Inventory Management Homework Set
You work in the administration of a major hospital in the Twin Cities. One of your tasks is the scheduling of one of the operating rooms in the hospital. The room is used for a specific elective surgery. You allocate a certain amount of time for a surgery; if the actual duration of the surgery exceeds the allocated time, the surgery scheduled next has to start later, and this usually results in overtime at the end of the day where surgery personnel have to stay late into the evening hours. If the actual duration of the surgery is less than the allocated time, the operating rooms remains idle until the next scheduled surgery, since the required resources for the surgery to start (staff, surgeon, equipment, patient) do not become available earlier.
You currently allocate 90 minutes for each surgery (from the beginning until the room is ready for the next patient). However, surgeons and personnel have voiced their opinion that they believe this is not enough time - too often do they run over, and too often do they have to stay late to resolve schedule overruns. The higher levels of the administration agree, since overtime work is generally associated with higher costs as well as possibly worse patient outcomes. You decide to manage this process more rigorously, and download data on 200 completed surgeries that contains information on the actual durations of the surgeries (beginning until the room is ready again), as well as some data on which surgery team was involved, and some patient specific data (Body Mass Index, or BMI of patient).
Question 1: Your higher level managers in the hospital tell you that surgeries should finish within the allocated time 99% of all times. Calculate the amount of time you should allocate per surgery to make that happen. How much safety buffer is included in this number? (Note that the safety buffer is the difference between your allocated time, and the time it would take to complete the surgery on average)
Question 2: You try to understand the precise cost factors associated with allocating too much and too little time to a surgery. While opinions diverge, most of your colleagues tell you that a minute of being overtime is about 3 times as bad as a minute of finishing early. Can you use this information to revise how much total time (and buffer time) you would allocate to a surgery?
