Constrained integrated inventory model for multi-item under mixture of distributions

2018 ◽  
Vol 52 (3) ◽  
pp. 849-893 ◽  
Author(s):  
R. Uthayakumar ◽  
M. Ganesh Kumar
Keyword(s):  
Cost Function ◽  
Lead Time ◽  
Inequality Constraints ◽  
Integrated Approach ◽  
Mixed Integer ◽  
Lagrangian Multiplier ◽  
Total Cost ◽  
Proposed Model ◽  
Integrated Inventory ◽  
Integrated Cost

When the demand of different customers are not identical during the lead time, then one cannot use only a single distribution to describe the demand during that lead time. Hence, in this paper we have studied a mixture of normal distributions and a mixture of distribution free for several products under vendor-buyer integrated approach (coordination between both parties). Many integrated inventory models have proved that the integrated total cost is minimum when compared to sum of the total cost of the individuals. The inventory is continuously reviewed by the buyer and next order is placed when the inventory reaches some level called reorder level. The buyer has limited warehouse space capacity and also limited budget to purchase all products. The lead time of receiving all products from the vendor is a variable which is controlled by adding crashing cost. Shortages are allowed for all products and a fraction of shortages will be backordered and the remaining are lost. A mathematical model is developed and a solution procedure is employed in this study to obtain optimum order quantities, lead time and number of shipments in which the integrated total cost function attains its minimum subject to the floor space constraint and budget constraint. The expected integrated cost function is non-linear mixed integer with inequality constraints. Therefore, the proposed model have been solved by using Lagrangian multiplier technique. Finally numerical examples and sensitivity analysis were performed to illustrate the effectiveness of the proposed model.

scholarly journals Fuzzy Constrained Probabilistic Inventory Models Depending on Trapezoidal Fuzzy Numbers

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Mona F. El-Wakeel ◽  
Kholood O. Al-yazidi
Keyword(s):  
Exact Solutions ◽  
Lead Time ◽  
Fuzzy Numbers ◽  
Total Cost ◽  
Continuous Review ◽  
Fuzzy Models ◽  
First Case ◽  
Proposed Model ◽  
Special Cases ◽  
Cost Components

We discussed two different cases of the probabilistic continuous review mixture shortage inventory model with varying and constrained expected order cost, when the lead time demand follows some different continuous distributions. The first case is when the total cost components are considered to be crisp values, and the other case is when the costs are considered as trapezoidal fuzzy number. Also, some special cases are deduced. To investigate the proposed model in the crisp case and the fuzzy case, illustrative numerical example is added. From the numerical results we will conclude that Uniform distribution is the best distribution to get the exact solutions, and the exact solutions for fuzzy models are considered more practical and close to the reality of life and get minimum expected total cost less than the crisp models.

Optimal planning of water and wastewater management infrastructure for insular areas: the role of water reuse

2015 ◽  
Vol 15 (4) ◽  
pp. 701-708 ◽  
Author(s):  
Petros Gikas ◽  
Songsong Liu ◽  
Lazaros G. Papageorgiou ◽  
Flora Konstantopoulou
Keyword(s):  
Water Reuse ◽  
Population Distribution ◽  
Mixed Integer ◽  
Wastewater Management ◽  
Water Reclamation ◽  
Total Cost ◽  
Groundwater Availability ◽  
Proposed Model ◽  
Water And Wastewater ◽  
Optimum Water

The present article estimates the financial benefits of water reuse by calculating the annualised total cost of water and wastewater management, using mixed integer linear programming. The programme is using as input: geographical data, population distribution, and groundwater availability (for a given area), to calculate the qualitative localised water needs, and to estimate the sizes and locations of water and wastewater management infrastructure, so as to minimise the relative annualised total cost (capital and operating). The programme is used to calculate the optimum water and wastewater infrastructure (and the relative annualised water and wastewater management cost), with and without the option for water reclamation and reuse. One case study is presented for the Greek islands of Santorini and Thirasia. The proposed model has showed significant computational benefit, compared with previous models. Thus, for Santorini–Thirasia Islands, the total annualised cost for optimum water and wastewater management infrastructures, with water reclamation, has been calculated as $2,153,694, while the above cost has been calculated as 19% higher, if water reclamation is not an option. It is obvious from the computational results that water reuse can reduce significantly the total water and wastewater management cost.

