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Description
Case Study The Calhoun Textile Mill is in the process of deciding on a production schedule. The Calhoun Mill wishes to know how to weave the various fabrics it will produce during the coming quarter. The sales department has confirmed orders for each of the 15 fabrics that are produced by Calhoun. The variable cost to produce each fabric and the cost to purchase the fabric outside the mill are given. There are two types of looms: dobbie and regular. Dobbie looms can be used to make all fabrics, and are the only looms that can weave certain fabrics such as plaids. The amount of loom time needed to produce a yard of each fabric on each type of loom is given. Note that if a fabric can be woven on each type of loom, then the time per yard is the same on each. Calhoun has 90 regular looms and 15 dobbie looms. The mill operates continuously during the quarter, 24 hours per day, 7 days per week. Therefore for the upcoming quarter there are 196,560 regular loom hours (24x7x13x90) available and 32,760 dobbie loom hours (24x7x13x15) available. For this exercise, assume the time requirement to change over a loom from one fabric to another is negligible. Fabrics woven at Calhoun proceed to the finishing department in the mill and are sold. Any fabrics that are not woven in the mill because of limited capacity will be bought on the outside market, finished at the Calhoun Mill. Management would like to know how to allocate the looms to the fabrics and which fabrics to buy on the market.
Hint a) objective - minimize total cost b) constraints - meet all demand; don't use regular looms for fabrics 1-4; dont allocate more loom work than there is loom availability
Results While I expect all of you will be able to solve the LP, the challenge is in substantiating the answers - viz: Please explain if any fabric was sub-contracted, why it was chosen by the solver. If anything other than fabric 1-4 was done by Dobbie, why was Dobbie used for it. Any other thoughts on this model
Calhoun Model
| Calhoun Mills | ||||||||||||||
| Parameters: | ||||||||||||||
| Dobbie | Regular | |||||||||||||
| Fabric | Demand | Dobbie Rate | Regular Rate | Hrs./Yd. | Hrs./Yd. | Mill Cost | Sub. Cost | TIME COST | MONEY COST | INDEX | ||||
| 1 | 16500 | 4.653 | 0 | 0.215 | 0.000 | $0.6573 | $0.8000 | 3,546.10 | $0.1427 | 3546.0992907801 | $2,354.55 | $0.66 | ||
| 2 | 52000 | 4.653 | 0 | 0.215 | 0.000 | $0.5550 | $0.7000 | 11,175.59 | $0.1450 | 11175.5856436708 | $7,540.00 | $0.67 | ||
| 3 | 45000 | 4.653 | 0 | 0.215 | 0.000 | $0.6550 | $0.8500 | 9,671.18 | $0.1950 | 9671.1798839458 | $8,775.00 | $0.91 | ||
| 4 | 22000 | 4.653 | 0 | 0.215 | 0.000 | $0.5542 | $0.7000 | 4,728.13 | $0.1458 | 4728.1323877069 | $3,207.60 | $0.68 | ||
| 5 | 76500 | 5.194 | 5.194 | 0.193 | 0.193 | $0.6097 | $0.7500 | 14,728.53 | $0.1403 | 14728.532922603 | $10,732.95 | $0.73 | ||
| 6 | 110000 | 3.809 | 3.809 | 0.263 | 0.263 | $0.6153 | $0.7500 | 28,878.97 | $0.1347 | 0.2625360987 | 0.2625360987 | 28878.970858493 | $14,817.0000 | $0.51 |
