7-2 Module: Data-based recommendations and Outcomes

Data

Use in Exhibit 1: Product Production Requirements
Criteria/Vendor	Face Cream	Body Cream	Hand Cream
Labor (hour/carton)
Stage 1	1.5	1.8	1.0
Stage 2	0.8	1.0	0.5
Total labour hours per carton	2.3	2.8	1.5
Material (pounds/carton)
Water	8.0	6.0	7.0
Oil	1.0	3.0	2.0
Scents and Colors	0.5	0.3	0.4
Emulsifiers	0.5	0.7	0.6
Total production overheads	10.0	10.0	10.0
Assume W commodities of face cream are produced; X body cream and Y hand cream
Production function will be given by;
(2.3 W+ 10W) + (2.8X+10X) + (1.5Y + 10Y)= Z USER: This is the production function
where Z is the total cost of production
12.3W + 12.8X + 11.5Y = Z

A. Labor Stages - Material Req

SHIFT DETAILS
Face Cream, Shift 1	Item	Resource Required	$/Unit	Cost ($)		Face Cream, Shift 2	Item	Resource Required	$/Unit	Cost ($)
	Labor Stage 1	1.50	10.00	15.00			Labor Stage 1	1.50	20.00	30.00
	Labor Stage 2	0.80	10.00	8.00			Labor Stage 2	0.80	20.00	16.00
	Water	8.00	10.00	80.00			Water	8.00	20.00	160.00
	Oils	1.00	10.00	10.00			Oils	1.00	20.00	20.00
	Scents/Colors	0.50	10.00	5.00			Scents/Colors	0.50	20.00	10.00
	Emulsifiers	0.50	10.00	5.00			Emulsifiers	0.50	20.00	10.00
	Total			123.00			Total			246.00
Body Cream, Shift 1	Item	Resource Required	$/Unit	Cost ($)		Body Cream, Shift 2	Item	Resource Required	$/Unit	Cost ($)
	Labor Stage 1	1.80	15.00	27.00			Labor Stage 1	1.80	10.00	18.00
	Labor Stage 2	1.00	15.00	15.00			Labor Stage 2	1.00	10.00	10.00
	Water	6.00	15.00	90.00			Water	6.00	10.00	60.00
	Oils	3.00	15.00	45.00			Oils	3.00	10.00	30.00
	Scents/Colors	0.30	15.00	4.50			Scents/Colors	0.30	10.00	3.00
	Emulsifiers	0.70	15.00	10.50			Emulsifiers	0.70	10.00	7.00
	Total			192.00			Total			128.00
Hand Cream Shift 1	Item	Resource Required	$/Unit	Cost ($)		Hand Cream, Shift 2	Item	Resource Required	$/Unit	Cost ($)
	Labor Stage 1	1.00	20.00	20.00			Labor Stage 1	1.00	15.00	15.00
	Labor Stage 2	0.50	20.00	10.00			Labor Stage 2	0.50	15.00	7.50
	Water	7.00	20.00	140.00			Water	7.00	15.00	105.00
	Oils	2.00	20.00	40.00			Oils	2.00	15.00	30.00
	Scents/Colors	0.40	20.00	8.00			Scents/Colors	0.40	15.00	6.00
	Emulsifiers	0.60	20.00	12.00			Emulsifiers	0.60	15.00	9.00
	Total			230.00			Total			172.50
Production Function
12.3W + 12.8X + 11.5Y = Z
Assuming production of;
10 face creams in shift 1, 15 body creams and 20 hand creams, the above calculations based on the production cost will be as indcated in the production tables above
Shift 2
20 face creams in shift 2, 10 body creams and 15 hand creams, the above calculations based on the production cost will be as indicated in the tables 2 above

B. Summary Table

Linear Programming Model Formulation (8 production variable, 11 constraints, minimization problem)
	Face Cream, Shift 1	Face Cream, Shift 2	Face Cream, Subcontracted	Body Cream, Shift 1	Body Cream, Shift 2	Body Cream, Subcontracted	Hand Cream, Shift 1	Hand Cream, Shift 2
Cost	10.00	20.00	30.00	15.00	10.00	25.00	20.00	15.00	min
Labor 11	165.00	630.00		297.00	198.00		220.00	165.00	≤	1,675
Labor 21	315.00	336.00		567.00	378.00		420.00	315.00	≤	2,331
Labor 12	96.00	360.00		324.00	216.00		240.00	180.00	≤	1,416
Labor 22	330.00	440.00		594.00	396.00		440.00	330.00	≤	2,530
Water	80.00	160.00		90.00	60.00		140.00	105.00	≤	635
Oils	10.00	20.00		45.00	30.00		40.00	30.00	≤	175
Scents/Colors	5.00	10.00		4.50	3.00		8.00	6.00	≤	37
Emulsifiers	5.00	10.00		10.50	7.00		12.00	9.00	≤	54
Amount (FC)	1	1	1						≥	2
Amount (BC)				1	1	1			≥	2
Amount (HC)							1	1	≥	2

C. Production Schedule

	Production Schedule - Based on Sensitivity Analysis
		Optimal Production Plan
	Method/Product	Face Cream	Body Cream	Hand Cream
	Shift 1	0	13	14
	Shift 2	0	0	0
	Vendor	12	13	N/A
	Total	12	26	14
	Total cost:	$645.38
Based on the production fuction
12.3W + 12.8X + 11.5Y = Z
At optimal level;
Z = 0

D. Decision Tree

	Create a Production Decision Tree

PRODUCTION OF BODY CREAMS

FACE CREAM

BODY CREAM

HAND CREAM

BUY FROM VENDOR

MAKE

BUY FROM VENDOR

MAKE

MAKE

BUY FROM VENDOR

E. Graphs

	Graphs with Product Amount Changes - Costs Remain the Same
	Optimal Production Plan - ORIGINAL					Optimal Production Plan - increase production by 10%
	Method/Product	Face Cream	Body Cream	Hand Cream		Method/Product	Face Cream	Body Cream	Hand Cream
	Shift 1	0	13	14		Shift 1	0	14	15
	Shift 2	0	0	0		Shift 2	0	0	0
	Vendor	12	13	N/A		Vendor	13	14	0
	Total	12	26	18,000		Total	13	29	15
	Total cost:	$1,368,178.00				Total cost:	2,241.77
	Optimal Production Plan - increase production by 15%					Optimal Production Plan - increase production by 20%
	Method/Product	Face Cream	Body Cream	Hand Cream		Method/Product	Face Cream	Body Cream	Hand Cream
	Shift 1	0	15	16		Shift 1	0	16	17
	Shift 2	0	0	0		Shift 2	0	0	0
	Vendor	14	15	0		Vendor	14	16	0
	Total	14	30	20,700		Total	14	32	17
	Total cost:	2,343.67				Total cost:	2,445.56