The ROLE OF CHINA-PAK ECONOMIC CORRIDOR (CPEC) IN LOGISTIC SYSTEM OF PAKISTAN’S AND CHINA’S

2019 ◽  
Vol 6 (1) ◽  
pp. 48-50
Author(s):  
Ikram Uddin
Keyword(s):  
Persian Gulf ◽  
Lead Time ◽  
Fiber Optic ◽  
Delivery Time ◽  
Fiber Optic Cable ◽  
Total Cost ◽  
Economic Complexity ◽  
Shipping Cost ◽  
The Impact

This study will explain the impact of China-Pak Economic Corridor (CPEC) on logistic system of China and Pakistan. This project is estimated investment of US $90 billion, CPEC project is consists of various sub-projects including energy, road, railway and fiber optic cable but major portion will be spent on energy. This project will start from Kashgar port of china to Gwadar port of Pakistan. Transportation is sub-function of logistic that consists of 44% total cost of logistic system and 20% total cost of production of manufacturing and mainly shipping cost and transit/delivery time are critical for logistic system. According to OEC (The Observing Economic Complexity) currently, china is importing crude oil which 13.4% from Persian Gulf. CPEC will china for lead time that will be reduced from 45 days to 10 days and distance from 2500km to 1300km. This new route will help to china for less transit/deliver time and shipping cost in terms of logistic of china. Pakistan’s transportation will also improve through road, railway and fiber optic cabal projects from Karachi-Peshawar it will have speed 160km per hour and with help of pipeline between Gwadar to Nawabshah gas will be transported from Iran. According to (www.cpec.inf.com) Pakistan logistic industry will grow by US $30.77 billion in the end of 2020.

scholarly journals A Spatiotemporal Convolutional Gated Recurrent Unit Network for Mean Wave Period Field Forecasting

2021 ◽  
Vol 9 (4) ◽  
pp. 383
Author(s):  
Ting Yu ◽  
Jichao Wang
Keyword(s):  
Lead Time ◽  
Wave Period ◽  
Data Driven ◽  
Lead Times ◽  
Proposed Model ◽  
Data Driven Approach ◽  
Mean Wave Period ◽  
Scattering Index ◽  
Gated Recurrent Unit ◽  
Methods Numerical

Mean wave period (MWP) is one of the key parameters affecting the design of marine facilities. Currently, there are two main methods, numerical and data-driven methods, for forecasting wave parameters, of which the latter are widely used. However, few studies have focused on MWP forecasting, and even fewer have investigated it with spatial and temporal information. In this study, correlations between ocean dynamic parameters are explored to obtain appropriate input features, significant wave height (SWH) and MWP. Subsequently, a data-driven approach, the convolution gated recurrent unit (Conv-GRU) model with spatiotemporal characteristics, is utilized to field forecast MWP with 1, 3, 6, 12, and 24-h lead times in the South China Sea. Six points at different locations and six consecutive moments at every 12-h intervals are selected to study the forecasting ability of the proposed model. The Conv-GRU model has a better performance than the single gated recurrent unit (GRU) model in terms of root mean square error (RMSE), the scattering index (SI), Bias, and the Pearson’s correlation coefficient (R). With the lead time increasing, the forecast effect shows a decreasing trend, specifically, the experiment displays a relatively smooth forecast curve and presents a great advantage in the short-term forecast of the MWP field in the Conv-GRU model, where the RMSE is 0.121 m for 1-h lead time.

scholarly journals Allocation and Scheduling of Handling Resources in the Railway Container Terminal Based on Crossing Crane Area

