DATA:

The particular problem that you are tasked to address is to recommend how to sequence a known set of surgeries for the next day with the objective of reducing surgeon and OR idle times, as well as OR overtime Assume you are in a situation in which a given set of known surgeries must be sequenced to be performed by a single surgeon in two ORs that function in parallel. That is, we want to decide in which order the surgeries should be done by the surgeon, and in which of the two ORs each of them will be performed. Each surgery i 1 is characterized by a sequence of three consecutive time spans: tp: preparation time (pre-incision time) tsi: surgery time (incision time) ta: clean-up time (post-incision time) We will assume that each OR has OR staff that handles preparation (pre-incision), clean-up (post-incision), and supports the surgeon during surgery (incision). Only the surgeon might go from one OR to the other (as needed) after completing the incision time in a surgery. Also, the surgeon is required only during the surgery time span ts of any surgery I EI. The OR staff in each of the two ORs is scheduled to work in a normal shift from time t = 0 to time t = T, where the length of the OR staff normal shift t is given. If the OR staff is needed to work beyond the normal shift length of Thours, then this time is considered as overtime. Furthermore, assume the OR manager has estimated the following parameters: CV: cost per hour of having an OR vacant (idle) Cw: cost per hour of having the surgeon waiting (idle) co: cost per hour of using OR staff in any of the ORs beyond their normal time shift of length 1: that is, during overtime OR 1 0 0 0 OR 11 (time) preparation (pro incision) time surgery surgery (inition) time surgery i urgentive) dess-up (post-incision) time sarpety Figure 1: Sumple sequencing of foar (4) surgeticelel. OR II vacant time. 1 surgeon waiting time, 14 OR I overtime (OR 11 overtime. In Figure 1, a sample sequencing of four surgeries is given, and the corresponding OR vacant, Surgeon waiting, and OR overtime is shown (Figure 1 is for explanation purposes and does not show the optimal sequencing of the surgeries, or reflects real times for the surgeries). As Figure 1 illustrates, we will make the following assumptions when considering the solution of the problem (a) All planned surgeries must be performed the next day. (b) Surgeon waiting time is defined as the time the surgeon is inactive (idle) between surgeries (c) We will assume that the surgeon can start a surgery in one OR right after finishing a surgery in the other OR (d) Patients are always ready to start the surgical procedure. (e) Clean-up (post-incision) time for a surgery starts right after the corresponding surgery (incision) time has been finished. Preparation (pre-incision) time for a surgery is always done as soon as possible. In particular, preparation (pre-incision) time for the next surgery in an OR will be started right after the clean- up (post-incision) time of the previous surgery has been finished. th) OR staff in both ORs is scheduled to work for a normal shit of Thours of length, beginning at time to where T is given. Any work by the OR staff in any of the Ors after completion of their T hours shift is considered as overtime incurring a cost of ca per hour) 6)Surgeries in the two ORs can overlap. Except during the surgery (incision) time (since there is a single surgeon). In particular, this allows the OR manager to possibly start the preparation of a surgery in one of the Ors, while the (single) surgeon is performing a surgery in the other OR Also the OR manager can possibly start preparation of a surgery in one of the ORs, while