The traveling salesman model was used because it could readily be made to fit the situation.
In this problem the “Salesman” (courier) travels from home to multiple destinations (Hospitals) then returns home.
In this model, Hermann was considered the home & each hospital was considered a destination.
The health clinics were considered in a separate model because there were no pickup times required on the weekends.
Not allowing the salesman to return home until he/she visits all destinations created an infeasible solutions for the courier service because all the specimens had to be delivered to Hermann within 2hr of being obtained by the courier.
In Model A, the best direct route was identified, with no consideration of the time limitation just mentioned. In other worlds, the shortest route that went to each hospital and then returned to Hermann was identified.
In Model B, forced a stop at Hermann while visiting each of the other hospitals. This model found the shortest route that originated at Hermann, went to at least one hospital, returned to Hermann, and then proceeded to the remaining hospitals before returning to Hermann.
In model C, forced two stops at Hermann while visiting each other hospital, then retuned to Hermann. The solution for these three models are shown in TableIII.
FB=Memorial Hermann Fort Bend; H=Memorial Hermann;
K=Memorial Hermann Kathy; MC=Memorial Hermann Memorial City;
NW=Memorial Hermann Northwest; SE=Memorial Hermann Southeast;
SW=Memorial Hermann Southwest; W=Memorial Hermann Woodlands
Model A: Shortest direct route H-SE-NW-MC-K-FB-SW-H 182 miles/259 min Model B: Shortest one-return H-SE-W-NW-MC-K-FB-SW 188 miles/275 min route H-SE-H Model C: Shortest two-return H-NW-MC-K-FB-SW-H 205 miles/297 min route H-SE-H H-W-H
Memorial Hermann Parceled routes from Round-trip time/miles Traveling salesman traveling salesman Model solutions Model A W-SE-H 130 min/101miles K-MC-NW-H 98 min/ 72 miles Total: 310 min/219 miles Model B No parceled routes satisfied the time demands Model C W-H 86 min/70 miles SE-H 60 min/72 miles K-MC-NW-H 98 min/72 miles FB-SW-H 82 min/46 miles Total:326 min/226 miles
Gantt chart included employee breaks, were used to show the system’s management a detailed schedule of the runs and to ensure that the selected routes (1A,2A, and 3A) met hospitals pickup/deliveries- one in early morning and one in the late evening.
Not more than 2hr could elapse prior to another scheduled visit, with the exception being visits after lunch and dinner.
Employee requirements were that each stop required 15 min lunch or dinner break.
Separate Gantt charts were used for day and evening services because the routes differed slightly due to the timings of lunch and dinner etc.
Total 13 Gantt charts (courier shifts) were necessary. Two of the hospital runs(2 & 4) included pickup/delivery from four health clinics. One run(7) is completely focused on the pickup/ delivery for the remaining seven health clinics.