#### Transcript INEN 601 Location Logistics

ISEN 601 Location Logistics Dr. Gary M. Gaukler Fall 2011 Setup of a Facility Location Problem • Locate new facilities • Considering: – Interaction with existing facilities – Customer demands – Customer locations – Potential locations of new facilities – Capacity considerations • Focus on “where to put the new facility” Classes of Facility Location Problems • Continuous Location Models – Customers anywhere on plane – New facilities anywhere on plane – Demand point = aggregated area demand – Distance calculations important • Euclidean distance • Rectilinear distance – In general, “quick and dirty” models Classes of Facility Location Problems • Continuous Location Models – Single Facility Minisum • Minimize sum of weighted distances from NF to customers – Single Facility Minimax • Minimize maximum weighted distance from NF to customers Classes of Facility Location Problems • Continuous Location Models – Multi-facility Minisum • Like SFMS, but place more than one NF – Location-Allocation • Like MFMS, but also determine optimal interaction between NFs Classes of Facility Location Problems • Network Location Models – Customers are on network nodes – NFs located on network nodes – Distances implicitly given by network – Network = tree or general network – Types of models: • Covering (“each customer is within 2 hours of a warehouse”) • Center (~ minimax principle) • Median (~ minisum principle) Classes of Facility Location Problems • Discrete Location Models – Uncapacitated / capacitated warehouse location models – Candidate NF locations – Facilities can split demand – Cost of opening warehouse vs. service coverage Single Facility Minisum • Ex: locating a machine in a shop, locating a warehouse in a sales region • Objective: minimize total cost – Total cost depends on location of NF • Notation: – m existing facilities, with facility j located at Pj = (aj, bj) – X location of NF, X = (x,y) Single Facility Minisum • Notation: – tj = number trips per month between j and NF – vj = avg velocity between j and NF – cj = cost of transportation per unit time – d(X,Pj) = distance between j and NF • So, monthly cost of moving material between j and NF is: Single Facility Minisum • Define: – Weight wj = cost of interaction per unit distance • So, total cost is: • Goal: SFMS with Rectilinear Distances • Rectilinear distance: • Total cost: SFMS with Rectilinear Distances • Properties of total cost function: • Graph: • Consequences: SFMS with Rectilinear Distances • Example 4.1: SFMS with Rectilinear Distances • Example 4.1: SFMS with Rectilinear Distances • Example 4.1: SFMS with Rectilinear Distances SFMS with Rectilinear Distances • Optimality properties: SFMS with Rectilinear Distances • Another example: SFMS with Rectilinear Distances • Another example: