Study on Quality Decisions in Supply Chain considering the Lagged Time and Retailers Competition

Table 1

Symbols and descriptions.

Symbol	Description
Φi(t)	Denotes the proportion of the service quality cost of retailer “i” paid by the manufacturer at time t and is a decision variable.
G(t)	Denotes the goodwill of a product at time t and is a decision variable.
	Denotes the quality level of the manufacturer’s product at t time and is a decision variable.
	Denotes the retailer’s service quality level at time t and is a decision variable; .
D	Denotes the lagged time when a product’s accumulated goodwill is affected by improving product quality, for example, by performing R&D, using new technology, and reforming the manufacturing process.
γ	Denotes quality’s efficiency to goodwill accumulation under the lagged time.
β	Denotes the competition coefficient between retailers.
λ	Denotes the discount rate.
PM	Denotes the manufacturer’s marginal profit.
PRi	Denotes the marginal profit of retailer “i.”
Di	Denotes the size of market demand at time t.
a	Indicates the potential market sales before an improvement in product quality and service quality; .
b	Indicates goodwill’s effectiveness on product market demand; b > 0.
μ	Indicates service quality’s effectiveness on product market demand > 0.
kM	Indicates cost parameter associated with product quality improvement by the manufacturer.
kRi	Indicates cost parameter associated with service quality improvement by the retailer i.
δ	Denotes the decline rate of product goodwill; δ > 0.