clean-up is being performed in the other OR atera surgery (incision) time has been completed For simplicity, we will consider that there's no it in the time the surgeon can work, or in the amount of overtime possibly incurred by OR staff in any of the ORS. In this case, assume that to for all I El are determine that is, they are known.e. expected durations will be realized once surgeries are performed before the surgeries have to be sequenced. With this assumption, your tasks are to a) (48 pts) Test the four simple heuristics that are discussed below to decide a good sequence of the surgeries, together with the OR in which they should be performed. Good is measured in terms of the total vacant and overtime costs of the Ors, plus the total waiting time cost of the surgeon Compare heuristics solutions with each other and analyze them. Provide the best one in terms of the total cost The heuristics you will test differ from each other with respect to (1) the sequencing rule, and (2) parameter that represents the duration of a surgery the are you going to consider only the incision time or the whole procedure time to represent the duration?). The alternatives you have for sequencing rules are VAR sequencing in increasing order of variance) and CoV (sequencing in increasing order of coefficient of variation). The parameters that you may consider while sequencing are either tsi ortpi+si+tal. Thus, you have to test the following four heuristics Apply VAR based on tsi values Apply VAR based on tpi + esi + tci values Apply cov based on tsi values Apply CoV based on tpi + tsi + tci values b) (12 pts) Discuss whether or not it is useful to have the two Rs available. To answer this question, test only the best performing heuristic from part al on the case where there is only one OR available. If your answer is yes, it is useful, the answer the following question. Increasing which cost parameter value would favor having only one Oravailable? The data for the above questions is contained in the asignment I data.xlsx" that can be downloaded at LMS. The first tab of the file "Coses provides the values of c, cw,co in dollars per hour. The second tab of the file ("Sequencing Instances defines an instance of the surgery sequencing problem by providing the normal OR staff at time Tin hours, and the surgeries of type A B.C.DE that should be sequenced in the instance. Finally, the third tab of the file "Surgery Times" provides sample historical data about the times tpi, tsi, tci in minutes) for all the surgery types. Note that you should use the sample mean values of the times given in the third tab Surgery Times" as the expected duration Costs(in $ per hour) Sequencing Instances Surgery Times (in minutes) OR Vacant Cost surgeon Waiting Cost OR Overtime Cost $1.209.60 $1.048,80 $806,40 co Costs(in $ per hour) Sequencing Instances Surgery Times (in minutes) Instance No. Surgeries to be Sequenced (by Type) [ (in hours) Surgeries S1 S2 S3 S4 S5 S6 6 ABCDDE Costs(in $ per hour) Sequencing Instances Surgery Times (in minutes) 19 Ip 79.00 31.00 tp D 28,70 31,40 78.80 25,20 IP A 11.30 2.20 4,10 4,60 6,20 2.10 6,70 4,80 4,30 4.10 4,10 3,60 5,00 1,80 2,90 3.10 3.10 3,00 tp B 29,70 41,00 80,40 37.10 40,80 31,70 27.10 23,70 63.90 62,90 64,30 60,20 17,50 26,90 39,00 34,00 15.50 33,90 3,30 4.80 2,20 2,50 3,80 3.30 2,70 2,90 lp E 201.80 99,50 89,60 112.50 191,50 122,00 102,50 152.00 225,40 130,10 106,40 144,20 123.90 157,00 150,50 146,70 121,20 121,00 27.50 25,60 34.80 34.50 34.00 67,80 49.90 30,20 37.00 29.00 20.00 51,70 47.80 65,70 19.50 1s B 100,00 34,80 119,40 57,70 63,00 76,90 31,40 70,50 53,70 116.50 87,20 37.00 90,10 125,00 5,50 59,10 130,50 A 3.30 11.60 9.50 