Coordination by Option Contracts in a Retailer-Led Supply Chain with

WANG Xiaolong (王小龙) et al:Coordination by Option Contracts in a Retailer-Led …
Table 1 illustrates the profit allocation issues in detail.
For these calculations, the new contract is feasible
only when 34.8o2 43.8.
For low o 2 in this range,
each party becomes strictly better off. In particular,
consider the best profit allocation situations for which
each side gets a double-digit share of the extra profit.
When o 2 is around 40, the supplier will get more
than 60% of the extra system profit which is double
what he earned before coordination. Such a rosy profit
improvement surely offers a strong incentive for the
supplier to accept the new contract. Most interestingly,
such profit allocations correspond to o2 39.6 which
N N
implies e+ o1 w1
and d = d1=
0. Thus, order
postponement (until the demand uncertainty is resolved)
can be beneficial to each party. This is contrast
to the traditional thought that suppliers always welcome
as-early-as-possible orders. Our opinion is that
suppliers hate late orders mostly because they make
the work of arranging production schedules more difficult.
However, a properly designed incentive mechanism,
which both clarifies the quantity that the supplier
should produce and brings extra profit, eliminates
these negative concerns. Such a result, however, needs
further proof from theory and practice.
Table 1 Profit allocations between the two parties
Extra profit allocation on supplier
Second-period option price
(% of improvement scope)
0 100
34.8 1
… …
39.6 67
39.9 63
40.2 58
40.5 53
40.8 48
41.1 44
41.4 39
41.7 35
42.0 30
42.3 26
… …
43.8 3
Note: For simplicity, we state here only the allocation status for the supplier.
Its counterpart for the retailer can be calculated since the sum is equal
to 1.
4 Conclusions
579
This analysis considers the coordination of option contracts
in a retailer-led supply chain where the retailer
designs the contract and the supplier’s production
needs to be coordinated with the contract. Consider the
case where the supplier operates two modes of production
and the retailer has the ability to update the demand
forecast as the selling season approaches. Within
this contract class, a set of pricing conditions are defined
that align the supplier and retailer to act in the
best interests of the channel. The analysis leads to
some interesting results.
First, option prices should be negatively correlated
to the price and should be in a relevant range. This
gives a trade-off between the higher unit compensation
the supplier requires and the lower repurchasing price
he will get. To assure that the option mechanism is an
effective incentive, the option prices should be within a
relevant range. The second-period option price should
be no greater than the difference between the second-
period unit production costs and the salvage value.
Otherwise, the supplier will earn little due to the rapidly
decreasing exercise price and the coordination will
fail.
Second, the first-period option price should be no
greater than the second-period price and should be
linearly correlated to the second-period option price
when the latter is beyond some threshold. This result is
true regardless of the specific functional form of the
market demand or market signal.
Third, the retailer’s ordering behavior is influenced
by the dual effect of the predictive power of the new
market information and option prices. Some extreme
pricing cases may result in the ordering behavior being
independent of the new market information. The influence
pattern is so complex that there is no closed
form solution to the retailer’s first-period optimal order
quantity. Fortunately, this does not prevent exploring
the optimal pricing conditions which are stated in
Proposition 3. A numerical example is given for the
profit allocation issues. An interesting result is that
order postponement may be beneficial to both parties,
though this needs further theoretical proof.