2021 ◽  
Vol 13 (3) ◽  
pp. 1190
Author(s):  
Gang Ren ◽  
Xiaohan Wang ◽  
Jiaxin Cai ◽  
Shujuan Guo
Keyword(s):  
Programming Model ◽  
Container Terminal ◽  
Simultaneous Optimization ◽  
Mixed Integer ◽  
Gantry Crane ◽  
Optimization Scheme ◽  
Long Distance ◽  
Proposed Model ◽  
Hybrid Heuristic Algorithm ◽  
Searching Ability

The integrated allocation and scheduling of handling resources are crucial problems in the railway container terminal (RCT). We investigate the integrated optimization problem for handling resources of the crane area, dual-gantry crane (GC), and internal trucks (ITs). A creative handling scheme is proposed to reduce the long-distance, full-loaded movement of GCs by making use of the advantages of ITs. Based on this scheme, we propose a flexible crossing crane area to balance the workload of dual-GC. Decomposing the integrated problem into four sub-problems, a multi-objective mixed-integer programming model (MIP) is developed. By analyzing the characteristic of the integrated problem, a three-layer hybrid heuristic algorithm (TLHHA) incorporating heuristic rule (HR), elite co-evolution genetic algorithm (ECEGA), greedy rule (GR), and simulated annealing (SA) is designed for solving the problem. Numerical experiments were conducted to verify the effectiveness of the proposed model and algorithm. The results show that the proposed algorithm has excellent searching ability, and the simultaneous optimization scheme could ensure the requirements for efficiency, effectiveness, and energy-saving, as well as the balance rate of dual-GC.

scholarly journals An Optimized Mathematical Model for Items Supplies Planning of a Logistic System

2016 ◽  
Vol 10 (10) ◽  
pp. 133
Author(s):  
Mohammad Ali Nasiri Khalili ◽  
Mostafa Kafaei Razavi ◽  
Morteza Kafaee Razavi
Keyword(s):  
Mathematical Model ◽  
Mixed Integer ◽  
Logistics System ◽  
Proposed Model ◽  
Multiple Objective Decision Making ◽  
System Requirements ◽  
Purchasing Logistics ◽  
The Cost ◽  
The Mathematical Model ◽  
First Time

Items supplies planning of a logistic system is one of the major issue in operations research. In this article the aim is to determine how much of each item per month from each supplier logistics system requirements must be provided. To do this, a novel multi objective mixed integer programming mathematical model is offered for the first time. Since in logistics system, delivery on time is very important, the first objective is minimization of time in delivery on time costs (including lack and maintenance costs) and the cost of purchasing logistics system. The second objective function is minimization of the transportation supplier costs. Solving the mathematical model shows how to use the Multiple Objective Decision Making (MODM) can provide the ensuring policy and transportation logistics needed items. This model is solved with CPLEX and computational results show the effectiveness of the proposed model.

A Least Cost Transmission Planning Model Considering Operation Cost

2014 ◽  
Vol 15 (2) ◽  
pp. 121-128
Author(s):  
Jorge Hans Alayo
Keyword(s):  
Test System ◽  
Mixed Integer ◽  
Transmission Planning ◽  
Integer Linear Programming Problem ◽  
Transmission Expansion ◽  
Planning Models ◽  
Proposed Model ◽  
Expansion Model ◽  
Operation Cost ◽  
Linearization Techniques

Abstract Existing transmission planning models consider basic aspects of the problem. In practice, a transmission utility needs to model other important details such as operation cost of the power system. In this article, a least cost transmission expansion model is proposed considering the operation cost in order to model the trade-off between building new transmission capacity and increasing the power system’s operation cost. The proposed model is transformed into a mixed integer linear programming problem using linearization techniques and solved with CPLEX. Finally, results of the model for the Garver test system and IEEE 24-bus test system are shown.