4.80 9.20 10,10 5.90 5,70 12.70 12,10 12.10 8,70 3,40 11.6.0 IRMO 11.40 8.50 62,20 21,30 53.60 31,20 7.80 23.00 31.40 52,00 19,70 16,30 44,10 17,20 19.40 28,70 17.20 15 C 81.50 280.20 166,50 189,90 95,40 59,80 251.10 155,30 23.40 145,30 64,30 289.10 105.00 163,00 122,80 117.50 171,90 15 E 45,40 177,70 $9,00 29,20 66,90 106,00 57,60 66,0 56,20 102.30 19,70 135,00 24,50 141.70 105,10 49,10 91,60 D 28,10 27.80 74,20 16.00 30,10 60.20 16,30 21,20 89.90 80.80 11.50 37,20 39.10 73.40 67.90 20,10 59.50 IC c. 95,30 17,90 38,60 25,0 31,90 110,30 29,70 6,0 17.40 28,70 16 B 32.10 38.30 46,10 24,40 34,10 37.40 53.80 17.10 24,30 78.60 91.80 12.00 44.00 87,70 40,10 48.10 78,70 21.50 1.80 IC E 66,10 54.90 65.90 48.40 67.40 40.80 81,50 51.10 $6.20 76,10 105,40 68.00 49.40 64.40 63.50 04.40 50.20 54.20 D 18,40 13.90 10,90 15,00 18,30 24.10 24.50 30.60 13.20 17.50 10.00 16,80 62,80 21,90 17.10 26,10 27,20 15,40 22.20 3.80 4,70 140 1.50 3.NO 1:40 4,70 2.60 3.50 17,20 46,00 35,0 31,00 24,10 68,70 30,00 Costs(in $ per hour) Sequencing Instances Surgery Times (in minutes) 3.50 3,80 5.00 3.80 11.10 6,90 6,00 30,90 28,20 86,30 53,10 49,20 47.20 37,10 84,10 6.30 33,90 33.60 25,00 63,50 60,70 72,30 46,10 60,20 33,00 $6,50 34.50 43,20 20,50 36,10 34,80 17,80 27,40 63.50 37,10 24,20 4,40 2.40 2.90 13,00 1,20 5,70 3,90 19.50 77.00 47.90 28.20 100,10 35.00 59.90 58.80 23.50 35.50 17.20 47.80 26,90 58.00 70.10 59.40 75,40 40,20 43.10 25,30 17.20 16,60 52,40 10,90 37,00 45,00 31,50 31.10 41,40 37,50 13,70 12,20 42,00 32,10 24,50 16,40 33,00 30,30 14,10 34,90 123,00 257,10 127.10 135.70 96,20 122.40 129,80 116,10 91.10 1970 101,00 129,70 181,70 214,10 151,30 187,20 146,60 180 40 98,30 63,40 5.80 9.00 8.90 19.30 12,70 8.00 15.40 15.00 9,40 9.30 14,10 8.00 12.60 14.00 16,10 4,90 9.50 19,40 13,60 89,30 90,00 75,90 91.00 79,50 96,50 64.90 76,70 R3,40 75,00 74,50 19,00 76,60 6,90 141,70 60,40 121.00 104,80 85,20 168,60 152,60 71,60 127,00 152,10 99,00 145,10 185,50 132,40 160,20 75,70 102,10 94.30 134,20 81.00 156,90 94.90 134,10 180,30 95,30 72,10 112,60 139.70 82,00 65,70 108,50 86,20 133,90 $3,20 $3,00 73,80 172,50 36.30 45,90 22.10 25.60 50.00 28.90 71.80 44,40 16.90 114.60 39,70 57.00 20.40 39,40 43.10 32.40 40.90 22.60 35,20 3.80 2.10 4.70 2,80 1.50 440 8.NO 4,80 4,40 5,70 2.NO 4.20 5,10 4,70 3,60 3,70 7,70 8.30 4.80 21,30 39.00 37.20 90.80 15,40 21.00 38.00 32.40 40,70 27.00 11.00 22.00 28.60 39.60 41.20 21.60 49,70 21.60 60.80 36 50 15,40 14.50 11.50 32,90 17.80 16,20 2240 19.50 19,20 26,00 37.00 24.90 17.00 12.90 12,10 38,50 26,80 19,00 17.40 23.30 54.80 119.10 61.50 93,10 84.60 103.70 53.60 60,20 $9.20 69.20 89,70 63.00 82.60 106,70 84,70 73.0 81.90 51.60 56.60 60.30 96.10 43,70 44,10 57,20 73,80 35,10 63,10 61,20 27,00 33,60 24,80 27,70 J.NO 236,00 51.90 116,80 137,60 225,30 9.30 4,50 3.90 5.80 6,90 Costs(in $ per hour) Sequencing Instances Surgery Times (in minutes) 7.10 12.30 7.50 10,80 9,60 60.30 69.90 68,10 72.20 43.90 66,30 56.60 85.10 6,90 4.50 5,30 4,10 7.30 5.00 5,50 3,00 5.80 7.30 4,00 5.80 2,50 2.80 3,80 4,50 4,90 3,40 5,00 5,10 43.10 103,20 30,50 122,00 100,00 85.80 26,50 102,40 67.60 81,70 76.70 24.20 24,00 68,90 15,40 45,00 44.90 24,60 31,60 16,90 32,30 75,50 18,00 21,50 62,00 17,20 42.10 18,70 58,40 56,70 33,40 25,30 27.00 30,00 94,00 62.70 41.10 39,20 39.10 $8.50 39.00 48.00 42,20 21.50 18.20 $2.40 23.10 45.20 30.50 38 50 42,40 34,90 18.20 18,20 36,00 27.70 20,10 6.40 16,10 26,90 38,90 29,50 14.20 18,30 44,10 45,60 29,50 76,50 35,30 18,10 8,90 63,40 117.90 78,10 118,30 115,00 172.90 162,70 155,60 159.10 117.90 153,50 119,80 94.00 121.90 119,40 136,90 163.60 185,10 72,10 95.20 80,30 81.80 111.30 102.10 128,20 69,00 27,00 48,20 29,40 139,20 