Most firms face a market in which some customers purchase in bulk at a discount and others buy single units or small lots at a higher price. Consider an owner of warehousing capacity in a supply chain. Warehousing capacity may be leased in bulk to a large company or in small amounts to large companies for their emergency needs or to small companies. The large company leasing space in bulk typically gets a discount compared to the others. The owner of warehousing space thus faces the following trade-off: It could lease the space to the bulk buyer at a discount or save some of the space for higher price demand for small amounts of warehouse space that may or may not arise.
In most instances, owners of supply chain assets prefer to fulfill all demand that arises from bulk sales and try to serve small customers only if any assets are left over. In contrast, a firm such as McMaster-Carr targets only customers with emergency demand for MRO goods. McMaster-Carr will turn down any bulk buyer seeking a discount. Using this strategy, McMaster-Carr is a very profitable firm. For a firm that wants to be a niche player, targeting one of the two extremes is a sensible strategy. It allows the firm to focus its operations on serving either only the bulk segment or only the spot market. For other firms, however, a hybrid strategy of serving both segments is appropriate. In this case, firms must decide what fraction of the asset to sell in bulk and what fraction of the asset to save for the spot market. The fundamental tradeoff is similar to a firm serving two market segments (see Section 16.2). The firm needs to decide on the prices to the bulk and spot segments and the amount of the asset to reserve for the spot market (where demand arises later). The prices to each segment can be determined using Equations 16.1 and 16.2. The amount reserved for the spot market should be such that the expected marginal revenue from the spot market equals the current revenue from a bulk sale. The reserved quantity is affected by the difference in margin between the spot market and the bulk sale and also by the distribution of demand from the spot market. If we consider the spot market to be the higher-price segment and the bulk purchasers to be the lower-price segment, the amount of asset to be saved for the spot market can be obtained using Equations 16.3 and 16.4.
A similar decision needs to be made by each purchaser of production, warehousing, and transportation assets in a supply chain. Consider a company looking for shipping capacity for global operations. One option is for it to sign a long-term bulk contract with a shipping firm. Another option is to purchase shipping capacity on the spot market. The long-term bulk contract has the advantage of a fixed, low price but has the disadvantage of being wasted if it is not used. The spot market has the disadvantage of a higher average price but has the advantage of never being wasted. The purchaser must consider this trade-off when deciding the amount of long-term bulk shipping contracts to sign.
Given that both the spot market price and the purchaser’s need for the asset are uncertain, a decision tree approach, as discussed in Chapter 6, should be used to evaluate the amount of long-term bulk contracts to sign. For the simple case in which the spot market price is known but demand is uncertain, the extent of the bulk contract can be evaluated using a formula. Let cB be the bulk rate, and let cS be the spot market price for the asset. Let Q* be the optimal amount of the asset to be purchased in bulk and let p* be the probability that demand for the asset does not exceed Q*. The marginal cost of purchasing another unit in bulk is cB. The expected marginal cost of not purchasing another unit in bulk and then purchasing it in the spot market is (1 – p*) cS. If the optimal amount of the asset is purchased in bulk, the marginal cost of the bulk purchase should equal the expected marginal cost of the spot market purchase; that is, cB = (1 – p*) cS. Thus, the optimal value p* is obtained as
If demand is normally distributed, with a mean of m and a standard deviation of s, the optimal amount, Q*, of the asset purchased in bulk is obtained as
The amount of bulk purchase increases if either the spot market price increases or the bulk price decreases. Evaluation of bulk contract purchases is illustrated in Example 16-6 (see worksheet Example16-6).
EXAMPLE 16-6 Long-Term Bulk Contracts versus the Spot Market
A manufacturer sources several components from China and has monthly transportation needs that are normally distributed, with a mean of m = 10 million units and a standard deviation of σ = 4 million units. The manufacturer must decide on the portfolio of transportation contracts to carry. A long-term bulk contract costs $10,000 per month for 1 million units. Transportation capacity is also available in the spot market at an average price of $12,500 per million units. For how much transportation capacity should the manufacturer sign a long-term bulk contract?
Analysis:
In this case, we have
Bulk contract cost, cB = $10,000 per million units
Spot market cost, cS = $12,500 per million units
Using Equation 16.9, we obtain
The optimal amount to be purchased using the long-term bulk contract is thus obtained using Equation 16.10 to be
Thus, the manufacturer should sign a long-term bulk contract for 6.63 million units per month and purchase any transportation capacity beyond that on the spot market.
Source: Chopra Sunil, Meindl Peter (2014), Supply Chain Management: Strategy, Planning, and Operation, Pearson; 6th edition.
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