Download COORDINATION OF SUPPLY CHAIN WITH BUYER`S

JOURNAL OF INDUSTRIAL AND
MANAGEMENT OPTIMIZATION
Volume 3, Number 4, November 2007
Website: http://AIMsciences.org
pp. 715–726
COORDINATION OF SUPPLY CHAIN WITH BUYER’S
PROMOTION
Juliang Zhang
Research Institute of Material Flow
School of Economics and Management
Beijing Jiaotong University
Beijing, 100044, China
(Communicated by Xinmin Yang)
Abstract. In this paper, we develop a model to analyze the coordination of a
supply chain with the demand influenced by the buyer’s promotion. The supply chain consists of a supplier and a group of homogeneous buyers. The buyers
choose inventories ex ante and promotional levels ex post. The annual demand
rate depends on the promotional level and the operating cost—including the
ordering and inventory holding cost—depends on the promotional level and
the order quantity. It is shown that quantity discount alone is not sufficient
to guarantee joint profit maximization. Then we propose a contract, discount
quantity with transfer profit contract, and show that this contract can coordinate the supply chain. Moreover, it is shown that this policy is robust because
it can allocate the supply chain profit arbitrarily between the supplier and the
buyer and lead the buyer to choose the joint optimal promotional level and the
supplier need not to observe and verify the buyer’s promotional level. For the
special case that the operating cost is a fixed constant, we show that there is no
contract which can coordinate the supply chain if the promotion is unobservable and unverifiable and the discount policy can guarantee the coordination
of the supply chain if the promotion is observable and verifiable.
1. Introduction. A supply chain consists of different members each having his
own decision variables. However, each member’s decision does affect other member’s
actions. For example, if a retailer takes an action (e.g., reduce promotional level)
which causes a decrease in the volume of a particular product, all members in the
supply chain observe the decreased volume and then react to it. Hence numerous
interactions take place between the channel decisions. Even if a supplier does not
observe a buyer’s action, the supplier may still respond to that action because the
supplier does observe a change in product volume. This fact illustrates that the
buyer can exercise some control over the supplier. This is true for all members
in the supply chain. Each member in the supply chain influences other members’
decision in this supply chain. Hence the members in a supply chain must coordinate
their decisions in order to achieve the maximal joint supply chain profit. Because of
this, supply chain coordination and cooperation have attracted numerous attentions
2000 Mathematics Subject Classification. Primary: 46N10, 47N10.
Key words and phrases. supply chain, discount quantity, promotion, contract, deterministic
models.
This work is supported in part by the National Natural Science Foundation of China (Grant No.
70302003, 70501014,70671100)and Science Foundation of Beijing Jiaotong University(2007RC014).
715