139,50 68,10 65,00 83,10 101,50 80,50 108.00 69,20 94,90 161.00 102,80 123,10 108,00 80.50 129,00 156.70 70,40 202.90 78,70 114,10 164,90 58.20 64,50 101,00 92,40 61,80 118.50 67.20 4,80 5.10 1,20 1.80 3,40 2,80 2,10 2.30 3.10 9.60 6,60 23.60 49.70 21.50 26,80 54,40 26,20 25,80 42.10 28.80 63,40 22,70 97.00 32.70 74.00 42.20 41.80 34.00 54.00 90.20 10.50 10.40 11.70 6,70 12.00 10,80 6,90 12.70 5.50 7.50 8.40 10.20 13.60 8,10 36.50 47.00 40,20 26,00 24.50 82.50 18.00 29.60 85.80 60.80 32.90 40.60 29.50 31,30 56.50 46,80 19.00 26,40 23.60 25,30 27,70 28.70 31,80 41,10 49,60 110,40 25.90 29,40 $2,80 50,90 47,10 111,50 93,40 49,80 30,90 66,80 71.90 49,70 52,30 25,70 21.30 26,00 47,80 33,60 57.40 18.20 31,60 18.50 24.20 25.50 27,90 15.40 11.50 23.90 17.10 24,80 8,80 27,40 17.80 26,00 61.10 83.00 91,30 223, 102.20 56,10 114.30 30,00 94,10 3.20 2,00 13.50 3.20 3.10 4.50 6,00 3.60 $2.50 69.40 47.90 $4,40 53.70 $9.20 63.10 62.30 76,00 $7.50 76 20 Costs(in $ per hour) Sequencing Instances Surgery Times (in minutes) 42.40 8.90 8.00 106,20 66.10 45.30 53.40 68.20 42.90 56.40 53.60 25,70 39,00 18,90 39,00 68,90 46,10 96,30 12,50 59 80 5,40 2,90 6,00 5.40 6,00 6,40 3,20 4,90 5,40 3.60 3,70 3.10 4,10 2,50 3,00 9.50 5.50 6,00 5.90 46.50 33,40 27,60 47,60 42,60 5.410 70,80 67,60 37,70 48,70 31.10 62,00 68,90 34,00 14,00 13.70 19.20 37,00 21,00 19.20 87.50 39,40 53,10 41.00 45.00 35,70 38.00 86,40 4520 32.20 43.60 30,70 47.00 116,00 74.50 27.70 27.10 37.10 29,00 24,80 57,90 37,70 46,70 26,20 23,20 21.40 35,10 31.10 34,20 26,70 32,20 10,50 10,90 57,20 16,20 70,20 95,20 96,00 99,10 136,40 129,00 230,40 120.80 159,80 148,60 95,00 148,10 144.80 123,10 100,10 134,10 136,80 121,70 175,00 178.50 6.90 11.40 6.50 6,00 10.70 13.70 11.40 8,70 8,40 7.90 9.90 6,40 18.10 9,10 10.10 8,40 17.10 8.70 105,70 38,0 115,00 56,00 76,20 123,00 76,00 77,90 70,70 108,80 67,0 20,00 67.10 65,50 82,50 62,20 56,00 138,00 106,50 122,30 157,70 241.00 66.30 178,30 62,00 120,10 122.00 166.90 63.50 5-4.50 20.20 60,30 139,10 86,70 108,70 169,30 3.60 5.40 4,00 6,70 4.50 7.30 2,80 5.80 2,80 6,90 2,00 3:40 2.NO 47,70 113.40 167,60 91,30 92.00 $5.50 66,70 125,60 75.40 $2,90 79,30 90,40 114,30 50,10 97,20 104,10 91,00 59,10 101.40 39,10 69.10 47.00 39.50 34 20 35.10 17.00 40,10 13.20 67.50 35.70 30,70 25.30 76,70 45,80 30.60 20.50 35.80 40.70 52.30 40.40 31,40 36,10 32.90 24.90 46.50 26,30 12.00 21.00 77.40 71.40 26,00 21,70 16,90 12,80 20,40 23.90 18,70 20,70 18.20 15,00 17,70 36.50 10,90 27.50 24,10 14.50 30,70 17.00 59,30 18,90 29,00 44.50 27,00 $2,10 25,70 31,70 57,00 15,90 25,80 76,20 63.70 103.60 70,70 61.80 38.40 60.00 40.80 73,40 70.20 40.50 56,10 N6.00 61,10 2,10 56.30 NO.10 83.60 93.70 1,70 7,20 4,00 1,50 6,50 6,40 27,10 37.10 77.00 175,60 178.50 6,50 6,40 2.80 56,20 3.50 6,00 5.90 8.40 8,10 4.90 4.40 2.90 4.40 4.50 10.00 3.30 21.00 19,20 47,80 24,90 53,40 45,60 50,60 16,50 51,00 78,30 56,70 53,70 47,90 48,70 29,20 39,70 20.90 67.00 16,20 70.20 20.40 49.10 17.50 17,70 SO 50 23,10 14.50 15.40 28.50 122,10 125, 10 115.50 122.60 148.00 160,50 204.00 141.90 17,10 8,70 7.90 7.30 10,20 12.00 9.80 5.20 6,70 10.00 6,90 62.20 56,60 81.90 66,30 67,40 85,30 97,00 163,10 90,20 45.00 29.20 108,70 169,30 104,50 147.50 84,70 120,50 103.60 128,50 133,20 61.40 121,20 35,70 30,70 42,00 81.90 37.30 29,10 5.40 75,00 33.80 55.90 38,00 59.10 101.40 106,20 103.90 86.90 59,00 140,70 90,80 71.00 129.60 58.10 3.80 3,60 3.20 5,80 4,10 7,00 77.40 71,40 36,50 47,00 29,70 48,50 47.10 19,80 32.50 67.60 47.70 35,90 25.80 21.40 104,40 15.60 56,50 41.40 12.10 29.40 80,20 13.00 17,60 59,30 11.30 12.80 17.20 14.10 15.40 32.80 43,00 30,40 44.10 83.60 93.70 120.20 $3,30 106,60 72,70 70.80 36,70 64.50 $2.10 110 