An Asymptotically Optimal Heuristic for Multi-Item Inventory Models with Joint Inventory Constraints

22 Pages Posted: 28 Sep 2022

See all articles by Awi Federgruen

Awi Federgruen

Columbia University - Columbia Business School, Decision Risk and Operations

Daniel Guetta

Columbia University - Columbia Business School, Decision Risk and Operations

Garud Iyengar

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Xujia Liu

Columbia University - Department of Industrial Engineering and Operations Research

Date Written: September 16, 2022

Abstract

We analyze a periodic review stochastic inventory model with T periods and I items. At the beginning of each period, the inventory position of each item can be adjusted by placing an order or by salvaging some of the inventory. There is a limited capacity for the total inventory held at the end of each period. Orders arrive and salvage batches deplete the inventory after a given lead time. In addition to variable order and salvaging costs, there are linear or convex holding and backlogging costs. In every period, the probability of the aggregate inventory level exceeding the prevailing inventory capacity must be smaller than a given tolerance.

In this paper we show that when demands are independent across items or when each item is correlated with at most O(1) other items, a simple structured policy can be found which is asymptotically optimal when the number of items I grows to infinity. We achieve these results by showing that the problem, specified with chance constraints on the overflow probability in each period, can be sandwiched in between two problems with sets of expected value constraints.

Keywords: Dynamic Programming, Inventory Production, Optimal Control

Suggested Citation

Federgruen, Awi and Guetta, Daniel and Iyengar, Garud and Liu, Xujia, An Asymptotically Optimal Heuristic for Multi-Item Inventory Models with Joint Inventory Constraints (September 16, 2022). Available at SSRN: https://ssrn.com/abstract=4221106 or http://dx.doi.org/10.2139/ssrn.4221106

Awi Federgruen

Columbia University - Columbia Business School, Decision Risk and Operations ( email )

New York, NY
United States

Daniel Guetta

Columbia University - Columbia Business School, Decision Risk and Operations ( email )

New York, NY
United States

Garud Iyengar

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

Xujia Liu (Contact Author)

Columbia University - Department of Industrial Engineering and Operations Research ( email )

500 W. 120th Street #315
New York, NY 10027
United States

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