scholarly journals Partially Smoothing and Gradient-Based Algorithm for Optimizing the VMI System with Competitive Retailers under Random Demands

2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
Hua Deng ◽  
Yinxue Li ◽  
Zhaoman Wan ◽  
Zhong Wan
Keyword(s):  
Inventory Management ◽  
Stackelberg Game ◽  
Programming Model ◽  
Participation Rate ◽  
Intersection Point ◽  
Holding Costs ◽  
Managerial Implications ◽  
Gradient Based ◽  
Smooth Optimization ◽  
Bilevel Programming Model

Vendor managed inventory (VMI) is an improved sustainable inventory management system, but it is difficult to establish and solve an integrated Stackelberg game model under the complicated practical environment. In this paper, a bilevel programming model is proposed to formulate the VMI system by taking into account the uncertainty of demand, the competition among retailers, the cooperative advertising, the shortage and holding costs, and the practical constraints. For the established stochastic model being associated with continuously random demands, a deterministic mathematical program with complementarity constraints (MPCC) is first derived by expectation method and the first-order optimality conditions of the lower-level problem. Then, with a partially smoothing technique, the MPCC is solved by transforming it into a series of standard smooth optimization subproblems. Finally, owing to complexity caused by evaluating the integrals with unknown decision variables in the objective function, an efficient algorithm is developed to solve the problem based on the gradient information of model. Sensitivity analysis has been employed to reveal a number of managerial implications from the constructed model and algorithm. (1) The participation rate depends on advertising expenditures from both the manufacturer and the retailer. There exists an optimal threshold of participation rate for the manufacturer, which can be provided by the intersection point of the manufacturer and retailer’s cost-profit curves. (2) The manufacturer’s advertising policy is less sensitive to uncertainty of demand than the change of the retailer’s advertising policy. (3) The manufacturer in the VMI system should concern about the differences caused by symmetric or asymmetric retailers.

scholarly journals Single-Manufacturer Multi-Retailer Supply Chain Models with Discrete Stochastic Demand

2021 ◽  
Vol 13 (15) ◽  
pp. 8271
Author(s):  
Yaqing Xu ◽  
Jiang Zhang ◽  
Zihao Chen ◽  
Yihua Wei
Keyword(s):  
Dynamic Programming ◽  
Supply Chain ◽  
Computational Complexity ◽  
Stackelberg Game ◽  
Programming Model ◽  
Dynamic Programming Method ◽  
Game Model ◽  
Chain Model ◽  
Stochastic Demands ◽  
Demand Models

Although there are highly discrete stochastic demands in practical supply chain problems, they are seldom considered in the research on supply chain systems, especially the single-manufacturer multi-retailer supply chain systems. There are no significant differences between continuous and discrete demand supply chain models, but the solutions for discrete random demand models are more challenging and difficult. This paper studies a supply chain system of a single manufacturer and multiple retailers with discrete stochastic demands. Each retailer faces a random discrete demand, and the manufacturer utilizes different wholesale prices to influence each retailer’s ordering decision. Both Make-To-Order and Make-To-Stock scenarios are considered. For each scenario, the corresponding Stackelberg game model is constructed respectively. By proving a series of theorems, we transfer the solution of the game model into non-linear integer programming model, which can be easily solved by a dynamic programming method. However, with the increase in the number of retailers and the production capacity of manufacturers, the computational complexity of dynamic programming drastically increases due to the Dimension Barrier. Therefore, the Fast Fourier Transform (FFT) approach is introduced, which significantly reduces the computational complexity of solving the supply chain model.