54.10 The particular problem that you are tasked to address is to recommend how to sequence a known set of surgeries for the next day with the objective of reducing surgeon and OR idle times, as well as OR overtime Assume you are in a situation in which a given set of known surgeries must be sequenced to be performed by a single surgeon in two ORs that function in parallel. That is, we want to decide in which order the surgeries should be done by the surgeon, and in which of the two ORs each of them will be performed. Each surgery i 1 is characterized by a sequence of three consecutive time spans: tp: preparation time (pre-incision time) tsi: surgery time (incision time) ta: clean-up time (post-incision time) We will assume that each OR has OR staff that handles preparation (pre-incision), clean-up (post-incision), and supports the surgeon during surgery (incision). Only the surgeon might go from one OR to the other (as needed) after completing the incision time in a surgery. Also, the surgeon is required only during the surgery time span ts of any surgery I EI. The OR staff in each of the two ORs is scheduled to work in a normal shift from time t = 0 to time t = T, where the length of the OR staff normal shift t is given. If the OR staff is needed to work beyond the normal shift length of Thours, then this time is considered as overtime. Furthermore, assume the OR manager has estimated the following parameters: CV: cost per hour of having an OR vacant (idle) Cw: cost per hour of having the surgeon waiting (idle) co: cost per hour of using OR staff in any of the ORs beyond their normal time shift of length 1: that is, during overtime OR 1 0 0 0 OR 11 (time) preparation (pro incision) time surgery surgery (inition) time surgery i urgentive) dess-up (post-incision) time sarpety Figure 1: Sumple sequencing of foar (4) surgeticelel. OR II vacant time. 1 surgeon waiting time, 14 OR I overtime (OR 11 overtime. In Figure 1, a sample sequencing of four surgeries is given, and the corresponding OR vacant, Surgeon waiting, and OR overtime is shown (Figure 1 is for explanation purposes and does not show the optimal sequencing of the surgeries, or reflects real times for the surgeries). As Figure 1 illustrates, we will make the following assumptions when considering the solution of the problem (a) All planned surgeries must be performed the next day. (b) Surgeon waiting time is defined as the time the surgeon is inactive (idle) between surgeries (c) We will assume that the surgeon can start a surgery in one OR right after finishing a surgery in the other OR (d) Patients are always ready to start the surgical procedure. (e) Clean-up (post-incision) time for a surgery starts right after the corresponding surgery (incision) time has been finished. Preparation (pre-incision) time for a surgery is always done as soon as possible. In particular, preparation (pre-incision) time for the next surgery in an OR will be started right after the clean- up (post-incision) time of the previous surgery has been finished. th) OR staff in both ORs is scheduled to work for a normal shit of Thours of length, beginning at time to where T is given. Any work by the OR staff in any of the Ors after completion of their T hours shift is considered as overtime incurring a cost of ca per hour) 6)Surgeries in the two ORs can overlap. Except during the surgery (incision) time (since there is a single surgeon). In particular, this allows the OR manager to possibly start the preparation of a surgery in one of the Ors, while the (single) surgeon is performing a surgery in the other OR Also the OR manager can possibly start preparation of a surgery in one of the ORs, while