Integer linear programming • a few basic facts • branch-and-bound 18–1. Deﬁnitions integer linear program (ILP) minimize cTx subject to Ax≤ b facility location problem • npotential facility locations, mclients • ci: cost of opening a facility at location i • dij: cost of serving client ifrom location j . X2 = Amount of money to invest in Bond B X3 = Amount of money to invest in Bond C X4 = Amount of money to invest in Bond D X5 = Amount of money to invest in Bond E Objective Function: Objective is to maximize the total annual return. Maximize f(X1, X2, X3, X4, X5) = %X1 + 8%X2 + 9%X3 + 9%X4 + 9%X5 Constraints: Total investment: X1 + X2 + X3 + X4 + X5 = , Integer Programming & Combinatorial Optimization Module on Large-Scale Integer Programming & Combinatorial Optimization o Traveling salesman problem o Facility location o Network design o Traveling salesman problem o (Based on Ahuja, Magnanti, Orlin’s book Network FlowsNetwork Flows)) Traveling salesman problem thro cities in. In this research, the minimization of the fire station model is constructed. The maximum time data required by the firefighter is used to construct the minimization model of the fire station in Padang. The model is used to determine the minimum number of the available fire station in Padang town. By using Matlab a, the solution of the model can be found based on the Branch and Bound method.

INTRODUCTION TO INTEGER LINEAR PROGRAMMING WAREHOUSE LOCATION Prof. Stephen Graves A firm wants to decide where to locate its warehouses to best serve its customer base. It has aggregated the customer base according to three-digit zip code regions; for each aggregate customer, the firm has estimated the annual product demand for that region. An integer programming model was developed to assign members of a women's gymnastics team to the four events conducted at a typical NCAA meetvault, uneven bars, balance beam, and floor exercises. Each team can enter up to six gymnasts in each event, and the top five scores among these entrants contribute to the team score. Facility Location Choice The mathematical model uses a simple mixed-integer linear programming formulation and can be easily solved by using a standard solver for small and medium datasets. An electronic version of this book is available through the ‘Help’ menu. (Note: the coordinates are adjusted to the map and therefore differ. Definitions: Integer Programming. Integer programming problem (or discrete programming problem) is a type of problem in which some, or all, of the variables are allowed to take only integral values. The focus of this chapter is on solution techniques for integer programming models. In this chapter, we drop the assumption of divisibility.

Facility Location; Traveling Salesman Problem; This section contains examples that illustrate the options and syntax of the MILP solver in PROC OPTMODEL. Example illustrates the use of PROC OPTMODEL to solve an employee scheduling problem. Example discusses a multicommodity transshipment problem with fixed charges. INTEGER PROGRAMMING METHODS FOR RESERVE SELECTION AND DESIGN 45 species across sites (Equation ) and restrictions on the decision variables (Equation ). This land allocation problem illustrates three properties of linear programmes: proportional-ity, . (b) Open the cheapest facility in Nj, and assign every j′ s.t. Nj ∩ Nj′ 6= ∅ to the cheapest facility in Nj. 3. Repeat step 2 with the unassigned clients until every client is assigned. Figure 3: An LP rounding algorithm for the metric uncapacitated facility location problem. I am trying to create a linear programming formulation based on a facility location problem. In this problem, it is the goal to minimize the costs of travelling from 50 customers to 3 facilities. These have yet to be built and there are 20 possible locations for these facilities.