| The objective is to design an 18-hole course to fit within 42 acres of land for Paradise Palm Golf Club, which will maximise golfer enjoyment. | ||||||||||||||||||
| While designing this Golfcourse, few things needs to be taken into account as mentioned below: | ||||||||||||||||||
| 18 hole details and cost | ||||||||||||||||||
| Kind of hole | Straight par 5 | Dogleg par 5 | Straight par 4 | Dogleg par 4 | Long par 3 | Short par 3 | ||||||||||||
| Acreage taken up by hole | 3 | 3.5 | 2 | 2.5 | 1 | 0.75 | ||||||||||||
| Enjoyability points | 2 | 1.5 | 1.5 | 2 | 1.75 | 2.25 | ||||||||||||
| Cost | $50,000.00 | $60,000.00 | $40,000.00 | $45,000.00 | $35,000.00 | $30,000.00 | ||||||||||||
| Clubhouse detailes | ||||||||||||||||||
| Kind of clubhouse | Standard | Big | ||||||||||||||||
| Acreage taken up by clubhouse | 2 | 4 | ||||||||||||||||
| Enjoyability points | 0 | 4 | ||||||||||||||||
| Cost | $3,50,000.00 | $5,00,000.00 | ||||||||||||||||
| Formulating the Problem | ||||||||||||||||||
| The decision variables in this golfcourse design problems correspond to the number of each type of holes that should be designed in addition with which type of clubhouse will be designed for maximizing golfer enjoyments. In this situtation, to model the maximize enjoyment decision as an linear programming problem, we let: | ||||||||||||||||||
| S5 | = Number of Straight par 5 holes | |||||||||||||||||
| D5 | = Number of Dogleg par 5 holes | |||||||||||||||||
| S4 | = Number of Straight par 4 holes | |||||||||||||||||
| D4 | = Number of Dogleg par 4 holes | |||||||||||||||||
| L3 | = Number of Long par 3 holes | |||||||||||||||||
| S3 | = Number of Short par 3 holes | |||||||||||||||||
| SC | = Standard Clubhouse | |||||||||||||||||
| BC | = Big Clubhouse | |||||||||||||||||
| Maximize amount of enjoybility | ||||||||||||||||||
| The constraints control the enjoybility points | ||||||||||||||||||
| Kind of holes | Club house Type | |||||||||||||||||
| Straight par 5 | Dogleg par 5 | Straight par 4 | Dogleg par 4 | Long par 3 | Short par 3 | Standard | Big | |||||||||||
| Enjoyability points | 2 | 1.5 | 1.5 | 2 | 1.75 | 2.25 | 0 | 4 | ||||||||||
| Solution | ||||||||||||||||||
| Total Enjoybility | 0 | |||||||||||||||||
| Constraints | Straight par 5 | Dogleg par 5 | Straight par 4 | Dogleg par 4 | Long par 3 | Short par 3 | Standard | Big | LHS | RHS | ||||||||
| Straight par 5 | 1 | 0 | >= | 1 | The model designed considering the given information is returning error as the model did not satisfy all the constraints given in this problem. To resolve this and to found a feasible solution, therefore it requires some modification in the limits given in the case study. This improvement is done on trial and error basis and every time excel solver has been run to find the impact of any changes. | |||||||||||||
| Dogleg par 5 | 1 | 0 | >= | 1 | ||||||||||||||
| Straight par 4 | 1 | 0 | >= | 2 | ||||||||||||||
| Dogleg par 4 | 1 | 0 | >= | 2 | ||||||||||||||
| Long par 3 | 1 | 0 | >= | 1 | ||||||||||||||
| Short par 3 | 1 | 0 | >= | 1 | ||||||||||||||
| Par 5 | 1 | 1 | 0 | <= | 4 | |||||||||||||
| Par 4 | 1 | 1 | 0 | <= | 14 | |||||||||||||
| Par 3 | 1 | 1 | 0 | <= | 4 | |||||||||||||
| Total Par | 5 | 5 | 4 | 4 | 3 | 3 | 0 | >= | 70 | |||||||||