clean-up is being performed in the other OR atera surgery (incision) time has been completed For simplicity, we will consider that there's no it in the time the surgeon can work, or in the amount of overtime possibly incurred by OR staff in any of the ORS. In this case, assume that to for all I El are determine that is, they are known.e. expected durations will be realized once surgeries are performed before the surgeries have to be sequenced. With this assumption, your tasks are to a) (48 pts) Test the four simple heuristics that are discussed below to decide a good sequence of the surgeries, together with the OR in which they should be performed. Good is measured in terms of the total vacant and overtime costs of the Ors, plus the total waiting time cost of the surgeon Compare heuristics solutions with each other and analyze them. Provide the best one in terms of the total cost The heuristics you will test differ from each other with respect to (1) the sequencing rule, and (2) parameter that represents the duration of a surgery the are you going to consider only the incision time or the whole procedure time to represent the duration?). The alternatives you have for sequencing rules are VAR sequencing in increasing order of variance) and CoV (sequencing in increasing order of coefficient of variation). The parameters that you may consider while sequencing are either tsi ortpi+si+tal. Thus, you have to test the following four heuristics Apply VAR based on tsi values Apply VAR based on tpi + esi + tci values Apply cov based on tsi values Apply CoV based on tpi + tsi + tci values b) (12 pts) Discuss whether or not it is useful to have the two Rs available. To answer this question, test only the best performing heuristic from part al on the case where there is only one OR available. If your answer is yes, it is useful, the answer the following question. Increasing which cost parameter value would favor having only one Oravailable? The data for the above questions is contained in the asignment I data.xlsx" that can be downloaded at LMS. The first tab of the file "Coses provides the values of c, cw,co in dollars per hour. The second tab of the file ("Sequencing Instances defines an instance of the surgery sequencing problem by providing the normal OR staff at time Tin hours, and the surgeries of type A B.C.DE that should be sequenced in the instance. Finally, the third tab of the file "Surgery Times" provides sample historical data about the times tpi, tsi, tci in minutes) for all the surgery types. Note that you should use the sample mean values of the times given in the third tab Surgery Times" as the expected duration Costs(in $ per hour) Sequencing Instances Surgery Times (in minutes) OR Vacant Cost surgeon Waiting Cost OR Overtime Cost $1.209.60 $1.048,80 $806,40 co Costs(in $ per hour) Sequencing Instances Surgery Times (in minutes) Instance No. Surgeries to be Sequenced (by Type) [ (in hours) Surgeries S1 S2 S3 S4 S5 S6 6 ABCDDE Costs(in $ per hour) Sequencing Instances Surgery Times (in minutes) 19 Ip 79.00 31.00 tp D 28,70 31,40 78.80 25,20 IP A 11.30 2.20 4,10 4,60 6,20 2.10 6,70 4,80 4,30 4.10 4,10 3,60 5,00 1,80 2,90 3.10 3.10 3,00 tp B 29,70 41,00 80,40 37.10 40,80 31,70 27.10 23,70 63.90 62,90 64,30 60,20 17,50 26,90 39,00 34,00 15.50 33,90 3,30 4.80 2,20 2,50 3,80 3.30 2,70 2,90 lp E 201.80 99,50 89,60 112.50 191,50 122,00 102,50 152.00 225,40 130,10 106,40 144,20 123.90 157,00 150,50 146,70 121,20 121,00 27.50 25,60 34.80 34.50 34.00 67,80 49.90 30,20 37.00 29.00 20.00 51,70 47.80 65,70 19.50 1s B 100,00 34,80 119,40 57,70 63,00 76,90 31,40 70,50 53,70 116.50 87,20 37.00 90,10 125,00 5,50 59,10 130,50 A 3.30 11.60 9.50 