Production and Operations Analysis, Seventh Edition
7th Edition
ISBN: 9781478623069
Author: Steven Nahmias, Tava Lennon Olsen
Publisher: Waveland Press, Inc.
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Chapter 9.7, Problem 15P
Summary Introduction
Interpretation: The time to see advisers in order to minimize the total time for both to complete the advising by M and MB.
Concept Introduction: The time difference between the starting and finishing of a sequence of jobs or tasks is referred to as the make span.
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Four automobiles have entered Ilham’s Repair Shop for various types of work, ranging from a transmission overhaul to a brake job. The experience level of the mechanics is quite varied, and Ilham would like to minimize the time required to complete all of the jobs. He has estimated the time in minutes for each mechanic to complete each job. Shima can complete job 1 in 400 minutes, job 2 in 90 minutes, job 3 in 60 minutes, and job 4 in 120 minutes. Dekmal will finish job 1 in 650 minutes, job 2 in 120 minutes, job 3 in 90 minutes, and job 4 in 180 minutes. Tia will finish job 1 in 480 minutes, job 2 in 120 minutes, job 3 in 80 minutes, and job 4 in 180 minutes. Hazza will complete job 1 in 500 minutes, job 2 in 110 minutes, job 3 in 90 minutes, and job 4 in 150 minutes. Each mechanic should be assigned to just one of these jobs.
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The director of Burtonsville Civil Defense Agency has been ordered to draw up a disaster plan for assigning casualties to hospitals in the event of a serious earthquake. For simplicity, we will assume that causalities will occur at two points in the city and will be transported to three hospitals. It is estimated that there will be 300 casualties at point A and 200 at point B. Travel times to hospitals 1, 2, and 3 are 25, 15, and 10 minutes, respectively; from point B they are 20, 5, and 15 minutes. Hospital capacities for emergency cases are 250, 150, and 150 patients. How should the victims be assigned to hospitals to minimize the total time lost in transporting them?
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Airline Scheduling. Alpha Airline wishes to schedule no more than one flight out of a given airport to each of the following cities: C, D, L, and N. The available departure slots are 8 a.m., 10 a.m., and 12 noon. Alpha leases the airplanes at the cost of $5000 before and including 10 a.m. and $3000 after 10 a.m., and is able to lease at most two per departure slot. Also, if a flight leaves for location N in a time slot, there must be a flight leaving for location L in the same time slot. The expected profit (in $1000) contribution before rental costs per flight is shown in the table below.
Time Slot
8
10
12
C
10
6
6
D
9
10
9
L
14
11
10
N
18
15
10
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a) Formulate an integer linear program model that can be used to find the profit-maximizing schedule. Define your decision variables as Xij = 1 if a flight to destination i occurs in time slot j and Xij = 0 otherwise; and Yj = number of airplanes rented for time slot j. Write the objective function and all the constraints.
b)…
Chapter 9 Solutions
Production and Operations Analysis, Seventh Edition
Ch. 9.5 - Prob. 1PCh. 9.5 - Prob. 2PCh. 9.5 - Prob. 3PCh. 9.5 - Prob. 4PCh. 9.5 - Prob. 5PCh. 9.6 - Prob. 6PCh. 9.6 - Prob. 7PCh. 9.6 - Prob. 8PCh. 9.6 - Prob. 9PCh. 9.6 - Prob. 10P
Ch. 9.7 - Prob. 11PCh. 9.7 - Prob. 12PCh. 9.7 - Prob. 13PCh. 9.7 - Prob. 14PCh. 9.7 - Prob. 15PCh. 9.7 - Prob. 16PCh. 9.7 - Prob. 17PCh. 9.8 - Prob. 18PCh. 9.8 - Prob. 19PCh. 9.8 - Prob. 20PCh. 9.8 - Prob. 21PCh. 9.8 - Prob. 22PCh. 9.9 - Prob. 23PCh. 9.9 - Prob. 24PCh. 9.9 - Prob. 25PCh. 9.10 - Prob. 27PCh. 9.10 - Prob. 28PCh. 9.10 - Prob. 29PCh. 9 - Prob. 30APCh. 9 - Prob. 31APCh. 9 - Prob. 32APCh. 9 - Prob. 33APCh. 9 - Prob. 34APCh. 9 - Prob. 35APCh. 9 - Prob. 36APCh. 9 - Prob. 37APCh. 9 - Prob. 38APCh. 9 - Prob. 39APCh. 9 - Prob. 40APCh. 9 - Prob. 41APCh. 9 - Prob. 42APCh. 9 - Prob. 43APCh. 9 - Prob. 44APCh. 9 - Prob. 45APCh. 9 - Prob. 46APCh. 9 - Prob. 47AP
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