Inequity aversion in a joint economic lot sizing environment with asymmetric holding cost information

Abstract

Screening contracts (or ‘menu of contracts’) are frequently used for aligning the incentives in supply chains with private information. In this context, it is assumed that all supply chain parties are strictly (expected) profit-maximizing. However, previous empirical work shows that this is a critical assumption. In fact, it seems that inequity adverse subjects are willing to invest money for achieving higher relative payoffs. Interestingly, the classical approach to design incentive compatible mechanisms gives the agent cheap leeway to increase relative pecuniary payoffs and thereby achieving more equitable profit allocations, because the agent is left (almost) indifferent between two contract alternatives. In other words, we argue (and actually observe in laboratory experiments) that this classical approach of contract design allows the agent to achieve more equitable outcomes at low cost. Since the agent’s better relative performance solely stems from reducing the principal’s payoffs, we observe a substantial negative impact on the overall supply chain performance. The present work relaxes the assumption of the profit-maximizing buyer (agent) in a serial supply chain for a lot sizing framework with asymmetrically distributed holding cost information and deterministic end-customer demand. The study provides researchers and managers an approach on how to account for disadvantageous inequity aversion (ie, the agent suffers from profits being lower than the principals profits) by designing a contract that anticipates such behaviour while providing a solution method for the resulting non-linear mathematical program. We denote the resulting contract as ‘behavioural robust’, since it limits the inefficiency losses that result if agents exhibit disadvantageous inequity aversion instead of being strictly profit-maximizing. A numerical study compares the advantages of the ‘behavioural robust’ contract against the classical screening contract. The results highlight that supply chain performance losses can be substantially reduced under the behavioural robust contract.

Keywords:

• asymmetric information
• supply chain coordination
• contracting
• behavioural modelling

Supplementary information accompanies this article on the Journal of the Operational Research Society website (www.palgrave-journals.com/jors)

Supplementary information accompanies this article on the Journal of the Operational Research Society website (www.palgrave-journals.com/jors)

Notes

1 We refer to economic lot sizing models under asymmetric information that are in nature similar to the stylized strategic lot sizing model presented in the underlying work to Corbett and de Groote, 2000; Ha, 2001; Sucky, 2006; Hsieh et al, 2008, and Voigt and Inderfurth, 2011.

2 Strictly indifferent means that there is no profit difference between two contract alternatives, whereas weakly indifferent means that an arbitrarily low incentive is given for choosing the self-selection contract.

3 Note that we are focusing on distributional fairness preferences as the main behavioural factor affecting the buyer’s contract choice behaviour and do not consider other forms of other-regarding preferences such as preference for reciprocal responses and trust (see Rabin, 1993; Dufwenberg and Kirchsteiger, 2004), altruistic behaviour (see Cox, 2004), procedural fairness (see Bolton et al, 2005), or peer-induced fairness (Ho et al, 2014).

4 Note that we are not incorporating supplier's advantageous inequity aversion (ie, the supplier suffers from having higher profits than the buyer). We are discussing potential effects of the principal’s inequality aversion in the outlook (see Section 7).

5 The participation constraint is calculated as if the charged transfer price is w^fictional=w+t. Thus, t can be interpreted as a fictional discount on a fictional transfer price, that is, w=w^fictional−t.

6 In the continuous formulation of the principal-agent problem, for example, bunching is ruled out by assuming a probability distribution that follows a monotone hazard rate. In contrast, in the discrete type case, bunching will never occur in the two-type case, or if the a priori distribution and utility function satisfies certain conditions (see Kerschbamer and Maderner, 1998).

7 Methods for optimal bunching have been developed for the continuous type case (see, eg, Nöldeke and Samuelson, 2007); however, to the best of our knowledge there have been no systematic approach being reported for the discrete type case.

8 In order to investigate the propensity of bunching, the numerical example is based on three buyer types, since bunching will never occur in the two-type case. For a discussion that two distinctive types are not sufficient for analysing all effects in screening models, see Kerschbamer and Maderner (1998).

9 Note that the effects of changes in the fixed cost level, f, are identical to changes of demand rate, d.