*4.1. Lead-Time Reduction*

Suppose that a buyer purchases products from an offshore supplier and sells them in a market with uncertain demand. The buyer places the purchase order at time *t<sup>l</sup>* , and the products are delivered at time *t<sup>n</sup>* such that *t*<sup>0</sup> ≤ *t<sup>l</sup>* ≤ *tn*. The buyer sells the products in the market at time *tn*. This setting applies to fashion apparel brands that use contract manufacturers to make their clothes and sell them to retail stores at the beginning of each selling season. The length of *t<sup>n</sup>* − *t<sup>l</sup>* is the decision lead time, which is the time elapsed between when the ordering decision is made and when the actual demand is observed. The demand is highly uncertain at time *t<sup>l</sup>* , which in turn exposes the buyer to excess inventory risk.

We assume that the selling price is \$*p* per unit, and the salvage value is \$*s* per unit. We use *c<sup>l</sup>* to denote the cost of ordering from the offshore supplier per unit. Then, the optimal order quantity can be found by Equation (5). When the buyer places the optimal order quantity, its expected profit and expected excess inventory can be found by Equations (7) and (8) conditional on the optimal order quantity.

We now consider the case that the buyer aims to reduce the lead time by switching to a local responsive supplier. This makes it possible for the buyer to place the order at time *t<sup>s</sup>* such that *t<sup>s</sup>* ≥ *t<sup>l</sup>* . However, the buyer incurs a higher purchasing cost when buying products from the local supplier. We use *c<sup>s</sup>* to denote the cost per unit of ordering from the local supplier such that *c<sup>s</sup>* ≥ *c<sup>l</sup>* . Therefore, the buyer is exposed to a trade-off between postponing the ordering decision and incurring a higher ordering cost. This trade-off has a significant impact on the buyer's profits and the excess inventory.

In Figure 3, we present an example of a buyer who would like to decide whether to purchase products from an offshore or a domestic supplier. The selling price of the product is USD 300 per unit; the cost of purchasing from the offshore supplier is USD 40 per unit; the cost of purchasing from the domestic supplier is USD 50 per unit. Unsold inventory is thrown away, so the salvage value is set equal to zero. We normalize the initial demand forecast to one (*D*<sup>0</sup> = 1) and change the demand parameters accordingly. The drift rate of the multiplicative demand model is set equal to zero, and the volatility is equal to one. We also normalize the long lead time (i.e., when an order is placed with the offshore supplier) to one such that *t<sup>n</sup>* − *t<sup>l</sup>* = 1 by setting *t<sup>n</sup>* = 1 and *t<sup>l</sup>* = 0.

We present the percentage change in profit in Figure 3a when the buyer switches from the offshore supplier to the domestic supplier. The x-axis represents the time of ordering with the domestic supplier (i.e., *ts*), and the y-axis represents the percentage increase in profits. When the domestic supplier is not responsive enough, the benefits of local sourcing disappear, resulting in a loss of profit. As shown in the figure, the profit increase is negative when *t<sup>s</sup>* < 0.29. In this case, it is not advantageous for the buyer to order from the domestic supplier, so a buyer aiming to maximize profit would continue to source from the offshore supplier. If the domestic supplier is responsive enough to let the buyer postpone the ordering decision to later than *t* = 0.29—that is, *t<sup>s</sup>* > 0.29—the buyer would increase their profit by switching from the offshore supplier to the domestic supplier. If the lead time is reduced by half (i.e., *t<sup>s</sup>* = 0.5), Figure 3a shows that ordering from the domestic supplier leads to a profit increase of around 10%. If the lead time is reduced by 90% so that *t<sup>s</sup>* = 0.9, the buyer can increase their profit by around 40%.

In addition to these economic benefits, the lead-time reduction helps the buyer reduce waste, thus having a positive environmental impact on the sourcing process. Figure 3b shows the waste ratio, which is the ratio of excess inventory when the buyer orders from the domestic supplier to the excess inventory when they order from the offshore supplier. The x-axis represents the *t<sup>s</sup>* value, and the y-axis represents the waste ratio. When *t<sup>s</sup>* = 0, the lead time for ordering from the offshore supplier is the same as the lead time for ordering from the domestic supplier. Even if the lead times are the same for both sourcing alternatives, the waste ratio is lower than one for *t<sup>s</sup>* = 0, meaning that local sourcing helps reduce waste even in the absence of a lead-time reduction. The waste ratio of 0.8 for *t<sup>s</sup>* = 0 is a result of the difference in ordering costs between the domestic and offshore suppliers. The cost of ordering from the domestic supplier is more than ordering from the offshore supplier (*c<sup>s</sup>* > *c<sup>l</sup>* ). This leads to lower ordering levels when the domestic supplier is used rather than the offshore supplier. Therefore, the 20% reduction in waste for *t<sup>s</sup>* = 0 can only be attributed to the lower ordering levels, which is independent of the benefits of a lead-time reduction. However, this improvement is not attainable because Figure 3a shows that the buyer prefers the offshore supplier over the domestic one when *t<sup>s</sup>* = 0.

When the *t<sup>s</sup>* value increases, Figure 3b shows that the waste ratio decreases. Therefore, the buyer can reduce waste during the sourcing process by cutting the lead time with the domestic supplier. When sourcing from the domestic supplier makes it possible to reduce the lead time substantially, the buyer reaches alignment between the economic and environmental incentives of local sourcing. On the one hand, the buyer can increase their profit due to better matching between supply and demand. On the other hand, they can also reduce the waste at source by minimizing the excess inventory. Apart from these direct benefits, promoting local production may also help improve the extent of remanufacturing and recycling because it increases product know-how in local markets.