| Total Par | 5 | 5 | 4 | 4 | 3 | 3 | 0 | <= | 72 | |||||||||
| Total number of hole | 1 | 1 | 1 | 1 | 1 | 1 | 0 | = | 18 | |||||||||
| Total acreage | 3 | 3.5 | 2 | 2.5 | 1 | 0.75 | 2 | 4 | 0 | >= | 36 | |||||||
| Total acreage | 3 | 3.5 | 2 | 2.5 | 1 | 0.75 | 2 | 4 | 0 | <= | 42 | |||||||
| Total Budget | 50000 | 60000 | 40000 | 45000 | 35000 | 30000 | 350000 | 500000 | 0 | <= | 1200000 | |||||||
| Kind of holes | Club house Type | |||||||||||||||||
| Straight par 5 | Dogleg par 5 | Straight par 4 | Dogleg par 4 | Long par 3 | Short par 3 | Standard | Big | |||||||||||
| Enjoyability points | 2 | 1.5 | 1.5 | 2 | 1.75 | 2.25 | 0 | 4 | ||||||||||
| Solution | 1 | 1 | 2 | 10 | 1 | 3 | 0 | 1 | ||||||||||
| Total Enjoybility | 39 | |||||||||||||||||
| Constraints | Straight par 5 | Dogleg par 5 | Straight par 4 | Dogleg par 4 | Long par 3 | Short par 3 | Standard | Big | LHS | RHS | This is the first improved version of the original model. In order to findout a fesible solution, in this case few changes have been made and these are, revision of land size for big size club house, and revision of total budget. All these changes are highlighted in different colors. It can be seen that land size for big club house is reduced to 3 acre. Further, total budget is increased to $1.27 million. This improved model is returning a total 39 enjoybility points. The details answer has shown in answer report 1 sheet. | |||||||
| Straight par 5 | 1 | 1 | >= | 1 | ||||||||||||||
| Dogleg par 5 | 1 | 1 | >= | 1 | ||||||||||||||
| Straight par 4 | 1 | 2 | >= | 2 | ||||||||||||||
| Dogleg par 4 | 1 | 10 | >= | 2 | ||||||||||||||
| Long par 3 | 1 | 1 | >= | 1 | ||||||||||||||
| Short par 3 | 1 | 3 | >= | 1 | ||||||||||||||
| Par 5 | 1 | 1 | 2 | <= | 4 | |||||||||||||
| Par 4 | 1 | 1 | 12 | <= | 14 | |||||||||||||
| Par 3 | 1 | 1 | 4 | <= | 4 | |||||||||||||
| Total Par | 5 | 5 | 4 | 4 | 3 | 3 | 70 | >= | 70 | |||||||||
| Total Par | 5 | 5 | 4 | 4 | 3 | 3 | 70 | <= | 72 | |||||||||
| Total number of hole | 1 | 1 | 1 | 1 | 1 | 1 | 18 | = | 18 | |||||||||
| Total acreage | 3 | 3.5 | 2 | 2.5 | 1 | 0.75 | 2 | 3 | 41.75 | >= | 36 | |||||||
| Total acreage | 3 | 3.5 | 2 | 2.5 | 1 | 0.75 | 2 | 3 | 41.75 | <= | 42 | |||||||
| Total Budget | 50000 | 60000 | 40000 | 45000 | 35000 | 30000 | 350000 | 500000 | 1265000 | <= | 1270000 | |||||||
| Engine: GRG Nonlinear | ||||||||||||||||||
| Solution Time: 2.891 Seconds. | ||||||||||||||||||
| Iterations: 2 Subproblems: 26 | ||||||||||||||||||
| Max Time Unlimited, Iterations Unlimited, Precision 0.000001 | ||||||||||||||||||
| Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Central | The answer report is showing that total 18 holes will be designed considering 10 dogleg par 4 holes, 3 short par 3 holes, 2 straight par 4 holes and rest 1 each along with big club house. This will return 39 enjoybility points towards golfer. | |||||||||||||||||
| Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 0%, Assume NonNegative | ||||||||||||||||||
| Cell | Name | Original Value | Final Value | |||||||||||||||
| $C$8 | Total Enjoybility Straight par 5 | 0 | 39 | |||||||||||||||
| Cell | Name | Original Value | Final Value | Integer | ||||||||||||||
| $C$7 | Solution Straight par 5 | 0 | 1 | Integer | ||||||||||||||
| $D$7 | Solution Dogleg par 5 | 0 | 1 | Integer | ||||||||||||||
