Small business Cool Room Furniture

(CRF) sells whole-room packages of furniture in the region around its single store and warehouse.

Each day it must decide how to assign needed deliveries i = 1,

c, m to available trucks j = 1,

c, n to fulfill commitments of timely delivery to customers at minimum total cost. Each delivery i requires a whole-truck round trip from warehouse to customer and back taking ti hours and costing cj,i dollars. But the same truck j may make multiple deliveries i if the total of their trip times is at most the trucks available for regular work hours aj. It is also possible for any truck to work up to an additional 4 hours of overtime at qj per hour.

The following table shows values of these parameters for a typical day with m = 9 loads and n = 5 trucks.

(a) Formulate CRF’s problem as a generalized assignment type ILP with extensions to allow buying overtime.

(b) Use class optimization software to compute an optimal plan.

Transcribed Image Text:

Deliveries i 1 i=2 i=3 i=4 i=5 i=6 i = 7 i=8 i=9 Time ti 4 6 2 3 7 1 4 39 Avail Otime Trucks j Trip Costs Cji j=1 210 50 89 115 151 77 40 160 145 = 2 150 40 69 95 131 57 30 120 125 210 50 89 115 151 77 40 160 145 88 8 aj 9j 50 70 50 150 40 69 95 131 57 30 120 125 6 70 = 5 190 45 79 105 141 67 35 140 135 8 60