scholarly journals Lagrangian Relaxation for an Inventory Location Problem with Periodic Inventory Control and Stochastic Capacity Constraints

2018 ◽  
Vol 2018 ◽  
pp. 1-27 ◽  
Author(s):  
Claudio Araya-Sassi ◽  
Pablo A. Miranda ◽  
Germán Paredes-Belmar
Keyword(s):  
Inventory Control ◽  
Lagrangian Relaxation ◽  
Location Problem ◽  
Subgradient Method ◽  
Capacity Constraints ◽  
Mixed Integer ◽  
Total System ◽  
Periodic Review ◽  
Decomposition Approach ◽  
Stochastic Capacity

We studied a joint inventory location problem assuming a periodic review for inventory control. A single plant supplies a set of products to multiple warehouses and they serve a set of customers or retailers. The problem consists in determining which potential warehouses should be opened and which retailers should be served by the selected warehouses as well as their reorder points and order sizes while minimizing the total costs. The problem is a Mixed Integer Nonlinear Programming (MINLP) model, which is nonconvex in terms of stochastic capacity constraints and the objective function. We propose a solution approach based on a Lagrangian relaxation and the subgradient method. The decomposition approach considers the relaxation of different sets of constraints, including customer assignment, warehouse demand, and variance constraints. In addition, we develop a Lagrangian heuristic to determine a feasible solution at each iteration of the subgradient method. The proposed Lagrangian relaxation algorithm provides low duality gaps and near-optimal solutions with competitive computational times. It also shows significant impacts of the selected inventory control policy into total system costs and network configuration, when it is compared with different review period values.

scholarly journals Locating Charging Stations of Various Sizes with Different Numbers of Chargers for Battery Electric Vehicles

Energies ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 3056 ◽  
Author(s):  
Shaohua Cui ◽  
Hui Zhao ◽  
Cuiping Zhang
Keyword(s):  
Electric Vehicles ◽  
Location Problem ◽  
Capacity Constraints ◽  
Sustainable Transportation ◽  
Market Potential ◽  
Sensitivity Analyses ◽  
Mixed Integer ◽  
Link Capacity ◽  
Battery Electric Vehicles ◽  
Charging Stations

Compared with traditional fuel vehicles, battery electric vehicles (BEVs) as a sustainable transportation form can reduce carbon dioxide emissions and save energy, so its market share has great potential. However, there are some problems, such as: Their limited range, long recharging time, and scarce charging facilities, hindering improvement in the market potential of BEVs. Therefore, perfect and efficient charging facility deployment for BEVs is very important. For this reason, the optimal locations for charging stations for BEVs are investigated in this paper. Instead of flow-based formulation, this paper is based on agents under strictly imposed link capacity constraints, where all agents can select their routes and decide on the battery recharging plan without running out of charge. In our study, not only the locations of charging stations, but also the size of charging stations with the different number of chargers, would be taken into consideration. Then, this problem is formulated as a location problem for BEV charging stations of multiple sizes based on agents under link capacity constraints. This problem is referred to as the agent-refueling, multiple-size location problem with capacitated network (ARMSLP-CN). We formulate the ARMSLP-CN as a 0–1 mixed-integer linear program (MILP) with the aim to minimize the total trip time for all agents, including four parts, namely, the travel time, queue time, fixed time for recharging, and variable recharging time depending on the type of charger and the amount of power recharged, in which commercial solvers can solve the linearized model directly. To demonstrate this model, two different numerical instances are designed, and sensitivity analyses are also presented.

scholarly journals Location of regional and international hub ports in liner shipping

2017 ◽  
Vol 2 (2) ◽  
pp. 114-125 ◽  
Author(s):  
Jianfeng Zheng ◽  
Cong Fu ◽  
Haibo Kuang
Keyword(s):  
Design Methodology ◽  
Location Problem ◽  
Programming Model ◽  
Liner Shipping ◽  
Mixed Integer ◽  
Eastern Asia ◽  
Hub Location ◽  
Hub Location Problem ◽  
Content Type ◽  
Western Asia

