Illustration of a constraint model for optimal outsourcing decision

Lets assume the client has shared the following volumetric and requested the service provider to bid for the Application maintenance deal:

Guiding factors:

Utilization %	60%
Call Data Period	1 Month

Call Characteristics:

Domain	Technology	Sev 1	Sev 2	Sev 3
Billing Application	Java	3	15	13
Customer Care	.Net	5	10	28

Required SLA:

		in Minutes
	Availability	Response Time	Resolution Time	Actual Resolution time (Billing)	Actual Resolution time (Customer Care)
Sev 1	24/7	5	60	45	60
Sev 2	8/5	15	240	160	173
Sev 3	8/5	120	480	300	390

Based on the above details we can apply the step-wise resolution step to shape the deal:

Step 1: Assuming that the demand is even and the incoming calls has a poisson distribution, the l

Since Sev 1 calls are 24/7 availability we are assuming the pattern is evenly spread over 24 hrs, 30 days and 60 minutes and l for sev 1 is Number of calls/(24*30*60)

	Sev 1	Sev 2	Sev 3
Billing Application	0.0001	0.0016	0.0014
Customer Care	0.0001	0.0010	0.0029

Step 2: Assuming the service rate is an exponential distribution, the m

Service rate = 1/(Actual resolution time in minutes)

	Sev 1	Sev 2	Sev 3
Billing Application	0.0222	0.0063	0.0033
Customer Care	0.0167	0.0058	0.0026

Step 3: The number of resources for each domain, the r

	Sev 1	Sev 2	Sev 3	Total	# of resource
Billing Application	0.0052	0.4167	0.6771	1.0990	2
Customer Care	0.0116	0.3003	1.8958	2.2078	3

Step 4: The deal optimization based on the above characteristics can be illustrated as follows:

Lets’ assume the following assumptions:

1. We consider 2 locations US and India for this deal

2. We assume there are no shift requirements and the support will be on-call basis

3. There is only 2 levels in workforce: Software engineer and System Analyst

4. The cost for onshore-offshore is as identified in the following table:

	All figures in USD per Hour
	India	US
System Analyst	21	65
Software engineer	19	60

5. Lets assume the pyramid definition is as follows:

	India	US	Engagement Pyramid
System Analyst	5%	95%	10%
Software engineer	95%	5%	90%

The objective function can be laid out as follows:

Min X_onshoreC_{onshore, System Analyst}R_{Onshore,System Analyst} + X_onshoreC_{onshore, Software Engineer} R_{Onshore,Software Engineer} +X_OffshoreC_{Offshore, System Analyst}R_{Offshore,System Analyst} + X_offshoreC_{offshore, Software Engineer} R_{Offshore,Software Engineer}

Based on the above equation we can represent it as follows:

Min X_onshore*65*R_{Onshore,System Analyst} + X_onshore*60*R_{Onshore,Software Engineer} +X_Offshore*21*R_{Offshore,System Analyst} + X_offshore*19* R_{Offshore,Software Engineer}

The constraint for this is defined as follows:

R_{Onshore,System Analyst} + R_{Onshore,Software Engineer} <= 5*X_onshore

R_{Offshore,System Analyst} + R_{Offshore,Software Engineer} <= 5*X_offshore

R_{Onshore,System Analyst}+ R_{Offshore,System Analyst} <= 0.5

R_{Onshore,Software Engineer}+ R_{Offshore,Software Engineer} <= 4.5

X_onshore + X_offshore = 1

X_offshore - X_onshore >= 0

Any Optimization engineer will be able to solve the above equation using a tool to arrive at the optimal deal parameters. We did the above and identified the following optimal function.

The above is an approach 1 for constraint model for outsourcing deal.....how do we do this in approach 2? What are the limitations of the above model?

We'll revisit these issues later...any ideas and recommendations....