Question 3: One of the surgery teams (let's leave it unspecified which one!) likes to schedule surgeries in continuous blocks. They tell you that they can handle three surgeries in a row; according to them, an advantage would be that all resources to start the next surgery early, in case they are done early, would be available. How much time would you allocate to such a block of three surgeries in a row (under the cost information from Q2)? Compare this time to the time you would normally allocate to three surgeries made by three different teams. How much buffer time can you save by blocking surgeries this way?
Question 4: The dataset contains both surgery team and patient level information. You get a sense that - since this information is available upfront - you could create better estimates on how long a surgery will take by making use of this information. Using regression analysis, can you show whether or not the specific surgery team involved and the body mass index of the patient influence the duration of a particular surgery? By how many minutes would you be able to reduce the buffer time in a surgery (under the cost information from Q2) by making use of this information?
DATA SET
| Surgery ID |
Surgery Duration |
Surgery Team |
BMI of Patient |
| 1 |
49 |
3 |
29 |
| 2 |
46 |
2 |
29 |
| 3 |
93 |
2 |
28 |
| 4 |
85 |
1 |
24 |
| 5 |
93 |
2 |
30 |
| 6 |
157 |
4 |
29 |
| 7 |
100 |
2 |
28 |
| 8 |
70 |
3 |
24 |
| 9 |
64 |
2 |
23 |
| 10 |
99 |
1 |
24 |
| 11 |
131 |
3 |
23 |
| 12 |
66 |
4 |
22 |
| 13 |
108 |
4 |
31 |
| 14 |
86 |
4 |
18 |
| 15 |
117 |
2 |
27 |
| 16 |
72 |
4 |
22 |
| 17 |
127 |
2 |
28 |
| 18 |
127 |
1 |
20 |
| 19 |
86 |
2 |
25 |
| 20 |
93 |
4 |
25 |
| 21 |
111 |
4 |
18 |
| 22 |
114 |
4 |
36 |
| 23 |
91 |
2 |
28 |
| 24 |
83 |
2 |
23 |
| 25 |
100 |
1 |
25 |
| 26 |
72 |
3 |
22 |
| 27 |
72 |
2 |
15 |
| 28 |
109 |
4 |
28 |
| 29 |
91 |
2 |
21 |
| 30 |
124 |
2 |
27 |
| 31 |
27 |
1 |
24 |
| 32 |
78 |
1 |
17 |
| 33 |
190 |
1 |
37 |
| 34 |
57 |
3 |
18 |
| 35 |
97 |
3 |
15 |
| 36 |
31 |
1 |
25 |
| 37 |
80 |
4 |
29 |
| 38 |
55 |
3 |
23 |
| 39 |
116 |
3 |
33 |
| 40 |
92 |
2 |
21 |
| 41 |
74 |
1 |
20 |
| 42 |
129 |
2 |
27 |
| 43 |
39 |
2 |
29 |
| 44 |
42 |
3 |
32 |
| 45 |
89 |
2 |
30 |
| 46 |
115 |
1 |
24 |
| 47 |
84 |
1 |
20 |
| 48 |
107 |
4 |
37 |
| 49 |
120 |
4 |
25 |
| 50 |
96 |
3 |
16 |
| 51 |
106 |
4 |
27 |
| 52 |
124 |
1 |
22 |
| 53 |
54 |
2 |
19 |
| 54 |
135 |
3 |
32 |
| 55 |
82 |
2 |
24 |
| 56 |
88 |
1 |
22 |
| 57 |
66 |
3 |
27 |
| 58 |
84 |
1 |
27 |
| 59 |
69 |
2 |
23 |
| 60 |
71 |
1 |
25 |
| 61 |
87 |
3 |
24 |
| 62 |
149 |
2 |
29 |
| 63 |
125 |
1 |
21 |
| 64 |
92 |
2 |
20 |
| 65 |
21 |
4 |
22 |
| 66 |
90 |
1 |
24 |
| 67 |
55 |
4 |
20 |
| 68 |
126 |
1 |
28 |
| 69 |
126 |
3 |
19 |
| 70 |
115 |
4 |
29 |
| 71 |
123 |
3 |
27 |
| 72 |
62 |
3 |
24 |
| 73 |
96 |
3 |
25 |
| 74 |
79 |
2 |
26 |
| 75 |
79 |
4 |
23 |
| 76 |
91 |
1 |
12 |
| 77 |
37 |
2 |
17 |
| 78 |
61 |
3 |
22 |
| 79 |
93 |
4 |
29 |
| 80 |
76 |
3 |
20 |
