inequity aversion in screening contracts: experimental evidence and model analysis
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Inequity aversion in screening contracts: experimental evidence and model analysis. IFORS, 15 th July 2014, Guido Voigt . Motivation Model Supply chain performance Outlook and discussion. Agenda. Asymmetric information (may) deteriorate supply chain performance …. - PowerPoint PPT PresentationTRANSCRIPT
Inequity aversion in screening contracts: experimental evidence and model analysis
IFORS, 15th July 2014, Guido Voigt
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G. Voigt –Magdeburg,
Agenda
• Motivation• Model• Supply chain performance• Outlook and discussion
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G. Voigt –Magdeburg,
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
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G. Voigt –Magdeburg,
Screening contracts: Basic Idea
Supplier (uninformed)Low cost buyer
High cost buyer?Contract “low”
Contract “high”
Buyers: Profit maximizer
Empirical: Buyers are insensitive to
small payoff differences
Research questions:• Impact on Supply Chain Performance ?• Behavioral robust contract design ?
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G. Voigt –Magdeburg,
Agenda
• Motivation• Model• Supply chain performance• Outlook and discussion
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G. Voigt –Magdeburg,
Model
• 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
Supplier (S) Buyer (B)
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G. Voigt –Magdeburg,
Classical Screening Model
• Probability distribution pi w.r.t. holding costs hi, i=1,…,n; h1<h2<…<hn
• Screening idea: One contract Ai = < qi, wi > for each possible holding cost realization hi
, 1
1 1
max ( ) . .
, 1,..., 12 2
2
i i
nw q S i ii
i
i ii i i i
nn n
fE P p d w s tq
h hw d q w d q i n
hw d q R d
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G. Voigt –Magdeburg,
Example for 3 holding cost levels - low (l), med (m), high (h)
ql= 400 wl= 9,83qm= 189 wm= 10,89qh= 129 wh= 11,78
Buyer's cost ql, wl qm, wm qh, wh Alternative
hl 1183 1183 1243 1500
hm 1583 1371 1371 1500
hh 1983 1560 1500 1500Supplier‘s profit 783 666 558 0
2 2l l
l l m mh hw d q w d q
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G. Voigt –Magdeburg,
Experimental results – Classical screening contracts
• Inderfurth et. al (2012):
• Profit maximum ≈ 70%
• Near profit maximum (10 cent difference) ≈ 26%– Huge cost effect on supply chain performance
• Other ≈ 4%
ql, wl
qm, wm
qh, wh
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G. Voigt –Magdeburg,
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:
, 111
max ( ) 1i i
nw q S i i i i ii
i i
f fE P p d w wq q
• Supplier does not exhibit inequity aversion if it is too costly• Frequency αi depends (linearly) on payoff difference ti between
alternatives
1 1, 1,..., 12 2
i ii i i i i
h hw t d q w d q i n
Slack
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G. Voigt –Magdeburg,
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
, , 111
1 1
max ( ) ( ) 1 ( )
. .
, 1,..., 12 2
2
i i i
nw q t S i i i i ii
i i
i ii i i i i
nn n n
f fE P p d t w t wq q
s th hw t d q w d q i n
hw t d q R d
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G. Voigt –Magdeburg,
Buyer's cost ql, wl qm, wm qh, wh Alternative
hl 1072 1106 1138 1500
hm 1472 1289 1289 1500
hh 1872 1471 1440 1500Supplier‘s profit 672 578 532 0
Behaviorally robust contract
ql= 400 wl= 8,72 tl= 0,35qm= 183 wm= 10,15 tm= 0qh= 151 wh= 10,62 th= 0,6
ql= 400 wl= 9,83qm= 189 wm= 10,89qh= 129 wh= 11,78
„Classical“ contract parameters
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G. Voigt –Magdeburg,
Agenda
• Motivation• Model• Supply chain performance• Outlook and discussion
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G. Voigt –Magdeburg,
Supply chain performance
Fraction of strictly profit maximizing buyers
Classical screening benchmark
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G. Voigt –Magdeburg,
Supply chain performance
Fraction of strictly profit maximizing buyers
Classical screening benchmark
Classical contract parameters
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G. Voigt –Magdeburg,
Supply chain performance
Fraction of strictly profit maximizing buyers
Classical screening benchmark
Classical contract parameters
Behavioral robust contract parameters
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G. Voigt –Magdeburg,
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
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G. Voigt –Magdeburg,
Numerical example: 3 buyer types• wi irrelevant for supply chain performance
• Behavioral robust parameters: Order size– q2 is lower (less likely)– q3 is higher (more likely)
+-
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G. Voigt –Magdeburg,
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)
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Parameters numerical example
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Complete set of profit/cost impact – Behavioral robust contract
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Impact of bunching (1/2)
0.1
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Impact of bunching (2/2)
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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. S29-S33
• Basov, S. and Danilkina, S. (2006). Quality and product variety in a monopolistic screening model with nearly rational consumers, Proceedings of the 35th 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