| 7 | 122000 | 4.185 | 4.185 | 0.239 | 0.239 | $0.6477 | $0.8000 | 29,151.73 | $0.1523 | 29151.7323775388 | $18,580.6000 | $0.64 | ||
| 8 | 62000 | 5.232 | 5.232 | 0.191 | 0.191 | $0.4880 | $0.6000 | 11,850.15 | $0.1120 | 0.1911314985 | 0.1911314985 | 11850.1529051988 | $6,944.0000 | $0.59 |
| 9 | 7500 | 5.232 | 5.232 | 0.191 | 0.191 | $0.5029 | $0.7000 | 1,433.49 | $0.1971 | 1433.4862385321 | $1,478.2500 | $1.03 | ||
| 10 | 69000 | 5.232 | 5.232 | 0.191 | 0.191 | $0.4351 | $0.6000 | 13,188.07 | $0.1649 | 13188.0733944954 | $11,378.1000 | $0.86 | ||
| 11 | 70000 | 3.733 | 3.733 | 0.268 | 0.268 | $0.6417 | $0.8000 | 18,751.67 | $0.1583 | 18751.6742566301 | $11,081.0000 | $0.59 | ||
| 12 | 82000 | 4.185 | 4.185 | 0.239 | 0.239 | $0.5675 | $0.7500 | 19,593.79 | $0.1825 | 19593.7873357228 | $14,965.0000 | $0.76 | ||
| 13 | 10000 | 4.439 | 4.439 | 0.225 | 0.225 | $0.4952 | $0.6500 | 2,252.76 | $0.1548 | 2252.7596305474 | $1,548.0000 | $0.69 | ||
| 14 | 380000 | 5.232 | 5.232 | 0.191 | 0.191 | $0.3128 | $0.4500 | 72,629.97 | $0.1372 | 72629.9694189602 | $52,136.0000 | $0.72 | ||
| 15 | 62000 | 4.185 | 4.185 | 0.239 | 0.239 | $0.5029 | $0.7000 | 14,814.81 | $0.1971 | 14814.8148148148 | $12,220.2000 | $0.82 | ||
| 256,394.95 | ||||||||||||||
| Hours Available | ||||||||||||||
| Dobbie | 32760 | |||||||||||||
| Regular | 196560 | |||||||||||||
| 229320 | ||||||||||||||
| Decision variables: | Model outputs: | |||||||||||||
| Total | Total | Unmet | Used | Unused | ||||||||||
| Fabric | Dobbie | Regular | Subcontract | Fabric | Provided | Demand | Demand | Cost | Dobbie Hrs. | 32760 | 0 | |||
| 1 | 16500 | 0 | 0 | 1 | 16500 | 16500 | 0.00 | $10,845 | Reg. Hrs. | 196560 | 0 | |||
| 2 | 52000 | 0 | 0 | 2 | 52000 | 52000 | 0.00 | $28,860 | ||||||
| 3 | 45000 | 0 | 0 | 3 | 45000 | 45000 | 0.00 | $29,475 | ||||||
| 4 | 22000 | 0 | 0 | 4 | 22000 | 22000 | 0.00 | $12,192 | ||||||
| 5 | 0 | 76500 | 0 | 5 | 76500 | 76500 | 0.00 | $46,642 | ||||||
| 6 | 0 | 6871.5102711304 | 103128.48972887 | 6 | 110000 | 110000 | 0.00 | $81,574 | ||||||
| 7 | 0 | 122000 | 0 | 7 | 122000 | 122000 | 0.00 | $79,019 | ||||||
| 8 | 0 | 62000 | 0 | 8 | 62000 | 62000 | 0.00 | $30,256 | ||||||
| 9 | 0 | 7500 | 0 | 9 | 7500 | 7500 | 0.00 | $3,772 | ||||||
| 10 | 19039.262617666 | 49960.737382334 | 0 | 10 | 69000 | 69000 | 0.00 | $30,022 | ||||||
| 11 | 0 | 70000 | 0 | 11 | 70000 | 70000 | 0.00 | $44,919 | ||||||
| 12 | 0 | 82000 | 0 | 12 | 82000 | 82000 | 0.00 | $46,535 | ||||||
| 13 | 0 | 10000 | 0 | 13 | 10000 | 10000 | 0.00 | $4,952 | ||||||
| 14 | 0 | 380000 | 0 | 14 | 380000 | 380000 | 0.00 | $118,864 | ||||||
| 15 | 0 | 62000 | 0 | 15 | 62000 | 62000 | 0.00 | $31,180 | ||||||
| 154539.262617666 | 928832.247653464 | Total | $599,108 | |||||||||||
Results
Calhoun Mills
Dobbie 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16500 52000 45000 22000 0 0 0 0 0 19039.262617665969 0 0 0 0 0 Regular 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 0 0 0 76500 6871.5102711303953 122000 61999.999999999985 7500 49960.737382334031 70000 82000 10000 380000 62000 Subcontract 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 0 0 0 0 103128.48972886959 0 0 0 0 0 0 0 0 0Fabric
Volume (yds.)