Optimization for Decision Making.

Question:

District administration wants to vaccinate population of n villages (numbered 1 to n), to the best possible, through mobile medical centers (vans). Every day, a medical van starts from the district headquarter, and makes its round of villages along its fixed daily route, and comes back to the headquarters. It spends a maximum of 10 hours between reaching the first village and leaving the last village of its route. The villages have been split into three categories - Category A with 20 families or less, category B with 20 to 40 families, and category C with more than 40 families. There are n1, n2 and n3 villages in categories A, B, and C respectively, n1 + n2 + n3 = n. It has been decided that a mobile medical centre will stay for 1 hour, 2 hours, and 3 hours in villages of categories A, B and C respectively. Given an availability of p mobile vans, suggest a method to find feasible allocations of routes to the p vans so that the number of families getting medical coverage gets maximized. Make reasonable and explicit assumptions, if necessary. The method suggested by you must be sufficiently detailed out.