A Multi-Period Evacuation Vehicle Routing Problem Model

2014 ◽  
Vol 931-932 ◽  
pp. 578-582
Author(s):  
Sunarin Chanta ◽  
Ornurai Sangsawang
Keyword(s):  
Vehicle Routing ◽  
Public Transportation ◽  
Vehicle Routing Problem ◽  
Programming Model ◽  
High Water ◽  
Mixed Integer ◽  
Routing Problem ◽  
Problem Model ◽  
Proposed Model ◽  
Evacuation Routing

In this paper, we proposed an optimization model that addresses the evacuation routing problem for flood disaster when evacuees trying to move from affected areas to safe places using public transportation. A focus is on the situation of evacuating during high water level when special high vehicles are needed. The objective is to minimize the total traveled distance through evacuation periods where a limited number of vehicles is given. We formulated the problem as a mixed integer programming model based on the capacitated vehicle routing problem with multiple evcuation periods where demand changing by the time. The proposed model has been tested on a real-world case study affected by the severe flooding in Thailand, 2011.

How can mixed integer linear programming assist dairy manufacturers by integrating supply decisions and production planning?

2021 ◽  
Vol 11 (2) ◽  
pp. 178-193
Author(s):  
Juliana Emidio ◽  
Rafael Lima ◽  
Camila Leal ◽  
Grasiele Madrona
Keyword(s):  
Linear Programming ◽  
Supply Chain ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Dairy Products ◽  
Raw Milk ◽  
Mixed Integer ◽  
Content Type ◽  
Proposed Model ◽  
By Products

PurposeThe dairy industry needs to make important decisions regarding its supply chain. In a context with many available suppliers, deciding which of them will be part of the supply chain and deciding when to buy raw milk is key to the supply chain performance. This study aims to propose a mathematical model to support milk supply decisions. In addition to determining which producers should be chosen as suppliers, the model decides on a milk pickup schedule over a planning horizon. The model addresses production decisions, inventory, setup and the use of by-products generated in the raw milk processing.Design/methodology/approachThe model was formulated using mixed integer linear programming, tested with randomly generated instances of various sizes and solved using the Gurobi Solver. Instances were generated using parameters obtained from a company that manufactures dairy products to test the model in a more realistic scenario.FindingsThe results show that the proposed model can be solved with real-world sized instances in short computational times and yielding high quality results. Hence, companies can adopt this model to reduce transportation, production and inventory costs by supporting decision making throughout their supply chains.Originality/valueThe novelty of the proposed model stems from the ability to integrate milk pickup and production planning of dairy products, thus being more comprehensive than the models currently available in the literature. Additionally, the model also considers by-products, which can be used as inputs for other products.

Sustainable optimal ordering quantity for non-instantaneous deteriorating items under joint replenishment with substitution and carbon emission

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ranu Singh ◽  
Vinod Kumar Mishra
Keyword(s):  
Cost Function ◽  
Carbon Emission ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Joint Replenishment ◽  
Content Type ◽  
Total Cost ◽  
Optimal Ordering ◽  
Ordering Quantity ◽  
Total Cost Function

Purpose Carbon emission is a significant issue for the current business market and global warming. Nowadays, most countries have focused to reduce the environmental impact of business with durable financial benefits. The purpose of this study is to optimize the entire cost functions with carbon emission and to find the sustainable optimal ordering quantity for retailers. Design/methodology/approach This paper illustrates a sustainable inventory model having a set of two non-instantaneous substitutable deteriorating items under joint replenishment with carbon emission. In this model demand and deterioration rate are considered as deterministic, constant and triangular fuzzy numbers. The objective is to find the optimal ordering quantity for retailers and to minimize the total cost function per unit time with carbon emission. The model is then solved with the help of Maple software. Findings This paper presents a solution method and also develop an algorithm to determine the order quantities which optimize the total cost function. A numerical experiment illustrates the improvement in optimal total cost of the inventory model with substitution over without substitution. The graphical results show the convexity of the cost function. Finally, sensitivity analysis is given to get the impact of parameters and validity of the model. Originality/value This study considers a set of two non-instantaneous substitutable deteriorating items under joint replenishment with carbon emission. From the literature review, in the authors’ knowledge no researcher has undergone this kind of study.

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