| $E$7 | Solution Straight par 4 | 0 | 2 | Integer | ||||||||||||||
| $F$7 | Solution Dogleg par 4 | 0 | 10 | Integer | ||||||||||||||
| $G$7 | Solution Long par 3 | 0 | 1 | Integer | ||||||||||||||
| $H$7 | Solution Short par 3 | 0 | 3 | Integer | ||||||||||||||
| $I$7 | Solution Standard | 0 | 0 | Binary | ||||||||||||||
| Cell | Name | Cell Value | Formula | Status | Slack | |||||||||||||
| $K$11 | Straight par 5 LHS | 1 | $K$11>=$M$11 | Binding | 0 | |||||||||||||
| $K$12 | Dogleg par 5 LHS | 1 | $K$12>=$M$12 | Binding | 0 | |||||||||||||
| $K$13 | Straight par 4 LHS | 2 | $K$13>=$M$13 | Binding | 0 | |||||||||||||
| $K$14 | Dogleg par 4 LHS | 10 | $K$14>=$M$14 | Not Binding | 8 | |||||||||||||
| $K$15 | Long par 3 LHS | 1 | $K$15>=$M$15 | Binding | 0 | |||||||||||||
| $K$16 | Short par 3 LHS | 3 | $K$16>=$M$16 | Not Binding | 2 | |||||||||||||
| $K$17 | Par 5 LHS | 2 | $K$17<=$M$17 | Not Binding | 2 | |||||||||||||
| $K$18 | Par 4 LHS | 12 | $K$18<=$M$18 | Not Binding | 2 | |||||||||||||
| $K$19 | Par 3 LHS | 4 | $K$19<=$M$19 | Binding | 0 | |||||||||||||
| $K$20 | Total Par LHS | 70 | $K$20>=$M$20 | Binding | 0 | |||||||||||||
| $K$21 | Total Par LHS | 70 | $K$21<=$M$21 | Not Binding | 2 | |||||||||||||
| $K$23 | Total acreage LHS | 41.75 | $K$23>=$M$23 | Not Binding | 5.75 | |||||||||||||
| $K$24 | Total acreage LHS | 41.75 | $K$24<=$M$24 | Not Binding | 0.25 | |||||||||||||
| $K$25 | Total Budget LHS | 1265000 | $K$25<=$M$25 | Not Binding | 5000 | |||||||||||||
| $C$7 | Solution Straight par 5 | 1 | $C$7>=0 | Not Binding | 1 | |||||||||||||
| $D$7 | Solution Dogleg par 5 | 1 | $D$7>=0 | Not Binding | 1 | |||||||||||||
| $E$7 | Solution Straight par 4 | 2 | $E$7>=0 | Not Binding | 2 | |||||||||||||
| $F$7 | Solution Dogleg par 4 | 10 | $F$7>=0 | Not Binding | 4 | |||||||||||||
| $G$7 | Solution Long par 3 | 1 | $G$7>=0 | Not Binding | 1 | |||||||||||||
| $H$7 | Solution Short par 3 | 3 | $H$7>=0 | Not Binding | 3 | |||||||||||||
| $C$7:$H$7=Integer | ||||||||||||||||||
| $I$7=Binary | ||||||||||||||||||
| Kind of holes | Club house Type | |||||||||||||||||
| Straight par 5 | Dogleg par 5 | Straight par 4 | Dogleg par 4 | Long par 3 | Short par 3 | Standard | Big | |||||||||||
| Enjoyability points | 2 | 1.5 | 1.5 | 2 | 1.75 | 2.25 | 0 | 4 | ||||||||||
| Solution | 2 | 1 | 2 | 9 | 1 | 3 | 1 | 0 | ||||||||||
| Total Enjoybility | 35 | |||||||||||||||||
| Constraints | Straight par 5 | Dogleg par 5 | Straight par 4 | Dogleg par 4 | Long par 3 | Short par 3 | Standard | Big | LHS | RHS | ||||||||
| Straight par 5 | 1 | 2 | >= | 1 | In this, the analyst further tried to improve the model performance by changing total land avaialbility. However, the model return less enjoybility score compared to model 1. In fact other possible changes are also indicating less enjoybility score. hence, model 1 has ben considered as the optimal model. | |||||||||||||
| Dogleg par 5 | 1 | 1 | >= | 1 | ||||||||||||||
| Straight par 4 | 1 | 2 | >= | 2 | ||||||||||||||
| Dogleg par 4 | 1 | 9 | >= | 2 | ||||||||||||||
| Long par 3 | 1 | 1 | >= | 1 | ||||||||||||||
| Short par 3 | 1 | 3 | >= | 1 | ||||||||||||||
| Par 5 | 1 | 1 | 3 | <= | 4 | |||||||||||||
| Par 4 | 1 | 1 | 11 | <= | 14 | |||||||||||||
| Par 3 | 1 | 1 | 4 | <= | 4 | |||||||||||||
