Two-stage robust optimization for perishable inventory management with order modification

Abstract In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying deterministic problem and an adversarial problem. For the deterministic problem any oracle can be used which returns an optimal solution for every possible scenario. We show that the latter lower bound can be implemented in a branch and bound procedure, where the branching is performed only over the first-stage decision variables. All results even hold for non-linear objective functions which are concave in the uncertain parameters. As an alternative solution method we apply a column-and-constraint generation algorithm to the binary two-stage robust problem with objective uncertainty. We test both algorithms on benchmark instances of the uncapacitated single-allocation hub-location problem and of the capital budgeting problem. Our results show that the branch and bound procedure outperforms the column-and-constraint generation algorithm.

Download Full-text

Linearized Robust Counterparts of Two-Stage Robust Optimization Problems with Applications in Operations Management

INFORMS Journal on Computing ◽

10.1287/ijoc.2020.0959 ◽

2020 ◽

Author(s):

Amir Ardestani-Jaafari ◽

Erick Delage

Keyword(s):

Robust Optimization ◽

Operations Management ◽

Optimization Problems ◽

Close Relation ◽

Bilinear Programming ◽

Two Stage ◽

Bilinear Models ◽

Robust Counterpart ◽

Adjustable Robust Counterpart ◽

Affinely Adjustable Robust Counterpart

In this article, we discuss an alternative method for deriving conservative approximation models for two-stage robust optimization problems. The method mainly relies on a linearization scheme employed in bilinear programming; therefore, we will say that it gives rise to the linearized robust counterpart models. We identify a close relation between this linearized robust counterpart model and the popular affinely adjustable robust counterpart model. We also describe methods of modifying both types of models to make these approximations less conservative. These methods are heavily inspired by the use of valid linear and conic inequalities in the linearization process for bilinear models. We finally demonstrate how to employ this new scheme in location-transportation and multi-item newsvendor problems to improve the numerical efficiency and performance guarantees of robust optimization.

Download Full-text

On robust optimization of two-stage systems

Mathematical Programming ◽

10.1007/s10107-003-0373-y ◽

2004 ◽

Vol 99 (1) ◽

pp. 109-126 ◽

Cited By ~ 71

Author(s):

Samer Takriti ◽

Shabbir Ahmed

Keyword(s):

Robust Optimization ◽

Two Stage

Download Full-text

State-of-the-art literature review on inventory models for perishable products

Journal of Advances in Management Research ◽

10.1108/jamr-09-2017-0091 ◽

2018 ◽

Vol 15 (3) ◽

pp. 306-346 ◽

Cited By ~ 12

Author(s):

Vaibhav Chaudhary ◽

Rakhee Kulshrestha ◽

Srikanta Routroy

Keyword(s):

Inventory Management ◽

Systemic Review ◽

Current Status ◽

Future Research ◽

Inventory Models ◽

Research Gaps ◽

Content Type ◽

Perishable Items ◽

Perishable Inventory ◽

The Future

PurposeThe purpose of this paper is to review and analyze the perishable inventory models along various dimensions such as its evolution, scope, demand, shelf life, replenishment policy, modeling techniques and research gaps.Design/methodology/approachIn total, 418 relevant and scholarly articles of various researchers and practitioners during 1990-2016 were reviewed. They were critically analyzed along author profile, nature of perishability, research contributions of different countries, publication along time, research methodologies adopted, etc. to draw fruitful conclusions. The future research for perishable inventory modeling was also discussed and suggested.FindingsThere are plethora of perishable inventory studies with divergent objectives and scope. Besides demand and perishable rate in perishable inventory models, other factors such as price discount, allow shortage or not, inflation, time value of money and so on were found to be combined to make it more realistic. The modeling of inventory systems with two or more perishable items is limited. The multi-echelon inventory with centralized decision and information sharing is acquiring lot of importance because of supply chain integration in the competitive market.Research limitations/implicationsOnly peer-reviewed journals and conference papers were analyzed, whereas the manuals, reports, white papers and blood-related articles were excluded. Clustering of literature revealed that future studies should focus on stochastic modeling.Practical implicationsStress had been laid to identify future research gaps that will help in developing realistic models. The present work will form a guideline to choose the appropriate methodology(s) and mathematical technique(s) in different situations with perishable inventory.Originality/valueThe current review analyzed 419 research papers available in the literature on perishable inventory modeling to summarize its current status and identify its potential future directions. Also the future research gaps were uncovered. This systemic review is strongly felt to fill the gap in the perishable inventory literature and help in formulating effective strategies to design of an effective and efficient inventory management system for perishable items.

Download Full-text