4.80 9.20 10,10 5.90 5,70 12.70 12,10 12.10 8,70 3,40 11.6.0 IRMO 11.40 8.50 62,20 21,30 53.60 31,20 7.80 23.00 31.40 52,00 19,70 16,30 44,10 17,20 19.40 28,70 17.20 15 C 81.50 280.20 166,50 189,90 95,40 59,80 251.10 155,30 23.40 145,30 64,30 289.10 105.00 163,00 122,80 117.50 171,90 15 E 45,40 177,70 $9,00 29,20 66,90 106,00 57,60 66,0 56,20 102.30 19,70 135,00 24,50 141.70 105,10 49,10 91,60 D 28,10 27.80 74,20 16.00 30,10 60.20 16,30 21,20 89.90 80.80 11.50 37,20 39.10 73.40 67.90 20,10 59.50 IC c. 95,30 17,90 38,60 25,0 31,90 110,30 29,70 6,0 17.40 28,70 16 B 32.10 38.30 46,10 24,40 34,10 37.40 53.80 17.10 24,30 78.60 91.80 12.00 44.00 87,70 40,10 48.10 78,70 21.50 1.80 IC E 66,10 54.90 65.90 48.40 67.40 40.80 81,50 51.10 $6.20 76,10 105,40 68.00 49.40 64.40 63.50 04.40 50.20 54.20 D 18,40 13.90 10,90 15,00 18,30 24.10 24.50 30.60 13.20 17.50 10.00 16,80 62,80 21,90 17.10 26,10 27,20 15,40 22.20 3.80 4,70 140 1.50 3.NO 1:40 4,70 2.60 3.50 17,20 46,00 35,0 31,00 24,10 68,70 30,00 Costs(in $ per hour) Sequencing Instances Surgery Times (in minutes) 3.50 3,80 5.00 3.80 11.10 6,90 6,00 30,90 28,20 86,30 53,10 49,20 47.20 37,10 84,10 6.30 33,90 33.60 25,00 63,50 60,70 72,30 46,10 60,20 33,00 $6,50 34.50 43,20 20,50 36,10 34,80 17,80 27,40 63.50 37,10 24,20 4,40 2.40 2.90 13,00 1,20 5,70 3,90 19.50 77.00 47.90 28.20 100,10 35.00 59.90 58.80 23.50 35.50 17.20 47.80 26,90 58.00 70.10 59.40 75,40 40,20 43.10 25,30 17.20 16,60 52,40 10,90 37,00 45,00 31,50 31.10 41,40 37,50 13,70 12,20 42,00 32,10 24,50 16,40 33,00 30,30 14,10 34,90 123,00 257,10 127.10 135.70 96,20 122.40 129,80 116,10 91.10 1970 101,00 129,70 181,70 214,10 151,30 187,20 146,60 180 40 98,30 63,40 5.80 9.00 8.90 19.30 12,70 8.00 15.40 15.00 9,40 9.30 14,10 8.00 12.60 14.00 16,10 4,90 9.50 19,40 13,60 89,30 90,00 75,90 91.00 79,50 96,50 64.90 76,70 R3,40 75,00 74,50 19,00 76,60 6,90 141,70 60,40 121.00 104,80 85,20 168,60 152,60 71,60 127,00 152,10 99,00 145,10 185,50 132,40 160,20 75,70 102,10 94.30 134,20 81.00 156,90 94.90 134,10 180,30 95,30 72,10 112,60 139.70 82,00 65,70 108,50 86,20 133,90 $3,20 $3,00 73,80 172,50 36.30 45,90 22.10 25.60 50.00 28.90 71.80 44,40 16.90 114.60 39,70 57.00 20.40 39,40 43.10 32.40 40.90 22.60 35,20 3.80 2.10 4.70 2,80 1.50 440 8.NO 4,80 4,40 5,70 2.NO 4.20 5,10 4,70 3,60 3,70 7,70 8.30 4.80 21,30 39.00 37.20 90.80 15,40 21.00 38.00 32.40 40,70 27.00 11.00 22.00 28.60 39.60 41.20 21.60 49,70 21.60 60.80 36 50 15,40 14.50 11.50 32,90 17.80 16,20 2240 19.50 19,20 26,00 37.00 24.90 17.00 12.90 12,10 38,50 26,80 19,00 17.40 23.30 54.80 119.10 61.50 93,10 84.60 103.70 53.60 60,20 $9.20 69.20 89,70 63.00 82.60 106,70 84,70 73.0 81.90 51.60 56.60 60.30 96.10 43,70 44,10 57,20 73,80 35,10 63,10 61,20 27,00 33,60 24,80 27,70 J.NO 236,00 51.90 116,80 137,60 225,30 9.30 4,50 3.90 5.80 6,90 Costs(in $ per hour) Sequencing Instances Surgery Times (in minutes) 7.10 12.30 7.50 10,80 9,60 60.30 69.90 68,10 72.20 43.90 66,30 56.60 85.10 6,90 4.50 5,30 4,10 7.30 5.00 5,50 3,00 5.80 7.30 4,00 5.80 2,50 2.80 3,80 4,50 4,90 3,40 5,00 5,10 43.10 103,20 30,50 122,00 100,00 85.80 26,50 102,40 67.60 81,70 76.70 24.20 24,00 68,90 15,40 45,00 44.90 24,60 31,60 16,90 32,30 75,50 18,00 21,50 62,00 17,20 42.10 18,70 58,40 56,70 33,40 25,30 27.00 30,00 94,00 62.70 41.10 39,20 39.10 $8.50 39.00 48.00 42,20 21.50 18.20 $2.40 23.10 45.20 30.50 38 50 42,40 34,90 18.20 18,20 36,00 27.70 20,10 6.40 16,10 26,90 38,90 29,50 14.20 18,30 44,10 45,60 29,50 76,50 35,30 18,10 8,90 63,40 117.90 78,10 118,30 115,00 172.90 162,70 155,60 159.10 117.90 153,50 119,80 94.00 121.90 119,40 136,90 163.60 185,10 72,10 95.20 80,30 81.80 111.30 102.10 128,20 69,00 27,00 48,20 29,40 139,20 