| Total Par | 5 | 5 | 4 | 4 | 3 | 3 | 71 | >= | 70 | |||||||||
| Total Par | 5 | 5 | 4 | 4 | 3 | 3 | 71 | <= | 72 | |||||||||
| Total number of hole | 1 | 1 | 1 | 1 | 1 | 1 | 18 | = | 18 | |||||||||
| Total acreage | 3 | 3.5 | 2 | 2.5 | 1 | 0.75 | 2 | 3 | 41.25 | >= | 36 | |||||||
| Total acreage | 3 | 3.5 | 2 | 2.5 | 1 | 0.75 | 2 | 3 | 41.25 | <= | 44 | |||||||
| Total Budget | 50000 | 60000 | 40000 | 45000 | 35000 | 30000 | 350000 | 500000 | 1120000 | <= | 1270000 | |||||||
| Engine: GRG Nonlinear | ||||||||||||||||||
| Solution Time: 2.734 Seconds. | ||||||||||||||||||
| Iterations: 1 Subproblems: 28 | ||||||||||||||||||
| Max Time Unlimited, Iterations Unlimited, Precision 0.000001 | ||||||||||||||||||
| Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Central | ||||||||||||||||||
| Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative | ||||||||||||||||||
| Cell | Name | Original Value | Final Value | |||||||||||||||
| $C$8 | Total Enjoybility Straight par 5 | 0 | 35 | |||||||||||||||
| Cell | Name | Original Value | Final Value | Integer | ||||||||||||||
| $C$7 | Solution Straight par 5 | 0 | 2 | Integer | ||||||||||||||
| $D$7 | Solution Dogleg par 5 | 0 | 1 | Integer | ||||||||||||||
| $E$7 | Solution Straight par 4 | 0 | 2 | Integer | ||||||||||||||
| $F$7 | Solution Dogleg par 4 | 0 | 9 | Integer | ||||||||||||||
| $G$7 | Solution Long par 3 | 0 | 1 | Integer | ||||||||||||||
| $H$7 | Solution Short par 3 | 0 | 3 | Integer | ||||||||||||||
| $I$7 | Solution Standard | 0 | 1 | Binary | ||||||||||||||
| Cell | Name | Cell Value | Formula | Status | Slack | |||||||||||||
| $K$11 | Straight par 5 LHS | 2 | $K$11>=$M$11 | Not Binding | 1 | |||||||||||||
| $K$12 | Dogleg par 5 LHS | 1 | $K$12>=$M$12 | Binding | 0 | |||||||||||||
| $K$13 | Straight par 4 LHS | 2 | $K$13>=$M$13 | Binding | 0 | |||||||||||||
| $K$14 | Dogleg par 4 LHS | 9 | $K$14>=$M$14 | Not Binding | 7 | |||||||||||||
| $K$15 | Long par 3 LHS | 1 | $K$15>=$M$15 | Binding | 0 | |||||||||||||
| $K$16 | Short par 3 LHS | 3 | $K$16>=$M$16 | Not Binding | 2 | |||||||||||||
| $K$17 | Par 5 LHS | 3 | $K$17<=$M$17 | Not Binding | 1 | |||||||||||||
| $K$18 | Par 4 LHS | 11 | $K$18<=$M$18 | Not Binding | 3 | |||||||||||||
| $K$19 | Par 3 LHS | 4 | $K$19<=$M$19 | Binding | 0 | |||||||||||||
| $K$20 | Total Par LHS | 71 | $K$20>=$M$20 | Not Binding | 1 | |||||||||||||
| $K$21 | Total Par LHS | 71 | $K$21<=$M$21 | Not Binding | 1 | |||||||||||||
| $K$23 | Total acreage LHS | 41.25 | $K$23>=$M$23 | Not Binding | 5.25 | |||||||||||||
| $K$24 | Total acreage LHS | 41.25 | $K$24<=$M$24 | Not Binding | 2.75 | |||||||||||||
| $K$25 | Total Budget LHS | 1120000 | $K$25<=$M$25 | Not Binding | 150000 | |||||||||||||
| $C$7 | Solution Straight par 5 | 2 | $C$7>=0 | Binding | 0 | |||||||||||||
| $D$7 | Solution Dogleg par 5 | 1 | $D$7>=0 | Not Binding | 1 | |||||||||||||
| $E$7 | Solution Straight par 4 | 2 | $E$7>=0 | Not Binding | 2 | |||||||||||||
| $F$7 | Solution Dogleg par 4 | 9 | $F$7>=0 | Not Binding | 9 | |||||||||||||
| $G$7 | Solution Long par 3 | 1 | $G$7>=0 | Not Binding | 1 | |||||||||||||
| $H$7 | Solution Short par 3 | 3 | $H$7>=0 | Not Binding | 3 | |||||||||||||
| $C$7:$H$7=Integer | ||||||||||||||||||
| $I$7=Binary | ||||||||||||||||||
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