Shim, Sang Ho Ph.D.
http://hdl.handle.net/11347/343
2020-09-24T14:39:14ZBoard 102 : Truck-Drone Two-tier Delivery Network Design
http://hdl.handle.net/11347/353
Board 102 : Truck-Drone Two-tier Delivery Network Design
Erdem, Ergin; Johson, Christopher; shim, Sang Ho; Williams, Jordan
We develop case study materials for the future of supply chain logistics; Truck-Drone two tier delivery network design. FedEx Headquarter (HQ) in a city was used as the networks root node or central distribution center (DC). FedEx Office locations were chosen as potential drone distribution facilities. Three locations were used but the model was developed to make drone facility additions as needed. We chose major zip-code areas supported by the HQ to use as drone drop off locations with zip-code populations serving as product demand. Ten zip-codes were chosen, but this number can also be fluctuated as needed in the truck-drone model. In a depiction of the truck-drone model with FedEx HQ as the root node, linehaul to drone facility is the first arc and drone facility to destination as the second arc.
Two methods were used to capture distance along network arcs. Linehaul distance from HQ to drone facility was found using Google Map technology. This technology provided best highway route, mileage, and time determination for truck travel, as well as longitude and latitude information. After longitude and latitude coordinates were determined, Haversine’s Formula, which calculates distance between points on spheres, was used to calculate distance between drone facilities and zip-code destinations. An independent Worksheet of assumptions is made for future use in more realistic assumptions. The main Worksheet invoke the input data from the Worksheet of assumptions.
After all data concerning the network model was established and fixed and variable costs were estimated, the next step was to model the truck-drone delivery network in Excel and utilize the software’s solver capabilities for optimal route generation. Excel provided sufficient functionality needed to develop the truck-drone model; the platform can handle the Linear Programming formulation used over the truck-drone model and using Excel allows the formulation to be understood at novice and expert levels. Column-row functionality provided by Excel also allows the truck-drone model to have dynamic features. Drone facilities and zip-code or destinations can be added or subtracted as desired.
The initial Excel Worksheet is designed by an undergraduate senior student taking an undergraduate research course in Spring 2017. Using Excel Solver an add-in to Micro Soft Excel, the student solved the problem to select drone distribution facilities among 3 possible locations. His Worksheet is being refined by other students taking a Supply Chain Engineering course as course project in Fall 2017. To increase the scale of the problem including a realistic scale of 10 or more potential locations in a city, they use Open Solver another add-in to Micro Soft Excel which is endorsed by Computational Infrastructure for Operations Research (COIN-OR.)
2018-06-01T00:00:00ZA steepest edge rule for a column generation approach to the convex recoloring problem
http://hdl.handle.net/11347/352
A steepest edge rule for a column generation approach to the convex recoloring problem
Erdem, Ergin; Gahler, Kenneth; Kim, Eunseok; Shim, Sang Ho
The convex recoloring problem is a clustering problem to partition nodes of a network into connected subnetworks. We develop a hybrid rule combining the Dantzig’s Rule and the Steepest Edge Rule to produce columns which enter into the basis of the master problem in the column generation framework introduced by Chopra et al. [2]. The hybrid
rule leads to only a small number of iterations and makes it possible to perform the column generation approach in an undergraduate class using Microsoft Excel. We perform a large scale computational experiment and show that the hybrid rule is effective.
2018-01-01T00:00:00ZOn the Problem of Determining which (n, k)-Star Graphs are Cayley Graphs
http://hdl.handle.net/11347/351
On the Problem of Determining which (n, k)-Star Graphs are Cayley Graphs
Cheng, Eddie; Li, Li; Liptak, Laszlo; Shim, Sang Ho; Steffy, Daniel E.
In this paper we work to classify which of the (n, k)-star graphs, denoted by Sn,k , are Cayley graphs. Although the complete classification is left open, we derive infinite and non-trivial classes of both Cayley and non-Cayley graphs. We give a complete classification of the case when k=2 , showing that Sn,2 is Cayley if and only if n is a prime power. We also give a sufficient condition for Sn,3 to be Cayley and study other structural properties, such as demonstrating that Sn,k always has a uniform shortest path routing.
2017-01-01T00:00:00ZThe worst case analysis of strong knapsack facets
http://hdl.handle.net/11347/350
The worst case analysis of strong knapsack facets
Shim, Sang Ho; Chopra, Sunil; Cao, Wenwei
In this paper we identify strong facet defining inequalities for the master knapsack polytope. Our computational experiments for small master knapsack problems show that 1 / k-facets for small values of k ( k≤4 ) are strong facets for the knapsack polytope. We show that this finding is robust by proving that the removal of these facets from the master knapsack polytope significantly weakens the resulting relaxation in the worst case. We show that the 1 / k-facets for k=1 are the strongest in that their removal from the master knapsack polytope weakens the relaxation by a factor of 3 / 2 in the worst case. We then show that the 1 / k-facets with k=3 or 4 are the next strongest. We also show that the strength of the 1 / k-facets weakens as k grows and that the 1 / k-facets with k even are stronger than the 1 / k-facets with k odd.
2017-01-01T00:00:00Z