139,50 68,10 65,00 83,10 101,50 80,50 108.00 69,20 94,90 161.00 102,80 123,10 108,00 80.50 129,00 156.70 70,40 202.90 78,70 114,10 164,90 58.20 64,50 101,00 92,40 61,80 118.50 67.20 4,80 5.10 1,20 1.80 3,40 2,80 2,10 2.30 3.10 9.60 6,60 23.60 49.70 21.50 26,80 54,40 26,20 25,80 42.10 28.80 63,40 22,70 97.00 32.70 74.00 42.20 41.80 34.00 54.00 90.20 10.50 10.40 11.70 6,70 12.00 10,80 6,90 12.70 5.50 7.50 8.40 10.20 13.60 8,10 36.50 47.00 40,20 26,00 24.50 82.50 18.00 29.60 85.80 60.80 32.90 40.60 29.50 31,30 56.50 46,80 19.00 26,40 23.60 25,30 27,70 28.70 31,80 41,10 49,60 110,40 25.90 29,40 $2,80 50,90 47,10 111,50 93,40 49,80 30,90 66,80 71.90 49,70 52,30 25,70 21.30 26,00 47,80 33,60 57.40 18.20 31,60 18.50 24.20 25.50 27,90 15.40 11.50 23.90 17.10 24,80 8,80 27,40 17.80 26,00 61.10 83.00 91,30 223, 102.20 56,10 114.30 30,00 94,10 3.20 2,00 13.50 3.20 3.10 4.50 6,00 3.60 $2.50 69.40 47.90 $4,40 53.70 $9.20 63.10 62.30 76,00 $7.50 76 20 Costs(in $ per hour) Sequencing Instances Surgery Times (in minutes) 42.40 8.90 8.00 106,20 66.10 45.30 53.40 68.20 42.90 56.40 53.60 25,70 39,00 18,90 39,00 68,90 46,10 96,30 12,50 59 80 5,40 2,90 6,00 5.40 6,00 6,40 3,20 4,90 5,40 3.60 3,70 3.10 4,10 2,50 3,00 9.50 5.50 6,00 5.90 46.50 33,40 27,60 47,60 42,60 5.410 70,80 67,60 37,70 48,70 31.10 62,00 68,90 34,00 14,00 13.70 19.20 37,00 21,00 19.20 87.50 39,40 53,10 41.00 45.00 35,70 38.00 86,40 4520 32.20 43.60 30,70 47.00 116,00 74.50 27.70 27.10 37.10 29,00 24,80 57,90 37,70 46,70 26,20 23,20 21.40 35,10 31.10 34,20 26,70 32,20 10,50 10,90 57,20 16,20 70,20 95,20 96,00 99,10 136,40 129,00 230,40 120.80 159,80 148,60 95,00 148,10 144.80 123,10 100,10 134,10 136,80 121,70 175,00 178.50 6.90 11.40 6.50 6,00 10.70 13.70 11.40 8,70 8,40 7.90 9.90 6,40 18.10 9,10 10.10 8,40 17.10 8.70 105,70 38,0 115,00 56,00 76,20 123,00 76,00 77,90 70,70 108,80 67,0 20,00 67.10 65,50 82,50 62,20 56,00 138,00 106,50 122,30 157,70 241.00 66.30 178,30 62,00 120,10 122.00 166.90 63.50 5-4.50 20.20 60,30 139,10 86,70 108,70 169,30 3.60 5.40 4,00 6,70 4.50 7.30 2,80 5.80 2,80 6,90 2,00 3:40 2.NO 47,70 113.40 167,60 91,30 92.00 $5.50 66,70 125,60 75.40 $2,90 79,30 90,40 114,30 50,10 97,20 104,10 91,00 59,10 101.40 39,10 69.10 47.00 39.50 34 20 35.10 17.00 40,10 13.20 67.50 35.70 30,70 25.30 76,70 45,80 30.60 20.50 35.80 40.70 52.30 40.40 31,40 36,10 32.90 24.90 46.50 26,30 12.00 21.00 77.40 71.40 26,00 21,70 16,90 12,80 20,40 23.90 18,70 20,70 18.20 15,00 17,70 36.50 10,90 27.50 24,10 14.50 30,70 17.00 59,30 18,90 29,00 44.50 27,00 $2,10 25,70 31,70 57,00 15,90 25,80 76,20 63.70 103.60 70,70 61.80 38.40 60.00 40.80 73,40 70.20 40.50 56,10 N6.00 61,10 2,10 56.30 NO.10 83.60 93.70 1,70 7,20 4,00 1,50 6,50 6,40 27,10 37.10 77.00 175,60 178.50 6,50 6,40 2.80 56,20 3.50 6,00 5.90 8.40 8,10 4.90 4.40 2.90 4.40 4.50 10.00 3.30 21.00 19,20 47,80 24,90 53,40 45,60 50,60 16,50 51,00 78,30 56,70 53,70 47,90 48,70 29,20 39,70 20.90 67.00 16,20 70.20 20.40 49.10 17.50 17,70 SO 50 23,10 14.50 15.40 28.50 122,10 125, 10 115.50 122.60 148.00 160,50 204.00 141.90 17,10 8,70 7.90 7.30 10,20 12.00 9.80 5.20 6,70 10.00 6,90 62.20 56,60 81.90 66,30 67,40 85,30 97,00 163,10 90,20 45.00 29.20 108,70 169,30 104,50 147.50 84,70 120,50 103.60 128,50 133,20 61.40 121,20 35,70 30,70 42,00 81.90 37.30 29,10 5.40 75,00 33.80 55.90 38,00 59.10 101.40 106,20 103.90 86.90 59,00 140,70 90,80 71.00 129.60 58.10 3.80 3,60 3.20 5,80 4,10 7,00 77.40 71,40 36,50 47,00 29,70 48,50 47.10 19,80 32.50 67.60 47.70 35,90 25.80 21.40 104,40 15.60 56,50 41.40 12.10 29.40 80,20 13.00 17,60 59,30 11.30 12.80 17.20 14.10 15.40 32.80 43,00 30,40 44.10 83.60 93.70 120.20 $3,30 106,60 72,70 70.80 36,70 64.50 $2.10 110 54.10