Mathematical Programming Approach to the Optimality of the Solution for Deterministic Inventory Models with Partial Backordering

Analysis of an EOQ inventory model with partial backordering and non-linear unit holding cost

A note on the deterministic EPQ with partial backordering

Most of the inventory models discuss two extreme situations with respect to the demand in stock-out period. In this research, the demand rate within stock-out period is assumed as a diminishing function of backorders. Shortage of inventory will lead to the opportunity cost of lost sales. This research considers backorders and lost sales to formulate an inventory model with partial backorders. The objective of the inventory model is to determine the time scales of inventory depletion and stock-out periods in order to minimise total relevant cost. An efficient algorithm is developed to find the optimal solution. Finally, a sensitivity analysis is performed to study the effects of the model parameters on the optimal solution. This research apparently makes an improvement compared to the previous works, and further fits the requirements of practical environment.

A note on “The EPQ with partial backordering and phase-dependent backordering rate”

This paper aims to develop a suitable restoration method by a joint usage of an Expert system (ES) and a Mathematical Programming (MP) approach. Under this devise, the optimal target system for storation is formulated as an MP problem and solved efficiently by the decomposition-coordination strategy; that is a whole problem is decomposed into subproblems according to the generic knowledge of experts. The introduction of a new concept ?>restorative operation cost ?> that reflects the various restoration strategies has decreased the number of rules in the knowledge-base to one third that of typical existing ES's. The validity and effectiveness of the combined method have been demonstrated by applying it to a practical size restoration problem.

The necessary and sufficient conditions for single extremality in non-convex problems of mathematical programming

Economic production lot size model for deteriorating items with partial back-ordering

Mathematical programming procedures to optimize the collector field subsystem of a power tower system

Mathematical programming is concerned with the extremization of a function f defined over an n-dimensional design space R n and bounded by a set S in the design space. The set S may be defined by equality or inequality constraints, and these constraints may assume linear or nonlinear form. The function f together with the set S in the domain of f is called a mathematical program or a mathematical programming problem. This terminology is in common usage in the context of problems which arise in planning and scheduling which are generally studied under operations research; the branch of mathematics concerned with the decision making process. Mathematical programming problems may be classified into several different categories depending on the nature and form of the design variables, constraint functions, and the objective function. However, only two of these categories are of interest to us, namely the linear and the nonlinear programming (commonly designated as LP and NLP, respectively).KeywordsDesign VariableLinear Programming ProblemCollapse MechanismCollapse LoadBasic Feasible SolutionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Purpose To examine the effect of order-size dependency on all-unit discount and the trade credit period at two levels, and formulate a total combined profit function for the manufacturer and the supplier. Also, to test this model by taking a numerical example and performing a sensitivity analysis to gain managerial insights and results. Design/methodology/approach This work presents an integrated inventory model with a bi-level trade credit period and an all-unit discount dependent on order size under capacity constraints. To address stockouts, this model uses a partial backorder approach. The concavity of the profit function is shown and an algorithm is developed to find the optimal decision policy for the manufacturer and supplier. Findings The supplier places more frequent orders to take benefit of trade credit whenever demand and interest earned rate increase. Joint profit generated by both the manufacturer and supplier grows, even though the manufacturer offers a price discount to the supplier. The supplier should order an amount of inventory that can be accommodated in their own warehouse instead of renting an additional warehouse. Originality/value Till now, as per our best knowledge, there is no existing literature that has simultaneously considered order size-dependent two-level trade credit, capacity constraint, all-unit discount linked to order purchase price and partial backordering. Combining these factors, this paper derives an integrated inventory model to maximize the total combined profit of the manufacturer and supplier. These unique factors set this paper apart from existing literature, providing distinct advantages.

This paper establishes a direct method for solving variational problems via a set of Radial basis functions (RBFs) with Gauss-Chebyshev collocation centers. The method consist of reducing a variational problem into a mathematical programming problem. The authors use some optimization techniques to solve the reduced problem. Accuracy and stability of the multiquadric, Gaussian and inverse multiquadric RBF is examined and compared by some numerical experiments.

This paper explores the most urgent task to initialize a virtual network in the network virtualization environment, which always called the virtual network embedding. Different to the previous works to take the embedding process as two steps: node mapping stage and then edge mapping stage, this paper contribute to solve these processes all in one discrete nonlinear combined optimization. Based on modeling the virtual network (VN) request and substrate network (SN), this paper proposed mathematical description to the embedding process which building the relationship between node mapping and edge mapping stages. After that, a virtual network embedding cost is introduced as an objective function, and then the virtual network embedding can be concluding to minimize the objective cost as a mathematical programming problem. The obtained programming results in LINGO9.0 show that the proposed method can finish a virtual network embedding by mathematical programming in one step.

The study deals with the multi-choice mathematical programming problem, where the right hand side of the constraints is multi-choice in nature. However, the problem of multi-choice linear programming cannot be solved directly by standard linear or nonlinear programming techniques. The aim of this paper is to transform such problems to a standard mathematical linear programming problem. For each constraint, exactly one parameter value is selected out of a multiple number of parameter values. This process of selection can be established in different ways. In this paper, we present a new simple technique enabling us to handle such problem as a mixed integer linear programming problem and consequently solve them by using standard linear programming software. Our main aim depends on inserting a specific number of binary variables and using them to construct a linear combination which gives just one parameter among the multiple choice values for each choice of the values of the binary variables. A numerical example is presented to illustrate our analysis.

Chapter 1 - Introduction

Necessary conditions of optimality are obtained for general mathematical programming problems on a product space. The cost functional is locally Lipschitz and the constraints are expressed as inclusion relations with unbounded linear operators and multivalued term. The abstract result is applied to an optimal control problem governed by an elliptic differential inclusion.