Purpose This paper aims to investigate the location of regional and international hub ports in liner shipping by proposing a hierarchical hub location problem. Design/methodology/approach This paper develops a mixed-integer linear programming model for the authors’ proposed problem. Numerical experiments based on a realistic Asia-Europe-Oceania liner shipping network are carried out to account for the effectiveness of this model. Findings The results show that one international hub port (i.e. Rotterdam) and one regional hub port (i.e. Zeebrugge) are opened in Europe. Two international hub ports (i.e. Sokhna and Salalah) are located in Western Asia, where no regional hub port is established. One international hub port (i.e. Colombo) and one regional hub port (i.e. Cochin) are opened in Southern Asia. One international hub port (i.e. Singapore) and one regional hub port (i.e. Jakarta) are opened in Southeastern Asia and Australia. Three international hub ports (i.e. Hong Kong, Shanghai and Yokohama) and two regional hub ports (i.e. Qingdao and Kwangyang) are opened in Eastern Asia. Originality/value This paper proposes a hierarchical hub location problem, in which the authors distinguish between regional and international hub ports in liner shipping. Moreover, scale economies in ship size are considered. Furthermore, the proposed problem introduces the main ports.

scholarly journals An inland-depots-for-empty-containers-model for the hinterland

2017 ◽  
Vol 2 (2) ◽  
pp. 126-141 ◽  
Author(s):  
Stephanie Finke ◽  
Herbert Kotzab
Keyword(s):  
Linear Optimization ◽  
Point Of View ◽  
Mixed Integer ◽  
Total System ◽  
Empty Container ◽  
Content Type ◽  
Shipping Company ◽  
Linear Optimization Model ◽  
Mixed Integer Linear Optimization ◽  
Empty Containers

Purpose The purpose of this paper is to figure out in which way a hinterland-based inland depot model can help a shipping company in solving the empty container problem at a regional level. The repositioning of empty containers is a very expensive operation that does not generate profits. Consequently, it is very important to provide an efficient empty container management. Design/methodology/approach In this paper, the empty container problem is discussed at a regional repositioning level. For solving this problem, a mixed-integer linear optimization model is developed and validated by using the German hinterland as a case. Findings The findings show that the hinterland-based solution is able to reduce the total system costs by 40 per cent. In addition, total of truck kilometres could be reduced by more than 30 per cent too. Research limitations/implications This research is based on German data only. Originality/value This paper closes the gap in empty container repositioning research by looking at the hinterland dimension from a single shipping company point of view.

scholarly journals Distribution-Free Model for Ambulance Location Problem with Ambiguous Demand

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Feng Chu ◽  
Lu Wang ◽  
Xin Liu ◽  
Chengbin Chu ◽  
Yang Sui
Keyword(s):  
Probability Distribution ◽  
Location Problem ◽  
Service Level ◽  
Mixed Integer ◽  
Distribution Free ◽  
Demand Information ◽  
The Mean ◽  
Constrained Model ◽  
Short Time ◽  
Ambulance Location

Ambulance location problem is a key issue in Emergency Medical Service (EMS) system, which is to determine where to locate ambulances such that the emergency calls can be responded efficiently. Most related researches focus on deterministic problems or assume that the probability distribution of demand can be estimated. In practice, however, it is difficult to obtain perfect information on probability distribution. This paper investigates the ambulance location problem with partial demand information; i.e., only the mean and covariance matrix of the demands are known. The problem consists of determining base locations and the employment of ambulances, to minimize the total cost. A new distribution-free chance constrained model is proposed. Then two approximated mixed integer programming (MIP) formulations are developed to solve it. Finally, numerical experiments on benchmarks (Nickel et al., 2016) and 120 randomly generated instances are conducted, and computational results show that our proposed two formulations can ensure a high service level in a short time. Specifically, the second formulation takes less cost while guaranteeing an appropriate service level.

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