Scope and Definition of B2B E-Commerce
Definition 3.2 Business-to-business markets are platforms on which B2B e-commerce may be conducted directly between buyer and seller or
4. Quantitative Models for B2B E-Commerce
4.3 Supplier Procurement Risk Management
In addition, the supply manager will also decide on an order (up to) policy, by trading off holding and penalty costs. This results in a quasi news-vendor model that incorporates the different lead times based on the contract’s type and the length of the horizon. Let be the aggregate inventory and shortage costs. The dynamic programming for- mulation is then given by
where is the discount factor. The simulation-based conclusions are very insightful and interesting. As stated above, the long-term contracts are characterized by the rate of cost improvement, and the first conclusion is that long-term contracts are worth considering if is higher than a threshold value so as to compensate for the high initial investment, K, incurred. This partially explains why managers are reluctant to establish a long-term relation with a supplier. A “wait and see” policy is usually adopted in a non-stationary environment where usage of the short term contract (or use of the spot market in our case) is more suitable at the beginning; then, based on the dynamics of the spot price, as described by the drift and volatility of the price process, the decision is made to either wait longer or to lock in the price in a long-term contract. This strategy clearly depends on the initial price distribution known to the managers, as well as their risk aversion. If the probability that the price will go up is high and the decision-maker is highly risk averse, a long- term contract is selected in some cases from the very beginning, even with high initial fixed investment, K. The main contribution of this work is to identify, in fairly general settings, the factors that contribute to a contract selection. These factors are the fixed investments, the length of the planning horizon, the improvement rate for long-term contracts, the risk aversion of the decision maker and finally the price uncertainty of the spot markets.
lytically intractable. For instance, a major difficulty introduced in the Cohen and Agrawal model was the non-stationarity of the spot mar- ket price. Although this factor could be of primary concern, relaxing it should enable us to get the right insights concerning how the two methods of procurement evolve together. Once we make the stationar- ity assumption, which corresponds to an equilibrium stage, the setting is equivalent to a one-period problem, as shown above, because the state space is then independent of time. What is optimal in a particular period will remain optimal in a subsequent period, i.e., a myopic policy is opti- mal. In the following paragraph, we describe two models addressing the question of whether a spot market and long-term contracts will coexist or not, with many similarities but several significantly complementary features. The first one considers a general setting with non-linear pricing for both a long-term supply mode and a spot market while still allowing us to draw analytical conclusions on the optimal procurement strategy.
The second model assumes specific distributions of the spot price and the demand, but it identifies in some cases closed form solutions of the optimal procurement strategy, and studies the sensitivity of the model, in general, to the different factors involved, including the risk preference of the decision maker. In any case, both models show the optimality of a mixed strategy in such an environment, i.e., both modes of supply will coexist.
4.3.1 A General Approach for a Risk-Neutral Decision- Maker. The main objective of this model by Araman et al. (2000b) is to determine the optimal strategy that the buyer should adopt (in the following we will interchangeably use buyer and manufacturer) when two main modes of supply are available: a procurement channel through the spot market and a long-term channel defined by a reservation capacity level. In line with the widely known fact that corporations should be risk- neutral for decisions involving small investments relative to their overall wealth (which is true for most procurement decisions), we model the manufacturer as a risk-neutral decision-maker. Furthermore, to reflect the recent trend towards customized products and just-in-time manu- facturing, as manifested in the automotive industry, we model the man- ufacturer’s production environment as make-to-order (MTO), which has the additional benefit of making our model easier to follow. The man- ufacturer has to satisfy an aggregated (end-market) demand, via the two procurement channels. The long-term contract, on one hand, specifies a unit price schedule and a capacity level that is reserved for the manufacturer. The spot market, on the other hand, is character-
ized by a price-quantity curve Figure 3.3 describes the conceptual framework, detailed in the next four subsections.
In order for the manufacturer to achieve her serviceability objective and hedge against the variability of demand and supply (which may also be impacted by the supplier’s capacity limitations), the manufacturer offers her supplier a long-term contract defined as follows: In period 1 the manufacturer will determine a capacity reservation level K, based on a pricing scheme Subsequently, in period 2, the manufacturer has to meet a random demand When the demand is lower than K, she will order from the supplier and pay a unit price of Similarly when the demand is higher than K, the manufacturer will order the maximum reserved capacity, i.e., K units, from the supplier at a unit price of In this case, however, in order for the manufacturer to meet her total demand, she will need to procure the remaining units from the spot market. We assume that the total demand has a continuous density function and admits finite first and second moments.
The Supplier Pricing Scheme. To allow for risk-sharing between the long-term supplier and the manufacturer, the long-term supplier will charge a unit price for an order of units. Clearly, this price depends on the capacity that the manufacturer reserved in the original contract, K, and on her actual order, If the reserved capacity is fully used, the supplier will charge a unit price of If only an amount with is used, he will charge to account for any losses due to the under-usage of reserved capacity. Hence
is the capacity reservation penalty. The assumptions on the pricing scheme are the following:
For all K the penalty is linear in This is similar to the ap- proaches by Li and Kouvelis (1999) as well as by Barnes-Schuster et al. (1998).
The cost of goods is always increasing with i.e., it costs more to buy more. As demand is random, the manufacturer and supplier commit to a risk-sharing agreement in the following sense:
the penalty in total supply cost for “under-ordering” with respect to K becomes smaller as the order quantity approaches K.
is independent of K. This assumption is for pedagogic reasons only. However, it can be interpreted as the result of the negotiation between manufacturer and supplier. The first wants to have non-increasing in K, whereas the latter prefers to see
being non-decreasing in K, which may lead to
independent of K. (See Araman et al. (2000b) for a more detailed justification and a model without this assumption).
Based on the previous assumptions, a linear function that fulfills all of these conditions has to be of the form:
Thus the penalty is given by: See Figure 3.4 below for an illustration of the long-term pricing schedule
Remark 3.3 We should note that we could relax the last assumption