Inventory control is a key decision for any firm since it helps to reduce the impact caused by

the mismatch between supply and demand. Inventory holding may reduce product shortage

and increase responsiveness. However, the excess of it could lead to higher holding costs and

product obsolescence. It is particularly important for perishable products or seasonal goods.

Products with a limited lifetime are highly affected by ordering decisions. For instance, in

the fashion industry, several collections are launched during the year with short selling periods

each. In these systems, production and supply must be exceptionally accurate in time and place

to meet customers' requirements. It implies ordering the adequate quantity at each location

aiming to avoid both overstocking and understocking. On the one hand, inventory shortage

of these high-end goods may considerably impact the company's revenue and goodwill. On

the other hand, inventory excess represents a loss of material, energy consumption, and the

additional cost incurred for the final disposition of the unsold goods at the end of the season.

In these particular environments, with short selling windows, and where stockouts imply very

high costs, a proven strategy to deal with the pressure of meeting demand on time is the

placement of emergency orders as a form of dual sourcing.

In the academic literature, dual sourcing might refer to a situation where a company has one

main supplier from whom it sources products exclusively, but uses a backup supplier to mitigate

the effects of potential disruptions, carrying with the extra cost of this decision [4]. It may

also take the form of a decision between transportation speeds or transportation modes [5]. In

this regard, it is considered the existence of a slow or periodic replenishment characterized by

low cost, and a fast and costly replenishment able to supply in case of unforeseen fluctuations.

This second form of dual sourcing is widespread in many industries. For example, some firms

that use ocean freight for shipping on a regular basis might switch to the speedier and more

expensive air freight in times of need [2]. The body of literature studying dual-sourcing supply

has been growing over the last years, moving from small and restrictive models to larger and

more realistic problems. In contrast to the majority of single-sourcing inventory models, in

which optimal policies are known, optimal policies for dual-sourcing inventory models are either

unknown or have a very complex structure and need to be defined individually regarding the

parameters of the system [5].

Some previous works have addressed the problem of dual sourcing considering two available

transportation modes: a slow mode with low cost and long and stochastic lead time, and a fast

mode with higher cost and shorter and deterministic lead time. For instance, [6] considers the

transport of car components under a limited budget for stock acquisition. The authors define a

replenishment policy based on the safety stock and the expected demand during the lead time

and present a simulation model for the periodic review inventory model. They conclude that

in the long run term, extra costs for fast replenishment can be avoided by increasing safety

stock. In [1] the effect of sea shipping lead time variability on the economic and environmental

performance of inventory systems is evaluated. The authors deal with the problem as if it was

an inventory system with lost sales, where every unit in stockout is supplied by an emergency

order at a higher cost. They determine the order size using an EOQ model and compute

the reorder point through simulation for two different objectives, minimization of total cost

and minimization of emissions. These previous works assume an infinite horizon in which

having a safety stock is a solution for the variability of the regular supplier. However, this

strategy to deal with lead time variability might be not effective in the finite horizon, when

inventory became useless and a penalty cost at the end of the selling season. In [3] the authors

consider finite horizon to address the problem of alternative procurement for perishable agrifood

products in the context of supply chain management risk. The regular supplier has a

restriction on the minimum volume to deliver, while the alternative supplier can supply even

low volumes in a short time at a higher price. A newsvendor model-type formulation is used

to model the supply chain and to compute the optimal order size for each supplier aiming to

maximize the expected profit. The authors show there is a boundary on the utilization of the

alternative supplier that depends on the ratio between the procurement cost of the regular

and the alternative supplier. To the best of our knowledge, no previous studies have addressed

simultaneously the evaluation of dual-sourcing strategies in the finite horizon with uncertain

lead time.

Motivated by the fashion industry, this work considers the inventory control of a single

product with a finite selling season in a two-echelon supply chain, consisting of a central

distribution center and an overseas depot. The central distribution center can replenish the

regional depot multiple times during the selling season to meet the uncertain demand for the

product. In particular, replenishment orders can be sent either by boat or by plane, each

one having different transportation costs, lead times and different contributions regarding

GHG emissions. Backorders are not allowed, and every stockout is considered a lost sale.

Every unit left in inventory at the end of the season is disposed of for an additional cost. We

formulate the problem as a stochastic dynamic programming model. We discuss the complexity

of the problem, we present formulations for some variations of the original problem regarding

alternatives for dual-sourcing use. We test the model utilizing industry data. We investigate

the impact of the decision regarding environmental performance. Finally, we discuss the result

of the models and present some managerial insights aiming at the definition of the inventory

policy for the system.