| 81 |
73 |
4 |
20 |
| 82 |
105 |
1 |
35 |
| 83 |
72 |
3 |
26 |
| 84 |
105 |
3 |
29 |
| 85 |
107 |
2 |
25 |
| 86 |
92 |
3 |
25 |
| 87 |
94 |
1 |
13 |
| 88 |
102 |
4 |
20 |
| 89 |
91 |
3 |
18 |
| 90 |
42 |
4 |
19 |
| 91 |
103 |
1 |
21 |
| 92 |
111 |
3 |
20 |
| 93 |
109 |
1 |
22 |
| 94 |
128 |
3 |
23 |
| 95 |
115 |
4 |
29 |
| 96 |
67 |
3 |
25 |
| 97 |
75 |
3 |
13 |
| 98 |
85 |
2 |
24 |
| 99 |
117 |
2 |
21 |
| 100 |
152 |
2 |
24 |
| 101 |
96 |
2 |
25 |
| 102 |
28 |
1 |
20 |
| 103 |
124 |
4 |
21 |
| 104 |
18 |
2 |
24 |
| 105 |
85 |
4 |
25 |
| 106 |
114 |
4 |
22 |
| 107 |
43 |
4 |
27 |
| 108 |
109 |
2 |
23 |
| 109 |
25 |
4 |
27 |
| 110 |
67 |
4 |
19 |
| 111 |
113 |
1 |
25 |
| 112 |
67 |
4 |
30 |
| 113 |
116 |
4 |
29 |
| 114 |
32 |
4 |
12 |
| 115 |
42 |
2 |
29 |
| 116 |
153 |
1 |
29 |
| 117 |
32 |
2 |
33 |
| 118 |
63 |
3 |
18 |
| 119 |
102 |
3 |
22 |
| 120 |
122 |
1 |
26 |
| 121 |
68 |
1 |
26 |
| 122 |
110 |
4 |
31 |
| 123 |
38 |
3 |
30 |
| 124 |
158 |
1 |
31 |
| 125 |
63 |
2 |
28 |
| 126 |
102 |
1 |
32 |
| 127 |
92 |
4 |
22 |
| 128 |
113 |
2 |
17 |
| 129 |
129 |
4 |
18 |
| 130 |
154 |
2 |
20 |
| 131 |
87 |
4 |
24 |
| 132 |
97 |
1 |
24 |
| 133 |
122 |
1 |
22 |
| 134 |
46 |
2 |
25 |
| 135 |
110 |
2 |
26 |
| 136 |
33 |
3 |
25 |
| 137 |
104 |
3 |
28 |
| 138 |
36 |
3 |
25 |
| 139 |
116 |
2 |
21 |
| 140 |
69 |
3 |
29 |
| 141 |
70 |
3 |
20 |
| 142 |
115 |
3 |
27 |
| 143 |
123 |
3 |
28 |
| 144 |
174 |
1 |
34 |
| 145 |
120 |
2 |
27 |
| 146 |
120 |
1 |
24 |
| 147 |
101 |
4 |
30 |
| 148 |
75 |
2 |
24 |
| 149 |
72 |
3 |
20 |
| 150 |
124 |
4 |
23 |
| 151 |
56 |
2 |
20 |
| 152 |
103 |
1 |
29 |
| 153 |
86 |
1 |
21 |
| 154 |
55 |
4 |
17 |
| 155 |
65 |
2 |
19 |
| 156 |
86 |
2 |
28 |
| 157 |
175 |
2 |
36 |
| 158 |
67 |
2 |
27 |
| 159 |
79 |
2 |
22 |
| 160 |
29 |
4 |
21 |
| 161 |
82 |
2 |
26 |
| 162 |
132 |
2 |
28 |
| 163 |
72 |
1 |
13 |
| 164 |
144 |
2 |
28 |
| 165 |
132 |
1 |
26 |
| 166 |
117 |
1 |
28 |
| 167 |
63 |
3 |
27 |
| 168 |
58 |
4 |
32 |
| 169 |
88 |
3 |
25 |
| 170 |
108 |
3 |
23 |
| 171 |
80 |
2 |
33 |
| 172 |
103 |
4 |
21 |
| 173 |
149 |
1 |
25 |
| 174 |
102 |
3 |
23 |
| 175 |
138 |
1 |
31 |
| 176 |
77 |
4 |
29 |
| 177 |
115 |
4 |
21 |
| 178 |
134 |
4 |
20 |
| 179 |
81 |
4 |
16 |
| 180 |
99 |
2 |
25 |
| 181 |
76 |
2 |
24 |
| 182 |
91 |
4 |
22 |
| 183 |
138 |
1 |
24 |
| 184 |
42 |
2 |
22 |
| 185 |
104 |
3 |
27 |
| 186 |
66 |
3 |
30 |
| 187 |
109 |
4 |
35 |
| 188 |
103 |
4 |
19 |
| 189 |
69 |
3 |
21 |
| 190 |
81 |
3 |
26 |
| 191 |
122 |
1 |
27 |
| 192 |
77 |
1 |
24 |
| 193 |
55 |
1 |
26 |
| 194 |
60 |
4 |
19 |
| 195 |
105 |
1 |
29 |
| 196 |
86 |
2 |
22 |
| 197 |
75 |
4 |
21 |
| 198 |
49 |
4 |
14 |
| 199 |
73 |
3 |
25 |
| 200 |
93 |
2 |
28 |