Inequity aversion in screening contracts experimental evidence and

Inequity aversion in screening contracts: experimental evidence and model analysis IFORS, 15 th July 2014, Guido Voigt

2 Agenda • • Motivation Model Supply chain performance Outlook and discussion G. Voigt –Magdeburg,

3 Asymmetric information in supply chains • Asymmetric information (may) deteriorate supply chain performance …. • …. evolve in many supply chain interactions – Joint lot-sizing (holding costs- and/or fixed costs) – Pricing decisions (production costs, end-customer demand) – Capacity decision (backorder costs, investment costs) • Solution concept: Screening contracts G. Voigt –Magdeburg,

4 Screening contracts: Basic Idea Supplier (uninformed) Contract “low” Contract “high” ? Low cost buyer High cost buyer Empirical: Buyers: Profit are insensitive to maximizer small payoff differences Research questions: • Impact on Supply Chain Performance ? • Behavioral robust contract design ? G. Voigt –Magdeburg,

5 Agenda • • Motivation Model Supply chain performance Outlook and discussion G. Voigt –Magdeburg,

6 Model Supplier (S) Buyer (B) • B asks S for smaller lot-sizes q – B: lower inventory holding costs (h /2 * q) – S: higher fixed costs ( f * d / q ) • B: may switch to alternative supplier (costs: R) – S does not know the buyer‘s actual benefit (h) – … but has to lower wholesale price ( w ) to induce higher order sizes G. Voigt –Magdeburg,

7 Classical Screening Model • Probability distribution pi w. r. t. holding costs hi, i=1, …, n; h 1<h 2<…<hn • Screening idea: idea One contract Ai = < qi, wi > possible holding cost realization hi G. Voigt –Magdeburg, for each

8 Example for 3 holding cost levels - low (l), med (m), high (h) ql= qm = q h= 400 189 129 Buyer's cost G. Voigt –Magdeburg, w l= w m= w h= 9, 83 10, 89 11, 78 ql, wl qm, wm qh, wh Alternative hl 1183 1243 1500 hm 1583 1371 1500 hh 1983 Supplier‘s profit 783 1560 666 1500 558 1500 0

9 Experimental results – Classical screening contracts • Inderfurth et. al (2012): ql, w l qm , w m q h, w h • Profit maximum ≈ 70% • Near profit maximum (10 cent difference) ≈ 26% – Huge cost effect on supply chain performance • Other ≈ 4% G. Voigt –Magdeburg,

10 Inequity aversion • Buyer hi not inequity averse with probability αi <wi, qi> • Buyer hi is inequity averse with probability (1 -αi) <wi+1, qi+1> • „Empirical“ objective function: • Supplier does not exhibit inequity aversion if it is too costly • Frequency αi depends (linearly) on payoff difference ti between alternatives Slack G. Voigt –Magdeburg,

11 Behaviorally robust Principal-Agent model • (OR) Challenge: Objective function not anymore concave, … but uni-modular for linear α(ti) • Note: „Bunching“, i. e. , qi=qi+1, occurs more frequently – derivation of optimal contract much more complex G. Voigt –Magdeburg,

12 Behaviorally robust contract „Classical“ contract parameters ql= 400 qm= 183 qh= 151 w l= w m= w h= 8, 72 10, 15 10, 62 Buyer's cost G. Voigt –Magdeburg, tl= 0, 35 t m= 0 th= 0, 6 ql= 400 qm= 189 qh= 129 wl= 9, 83 wm= 10, 89 wh= 11, 78 ql, wl qm, wm qh, wh Alternative hl 1072 1106 1138 1500 hm 1472 1289 1500 hh 1872 Supplier‘s profit 672 1471 578 1440 532 1500 0

13 Agenda • • Motivation Model Supply chain performance Outlook and discussion G. Voigt –Magdeburg,

14 Supply chain performance Classical screening benchmark Fraction of strictly profit maximizing buyers G. Voigt –Magdeburg,

15 Supply chain performance Classical contract parameters Classical screening benchmark Fraction of strictly profit maximizing buyers G. Voigt –Magdeburg,

16 Supply chain performance Classical contract parameters Behavioral robust contract parameters Classical screening benchmark Fraction of strictly profit maximizing buyers G. Voigt –Magdeburg,

17 Summary, conclusion, and Outlook • Critical assumption in screening theory: strict profit maximization • Neglecting behavioral irregularities leads to high performance losses • Main contribution – Derivation (and solution procedure) for the optimal „behavioral robust“ contract • Main limitation: linear dependency of αi and ti • Outlook: Experimental testing G. Voigt –Magdeburg,

18 Thanks! guido. voigt@ovgu. de G. Voigt –Magdeburg,

19 Numerical example: 3 buyer types • wi irrelevant for supply chain performance - + • Behavioral robust parameters: Order size – q 2 is lower (less likely) – q 3 is higher (more likely) G. Voigt –Magdeburg,

20 Relevant Literature • Probablistic choice models* and type dependent decision errors**: – The higher the profit of an alternative, the higher the probability that the alternative is chosen (not supported by experiments) – <wi, qi> ↔ <wi+1, qi+1> (not supported by experiment) • Increase pay-off differences between alternatives – Closest to the underlying work – Only for the case of 2 types (many aspects not addressed) – Restrictive assumption on „decision error“ (monotone hazard rate) * Basov and Danilkina (2006) and Basov (2009), ** Basov and Mirrless (2009) *** Laffont and Martimort, 2002 (Textbook) G. Voigt –Magdeburg,

21 Parameters numerical example G. Voigt –Magdeburg,

22 Complete set of profit/cost impact – Behavioral robust contract G. Voigt –Magdeburg,

23 Impact of bunching (1/2) G. Voigt –Magdeburg,

24 Impact of bunching (2/2) G. Voigt –Magdeburg,

25 References • Inderfurth, K. ; Sadrieh, A. and Voigt, G. (2012) The Impact of Information Sharing on Supply Chain Performance in Case of Asymmetric Information. Forthcoming in Production & Operations Management • Basov, S. (2009) Monopolistic Screening with Boundedly Rational Consumers, The Economic Record, 85, pp. S 29 -S 33 • Basov, S. and Danilkina, S. (2006). Quality and product variety in a monopolistic screening model with nearly rational consumers, Proceedings of the 35 th Australian Conference of Economists, pp. 1 -21, http: //www. business. curtin. edu. au/files/Basov_Danilkina. pdf • Laffont, J. -J. and Martimort, D. (2002) The theory of incentives: The Principal-Agent Model. Princeton University Press, Princeton/New Jersey G. Voigt –Magdeburg,