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
4.2 Simulation based Supply Contracts, Applied to a Private Market, and a Spot Market
As described above, the traditional supply chain literature does not account for the recent development in B2B e-commerce, especially with regard to Internet-based exchanges. Thus, there is an urgent need for new models that address B2B exchanges and their impact on current procurement practices. One can argue that the complexity of the prob- lems, the number of parameters involved and their characteristics make simulation techniques a useful approach for such problems.
The recent paper by Cohen and Agrawal (1999) solves a stochas- tic dynamic programming formulation using simulation to analyze the trade-off between long- and short-term contracts. Their model, however, only allows for the usage of either contract at a time, i.e., a mixed strat- egy is not considered. The model proposed in this paper can be used for the comparison of long-term contracts and a spot market since a spot market can be approximated by a short-term contract with a very short duration. We discuss this in more detail below. The elements that dom- inate are the uncertain prices of the spot market versus fixed investment
costs and learning cost reductions by the long-term supplier, along with the usual inventory and backlog costs.
As mentioned above, the paper by Cohen et al. proposes a simulation- based model comparing short and long-term contracts. They consider a planning horizon of several years divided into review periods. Each review period is, in general, of one year in length or divided into tactical review periods (a tactical review period is 1 week long and is thus equal to 52). If the long-term contract is selected at any point during the horizon, it lasts for the remainder of the horizon. The short term contract however lasts, if selected, for the duration of a review period. During each review period the system evolves according to the selected contract. We define as a 0-1 decision variable (0 for short term and 1 for long-term).
The model and the results are valid for a shorter review period, with smaller than 52. The only assumption needed is that the system reaches stationarity during one review period. Hence by shrinking the length of the short term contract as defined in Cohen et al. the short term contract could be replaced by a spot market as we defined it earlier in this work, both having almost the same characteristics as far as the model is concerned. Thus, we are interpreting the conclusions of the paper in our framework, so that the results and insights can be used in a B2B exchange framework. The supply managers will still face the same dilemma of choosing between either a short term or a long-term contract. The first option has the advantage of offering the flexibility to switch to different suppliers and is based on a speculative (or random, in the sense of not known a priori) market price, whereas the long-term relationship requires a fixed initial investment and is based on a price written into the contract. In addition, learning effects due to the long- term relationship are described by an annual percentage reduction, of the total cost incurred.
This paper considers a risk averse supplier whose problem is to select the optimal contract for each strategic period by minimizing the total disutility of costs over the entire horizon. To account for the buyer’s risk aversion, the authors suggest that the buyer follows a “mean-variance”
type of function to evaluate the total cost C, incurred in one review period:
where reflects the risk aversion of the buyer. (The more risk averse the buyer, the larger the value of Hence, the problem is formulated as a stochastic dynamic program, where at each review period the manager chooses one of the two types of contracts for that period, based mainly on the previous price of the spot market. He will
then need to decide on the tactical inventory policies. That is, he has to account for the cost of goods ( total purchase price paid during period ), the fixed investment when the long-term contract is selected, K, as well as the inventory and shortage costs. The optimization is performed over the entire horizon. Although the main focus of the paper is on the non-stationary, finite horizon setting, a first intuitive result shows that under the stationary, infinite horizon assumption (i.e., the spot market price is time stationary) a “now or never” kind of policy is adopted;
that is, the long-term contract is selected either at the very beginning or never. The reason is that the formulation of the problem is the same every period and is independent of the other periods. As a consequence of the non-stationarity, the formulation of the problem becomes similar to that of American call options for which the solution can only be determined numerically.
In what follows we will briefly describe the different parameters that are included in the model, present a summary of the results, and con- clude with some managerial insights. For a more detailed description of the model the reader is referred to Cohen and Agrawal (1999).
As we stated earlier, the spot price plays a major role in this model, and its non-stationarity is crucial. The distribution of the spot market price is assumed to follow a multiplicative Binomial process, and to only depend on the realization of the previous period. We let denote the random market price and the realization of the price at time Then
where and are two constants that determine the upward and downward trend of the price. and are usually assumed to equal 0.5. This results clearly in a non-stationary environment where the prices in successive periods are correlated. On the other hand, the price specified by the long-term contract at a given point in time is locked in for the remainder of the horizon, and is assumed to equal the spot market average price during this period. We note that the selection of the contract occurs before the spot price is revealed in this particular period. The total expected purchase cost during one review period is
where is the average demand and
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.