Dual Sourcing under Capacity Limits, Fixed Costs and Salvage Opportunities

24 Pages Posted: 11 Dec 2017 Last revised: 23 May 2019

See all articles by Awi Federgruen

Awi Federgruen

Columbia Business School - Decision Risk and Operations

Zhe Liu

Columbia University - Columbia Business School

Lijian Lu

Columbia University - Columbia Business School

Date Written: April 1, 2019

Abstract

This paper studies a finite horizon, single product, periodic review inventory system with two supply sources and salvage options. A challenging trade-off exists between the two sources because the expedited supplier has a shorter lead time but charges a higher per-unit price, while the regular supplier has a longer lead time but lower order costs. A further complication is the salvage option that allows for bilateral inventory adjustments. All inventory adjustments involve a fixed cost component in addition to variable costs or revenues and may be subject to capacity limits.

In each period, we show that an optimal policy first determines the size of an order with the expedited supplier, if any, or the size of any salvage quantity, based, exclusively, on the regular full inventory position. Thereafter, the inventory position is adjusted upward (by the expedited supplier order) or downward (by the salvage quantity); any order with the regular supplier is then determined as a function of the adjusted inventory position. Moreover, the dependence of the optimal order sizes and/or salvage quantity, on the period's starting inventory position follows a relatively simple structure. In the most general case, the optimal policy is characterized by four critical threshold levels of the inventory position. As far as the second stage ordering decision with the regular supplier is concerned, the optimal policy is characterized by two threshold parameters partitioning the adjusted inventory position line in up to three regions.

The above results apply to the special case where the lead times of the two suppliers differ by a single period. However, our structural results suggest effective heuristics for general lead time combinations, evaluated in the second part of the paper.

Keywords: dual sourcing, capacity constraints, lead time, inventory management, convexity, dynamic programming

Suggested Citation

Federgruen, Awi and Liu, Zhe and Lu, Lijian, Dual Sourcing under Capacity Limits, Fixed Costs and Salvage Opportunities (April 1, 2019). Columbia Business School Research Paper No. 18-3. Available at SSRN: https://ssrn.com/abstract=3082943 or http://dx.doi.org/10.2139/ssrn.3082943

Awi Federgruen

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

Zhe Liu (Contact Author)

Columbia University - Columbia Business School ( email )

3022 Broadway
New York, NY 10027
United States

Lijian Lu

Columbia University - Columbia Business School ( email )

3022 Broadway
New York, NY 10027
United States

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