Dynamic Type Matching

2021 ◽  
Author(s):  
Ming Hu ◽  
Yun Zhou
Keyword(s):  
Sufficient Conditions ◽  
Sharing Economy ◽  
Problem Definition ◽  
Periodic Review ◽  
Optimal Matching ◽  
Demand And Supply ◽  
Holding Costs ◽  
Current Period ◽  
Dynamic Type ◽  
Managerial Implications

Problem definition: We consider an intermediary’s problem of dynamically matching demand and supply of heterogeneous types in a periodic-review fashion. Specifically, there are two disjoint sets of demand and supply types, and a reward for each possible matching of a demand type and a supply type. In each period, demand and supply of various types arrive in random quantities. The platform decides on the optimal matching policy to maximize the expected total discounted rewards, given that unmatched demand and supply may incur waiting or holding costs, and will be fully or partially carried over to the next period. Academic/practical relevance: The problem is crucial to many intermediaries who manage matchings centrally in a sharing economy. Methodology: We formulate the problem as a dynamic program. We explore the structural properties of the optimal policy and propose heuristic policies. Results: We provide sufficient conditions on matching rewards such that the optimal matching policy follows a priority hierarchy among possible matching pairs. We show that those conditions are satisfied by vertically and unidirectionally horizontally differentiated types, for which quality and distance determine priority, respectively. Managerial implications: The priority property simplifies the matching decision within a period, and the trade-off reduces to a choice between matching in the current period and that in the future. Then the optimal matching policy has a match-down-to structure when considering a specific pair of demand and supply types in the priority hierarchy.

A Bi-objective Multi-Product Multi-Constraint EPQ Model in a Stochastic Environment and Partial Shortage

2020 ◽  
Vol 19 (03) ◽  
pp. 567-587
Author(s):  
Seyedeh Sanaz Mirkhorsandi ◽  
Seyed Hamid Reza Pasandideh
Keyword(s):  
Goal Attainment ◽  
Programming Model ◽  
Multi Objective ◽  
Holding Costs ◽  
Inventory Costs ◽  
Economic Production ◽  
Proposed Model ◽  
Demand Rate ◽  
Nonlinear Programming Model ◽  
Epq Model

One of the classical models for inventory control is economic production quantity (EPQ), which is widely used in industry. In this paper, an EPQ model with partial shortage is developed by considering the real world conditions, and costs related to the backorder demand are taken as fixed and time-dependent. In the proposed model, determination of the inventory cycle length, the length of positive inventory cycle and backordered demand rate are considered in shortage period. The aim of the presented research is to minimize the total inventory costs and the space required for storage products so that the stochastic and classic constraints including holding costs, lost sales, backorder, budget, total number of productions and average shortage times should be satisfied while optimizing the multi-objective problem. Presented model is a bi-objective nonlinear programming model. Then, to solve the proposed model, three multi-objective decision-making methods including Lp-metric, goal programming and goal attainment are used. Besides, numerical examples are executed in small, medium and large scales by use of GAMS software, and the performance of the methods is compared in terms of objective functions and required CPU time. Finally, sensitivity analysis is done to determine the effect of change in the main parameters of the model on the objective function value.

scholarly journals A Simultaneous Solution for Reserve Capacity Maximization and Delay Minimization Problems in Signalized Road Networks

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Ozgur Baskan ◽  
Huseyin Ceylan ◽  
Cenk Ozan
Keyword(s):  
Bilevel Programming ◽  
Road Network ◽  
Programming Model ◽  
Numerical Test ◽  
User Equilibrium ◽  
Reserve Capacity ◽  
Delay Minimization ◽  
Weighted Sum Method ◽  
Capacity Maximization ◽  
Bilevel Programming Model

In this study, we present a bilevel programming model in which upper level is defined as a biobjective problem and the lower level is considered as a stochastic user equilibrium assignment problem. It is clear that the biobjective problem has two objectives: the first maximizes the reserve capacity whereas the second minimizes performance index of a road network. We use a weighted-sum method to determine the Pareto optimal solutions of the biobjective problem by applying normalization approach for making the objective functions dimensionless. Following, a differential evolution based heuristic solution algorithm is introduced to overcome the problem presented by use of biobjective bilevel programming model. The first numerical test is conducted on two-junction network in order to represent the effect of the weighting on the solution of combined reserve capacity maximization and delay minimization problem. Allsop & Charlesworth’s network, which is a widely preferred road network in the literature, is selected for the second numerical application in order to present the applicability of the proposed model on a medium-sized signalized road network. Results support authorities who should usually make a choice between two conflicting issues, namely, reserve capacity maximization and delay minimization.

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