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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 0

Fabric

Volume (yds.)