On technical note : Solving inventory models by algebraic method

2021 ◽  
Vol 24 (7) ◽  
pp. 1533-1541
Author(s):  
Cenk Çalışkan
Keyword(s):  
Algebraic Method ◽  
Technical Note ◽  
Inventory Models

Technical Note—Time Inconsistency of Optimal Policies of Distributionally Robust Inventory Models

2020 ◽  
Vol 68 (5) ◽  
pp. 1576-1584 ◽  
Author(s):  
Alexander Shapiro ◽  
Linwei Xin
Keyword(s):  
Decision Making ◽  
Large Class ◽  
Risk Measures ◽  
Technical Note ◽  
Time Inconsistency ◽  
Base Stock ◽  
Risk Averse ◽  
Inventory Models ◽  
Optimal Policies ◽  
Distributionally Robust

The authors extend previous studies of time inconsistency to risk averse (distributionally robust) inventory models and show that time inconsistency is not unique to robust multistage decision making, but may happen for a large class of risk averse/distributionally robust settings. In particular, they demonstrate that if the respective risk measures are not strictly monotone, then there may exist infinitely many optimal policies which are not base-stock and not time consistent. This is in a sharp contrast with the risk neutral formulation of the inventory model where all optimal policies are base-stock and time consistent.

scholarly journals Solution Procedure for Inventory Models with Linear and Fixed Backorder Costs

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Daniel Yi-Fong Lin
Keyword(s):  
Optimal Solution ◽  
Algebraic Method ◽  
Solution Procedure ◽  
Objective Functions ◽  
Inventory Models

Several researchers applied the algebraic method to solve the optimal solution of EOQ and EPQ models with linear and fixed backorder costs. However, there are questionable derivations in their solution procedure such that researchers provided further examinations. We study two papers that are considered the same inventory models under different notation and slightly different objective functions to provide detailed discussions for their questionable results and our improvements.

Technical Note—Constant-Order Policies for Lost-Sales Inventory Models with Random Supply Functions: Asymptotics and Heuristic

2020 ◽  
Vol 68 (4) ◽  
pp. 1063-1073 ◽  
Author(s):  
Jinzhi Bu ◽  
Xiting Gong ◽  
Dacheng Yao
Keyword(s):  
Asymptotic Analysis ◽  
Technical Note ◽  
Lead Times ◽  
Lost Sales ◽  
Inventory Models ◽  
Supply Functions

Asymptotic analysis of constant-order policies for lost-sales inventory models with positive lead times and random supply functions.

scholarly journals A Detailed Examination of Sphicas (2014), Generalized EOQ Formula Using a New Parameter: Coefficient of Backorder Attractiveness

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 931 ◽  
Author(s):  
Luo
Keyword(s):  
Open Problem ◽  
Algebraic Method ◽  
Generalized Solution ◽  
Detailed Examination ◽  
Inventory Model ◽  
The Other ◽  
Inventory Models ◽  
Solution Approach ◽  
Feasible Domain ◽  
Parameter Coefficient

Researchers have used analytic methods (calculus) to solve inventory models with fixed and linear backorder costs. They have found conditions to partition the feasible domain into two parts. For one part, the system of the first partial derivatives has a solution. For the other part, the inventory model degenerates to the inventory model without shortages. A scholar tried to use the algebraic method to solve this kind of model. The scholar mentioned the partition of the feasible domain. However, other researchers cannot understand why the partition appears, even though the scholar provided two motivations for his derivations. After two other researchers provided their derivations by algebraic methods, the scholar showed a generalized solution to combine inventory models with and without shortages together. In this paper, we will point out that this generalized solution approach not only did not provide explanations for his previous partition but also contained twelve questionable results. Recently, an expert indicated questionable findings from two other researchers. Hence, we can claim that solving inventory models with fixed and linear backorder costs is still an open problem for future researchers.

scholarly journals Technical Note on(Q,r,L)Inventory Model with Defective Items

2010 ◽  
Vol 2010 ◽  
pp. 1-8 ◽  
Author(s):  
Cheng-Tan Tung ◽  
Yu-Wen Wou ◽  
Shih-Wei Lin ◽  
Peter Deng
Keyword(s):  
Analytical Approach ◽  
Optimal Solution ◽  
Technical Note ◽  
Inventory Model ◽  
Reasonable Assumption ◽  
Robust Method ◽  
Inventory Models ◽  
Defective Items ◽  
Stochastic Inventory ◽  
Stochastic Inventory Models

Under a reasonable assumption, we derive an analytical approach that verifies uniqueness of the optimal solution for stochastic inventory models with defective items. Our approach implies a robust method to find the optimal solution.

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