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Characteristics of coordination schemes
There are a number of different types of channel coordination contracts but they are not all complete. In the place of a complete classification, a set of features are explained below which generalizes the existing taxonomies by allowing classification along multiple viewpoints.
Problem characteristics
Horizon
Most of the related models consider either one-period horizon or two-period horizon with forecast update. In the latter, the production can be based on the preliminary forecast with normal production mode or on the updated forecast with emergency production, which means shorter lead-time, but higher cost. Besides, the horizon can consist of multiple periods and it can be even infinite. The practically most widespread approach is the rolling horizon planning, i.e., updating and extending an existing plan in each period.
Number of products
Almost all contract-based models regard only one product. Some models study the special cases of substitute or complementary products. However, considering more products in the general case is necessary if technological or financial constraints like capacity or budget limits exist.
Demand characteristic
On one hand, the demand can be stochastic (uncertain) or deterministic. On the other hand, it can be considered static (constant over time) or dynamic (e.g., having seasonality).
Risk treatment
In most of the models the players are regarded to be risk neutral. This means that they intend to maximize their expected profit (or minimize their expected costs). However, some studies regard risk averse players who want to find an acceptable trade-off considering both the expected value and the variance of the profit.
Shortage treatment
The models differ in their attitude towards stockouts. Most authors consider either backlogs, when the demand must be fulfilled later at the expense of providing lower price or lost sales which also includes some theoretical costs (e.g., loss of goodwill, loss of profit, etc.). Some models include a service level constraint, which limits the occurrence or quantity of expected stockouts. Even the 100% service level can be achieved with additional or emergency production (e.g., overtime, outsourcing) for higher costs.
Parameters and variables
This viewpoint shows the largest variations in the different models. The main decision variables are quantity-related (production quantity, order quantity, number of options, etc.), but sometimes prices are also decision variables. The parameters can be either constant or stochastic. The most common parameters are related to costs: fixed (ordering or setup) cost, production cost and inventory holding cost. These are optional; many models disregard fixed or inventory holding costs. There exist numerous other parameters: prices for the different contracts salvage value, shortage penalty, lead-time, etc.
Basic model and solution technique
Most of the one-period models apply the newsvendor model. On two-period horizon, this is extended with the possibility of two production modes. On a multiple period horizon the base-stock, or in case of deterministic demand the EOQ models are the most widespread. In such cases the optimal solution can be determined with simple algebraic operations. These simple models usually completely disregard technological constraints; however, in real industrial cases resource capacity, inventory or budget constraints may be relevant. This necessitates more complex models, such as LP, MIP, stochastic program, and thus more powerful mathematical techniques may be required.
As for the optimization criteria, the most usual objectives are the profit maximization or cost minimization, but other alternatives are also conceivable, e.g., throughput time minimization. Considering multiple criteria is not yet prevalent in the coordination literature.
Decentralization characteristics
Number and role of the players
The most often studied dilemmas involve the two players and call them customer and supplier (or buyer-seller). There are also extensions of this simple model: the multiple customers with correlated demand and the multiple suppliers with different production parameters. Multi-echelon extensions are also conceivable, however, sparse in the literature. When the coordination is within a supply chain (typically a customer-supplier relation), it is called vertical, otherwise horizontal. An example for the latter is when different suppliers of the same customer coordinate their transportation.
Sometimes the roles of the participants are also important. The most frequently considered companies are manufacturers, retailers, distributors or logistic companies.
Relation of the players
One of the most important characteristics of the coordination is the power relations of the players. The power is influenced by several factors, such as possessed process know-how, number of competitors, ratio in the value creation, access to the market and financial resources.
The players can behave in a cooperative or opportunistic way. In the former case, they share a common goal and act like a team, while in the latter situation each player is interested only in its own goals. These two behaviors are usually present in a mixed form, since the opportunistic claims for profitability and growth are sustainable usually only with a certain cooperative attitude.
The relation can be temporary or permanent. In the temporary case usually one- or two-period models are applied, or even an auction mechanism. However, the coordination is even more important in permanent relations, where the planning is usually done in a rolling horizon manner. When coordinating a permanent supply relation, one has to consider the learning effect, i.e., players intend to learn each other’s private information and behavior.
Goal of the coordination
The simplest possible coordination is aimed only at aligning the (material) flows within the supply chain in order to gain executable plans and avoid shortages. In a more advanced form of coordination, the partners intend to improve supply chain performance by approaching or even achieving the optimal plan according to some criteria. Generally, a coordinated plan may incur losses for some of the players compared to the uncoordinated situation, which necessitates some kind of side-payment in order to provide a win-win situation. In addition, even some sort of fairness may be required, but it is not only hard to guarantee, but even to define.
Most of the coordination approaches requires that the goal should be achieved in an equilibrium in order to exclude the possibility that an opportunistic player deviates from the coordinated plan.
Information structure
Some papers study the symmetric information case, when all of the players know exactly the same parameters. This approach is very convenient for cost and profit sharing, since all players know the incurring system cost. The asymmetric case, when there is an information gap between the players is more realistic, but poses new challenges. The asymmetry typically concerns the cost parameters, the capacities or the quantities like the demand forecast. The demand and the forecast are often considered to be qualitative, limited to only two possible values: high and low. In case of stochastic demand, the uncertainty of the forecasts can also be private information.
Decision structure
The decision making roles of the players depend on the specified decision variables. However, there is a more-or-less general classification in this aspect: forced and voluntary compliance. Under forced compliance the supplier is responsible for satisfying all orders of the customer, therefore it does not have the opportunity to decide about the production quantity. Under voluntary compliance, the supplier decides about the production quantity and it cannot be forced to fill an order. This latter is more complex analytically, but more realistic as well. Even so, several papers assume that the supplier decides about the price and then the customer decides the order quantity.
Game theoretic model
From the viewpoint of game theory the models can take cooperative or non-cooperative approaches. The cooperative approach studies, how the players form coalitions therefore these models are usually applied on the strategic level of network design. Other typical form of cooperative games involves some bargaining framework—e.g., the Nash bargaining model—for agreeing upon the parameters of the applied contracts.
On the other hand, on the operational level, the non-cooperative approach is used. Usually the sequential Stackelberg game model is considered, where one of the players, the leader moves first and then the follower reacts. Both cases—the supplier or the customer as the Stackelberg leader—are widely studied in the literature. In case of information asymmetry, a similar sequential model is used and it is called principal–agent setting. The study of the long-term supply relationship can also be modeled as a repeated game.
To sum up, collaboration generally consists of a cooperative, followed by a non-cooperative game. However, most researches concentrate only on one of the phases.
Involvement of a mediator
Some coordination mechanisms require the existence of an independent, trusted third party. If such a mediator exists, the powerful theory of the market mechanism design can be applied for channel coordination. Although at first glance the involvement of a third party seems to be unrealistic, in the area of planning such mediators already exist as application service providers.
