalities are among the most effective valid inequalities for solving capacitated fixed-charge network flow problems. These valid inequalities are implications on the flow quantity on the cut arcs of a two-partitioning of the network, depending on whether some of the cut arcs are open or closed. As the implications are only on the cut arcs, flow cover inequalities can be modeled b...
متن کاملPath Cover and Path Pack Inequalities for the Capacitated Fixed-Charge Network Flow Problem
Capacitated fixed-charge network flows are used to model a variety of problems in telecommunication, facility location, production planning and supply chain management. In this paper, we investigate capacitated path substructures and derive strong and easy-to-compute path cover and path pack inequalities. These inequalities are based on an explicit characterization of the submodular inequalitie...
متن کاملFlow pack facets of the single node fixed-charge flow polytope
i∈N yi ≤ b, yi ≤ uixi ∀i ∈ N}, where variable yi is the flow on arc i with capacity ui, xi is a binary variable that indicates whether arc i is open or closed, and N = N ∪N. The single node fixed–charge flow model is interesting not only because it is a relaxation of the fixed–charge network flow problem, but also because it is possible to derive relaxations of the form S of a general MBIP prob...
متن کاملA Cutting-Plane Algorithm for Multicommodity Capacitated Fixed-Charge Network Design
We improve the mixed-integer programming formulation of the multicommodity capacitated fixed-charge network design problem by incorporating valid inequalities into a cutting-plane algorithm. We use five classes of valid inequalities: the strong, cover, minimum cardinality, flow cover, and flow pack inequalities, the last four being expressed in terms of cutsets of the network. We develop effici...
متن کاملFixed-Charge Transportation on a Path: Linear Programming Formulations
The fixed-charge transportation problem is a fixed-charge network flow problem on a bipartite graph. This problem appears as a subproblem in many hard transportation problems, and is also both a special case and a strong relaxation of the challenging bigbucket multi-item lot-sizing problem. In this paper, we provide a polyhedral analysis of the polynomially solvable special case in which the as...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Networks
دوره 67 شماره
صفحات -
تاریخ انتشار 2016