Analysis of back-office outsourcing contracts for financial services operations

Abstract

Managing back-office operations for financial services is a challenging task because of highly volatile and dynamic demand requirements. Lack of service inventories, the inability to backlog demand and significant shortage and overage costs complicate the problem. In such situations, outsourcing all or part of the demand to third-party vendors provides a viable and cost effective option for the firm. Motivated by the remittance processing operations of a Fortune 100 company we examine the usefulness of complementing in-house staffing with different outsourcing arrangements. We study capacity-based and volume-based contracts between a financial services firm and an outsourcing vendor. We examine the impact of demand characteristics on the parameters of contract choice. Through extensive numerical analysis, we ascertain that neither contract is universally preferred, but cost and revenue structures along with demand characteristics determine contract choice.

Appendix

Proof of Lemma 1:

• Since we are proving the analytical results for the single period formulation, we drop the subscript t form our notations. To prove the above result, we first represent the positive and negative deviations, S _k ⁺ and S _k ⁻, that satisfy the overtime constraint as follows:

  

  and

  

  Then, the firm's cost minimization objective can be written as:

  

  We will show that at p ^o=c _f , the firm incurs lower cost if it outsources zero volume and covers the demand requirements with only in-house operations rather than outsourcing V ^o with U number of full-time employees.

  Without any loss of generality, we pick, U+V ^o=M(<K).

  We denote, the firm's cost when it outsources zero volume and uses M number of full-time employees as Ω₁ ^o and when it outsources V ^o with U number of full-time employees as Ω₂ ^o. We need to show that Ω₁ ^o<Ω₂ ^o.

  
  

  Since, c _e ⩾0 and V ^o−k⩾0 for 0⩽k⩽V ^o, we can conclude from (A.1) and (A.2): Ω₁ ^o<Ω₂ ^o. Therefore, at p ^o=c _f , the firm will never outsource any volume. Hence, the optimal price charged by the vendor has to be less than c _f otherwise the vendor will earn zero revenue. When c _e =0, it follows that the optimal price charged by the vendor has to be ⩽c _f , that is, p ^o⩽c _f . □

Proof of Lemma 2:

• As we had done in the proof for Proposition 1, we first represent the positive and negative deviations, S _k ⁺ and S _k ⁻, that satisfy the overtime constraint as follows:

  

  and

  

  Then the firm's cost minimization objective can be written as follows:

  

  To prove that p ⁱ⩾c _f we first show that for p ⁱ=c _f the firm outsources all the workload. Let Ω₁ ⁱ be the firm's total cost if all the workload is outsourced and Ω₂ ⁱ be the firm's total cost if volume equal to d _jk ⁱ is kept in-house with U number of full-time employees at p ⁱ=c _f . We will show that Ω₁ ⁱ<Ω₂ ⁱ. d _jk ⁱ and U are picked without any loss of generality.

  

  Since, c _d >c _f , we denote c _d =c _f +c̃. Then

  

  Clearly, Ω₁ ⁱ<Ω₂ ⁱ.

  Therefore, at p ⁱ=c _f , the firm incurs lower costs if it outsources all the workload. Using similar arguments as above we can easily show that for p ⁱ<c _f it is optimal for the firm to outsource the entire workload. Hence, we prove that for p ⁱ⩽c _f , the vendor gets the entire volume of workload. For p ⁱ⩽c _f , vendor's profit would be maximum if he charges p ⁱ=c _f . So the vendor would never charge a price less than c _f . Therefore, c _f gives the lower bound for p ⁱ. □

Proof of Lemma 3:

• Suppose the optimal price charged by the vendor is p ^o and the optimal volume outsourced by the firm is V ^o and the number of full-time employees is U. Let Δ be the difference in cost for the firm if the firm outsources an unit less than V ^o and covers that by an additional full-time employee and if the firm outsources V ^o with U full-time employees at outsourcing price p ^o.

  We will show that Δ is non-decreasing in demand. Let Ω₁ ^o be the cost incurred by the firm if it outsources V ^o and employs U full-time employees and Ω₂ ^o be the cost incurred by the firm if it outsources V ^o−1 and employs U+1 full-time employees at outsourcing price p ^o.

  
  

  Therefore,

  

  As demand increases decreases by stochastic dominance.

  Hence, Δ is non-decreasing in demand. That is if demand increases it is not cost efficient for the firm to decrease volume outsourced and increase the number of full-time employees by even an unit volume. Hence, it is not beneficial for the firm to increase the number of full-time employees and decrease volume outsourced under identical prices when demand increases. □

Proof of Theorem 2:

• From Lemma 3 we know that at the same outsourcing price p ^o, the outsourcing volume of the firm is non-decreasing in demand. Hence, at the same price the vendor earns more revenue as demand increases. Therefore, the profit earned by the vendor at the optimal price has to be higher or at least equal to the profit earned under identical pricing. □

Proof of Theorem 3:

• We know from Lemma 2 that at p ⁱ=c _f the firm outsources all the volume and that p ⁱ⩾c _f . Suppose the optimal price charged at a certain demand volume is p ⁱ=c _f . Then as demand increases at p ⁱ the firm still outsources all the volume. Therefore, the revenue and in turn the profits for the vendor increases even if he continues to charge p ⁱ=c _f . However, if the optimal price charged is more then the increment in profit is also higher.

  From the firm's perspective the vendor either charges p ⁱ=c _f or a price >c _f as demand increases. Therefore, the firm cost has to increase because the firm now has to cover for more jobs and the outsourcing price is also non-decreasing. □