Unit Transportation Cost Research Articles

A transportation problem with fuzzy-stochastic cost

In this paper, we consider some transportation problems (TPs) with different types of fuzzy-stochastic unit transportation costs and budget constraints. These fuzzy stochastic costs are reduced to corresponding crisp ones in two different ways. For the first method, using the definition of α-cut of the fuzzy numbers, expectation is taken separately on both lower and upper α-cuts and then mean expectation is calculated with the help of signed distance. In the second procedure, we realize fuzzy random events (ξ⩾r) and (ξ⩽r) for the fuzzy random variable (ξ). Using credibility measure of these events, mean chances for the above fuzzy random events are calculated and then expectation is taken to get the crisp expressions. The reduced deterministic problems of the fuzzy stochastic TP are solved using a real coded genetic algorithm with Roulette wheel selection, arithmetic crossover and random mutation. Few numerical examples are demonstrated to find the optimal solutions of the proposed models.

Fixed charge transportation problem with type-2 fuzzy variables

This paper considers two fixed charge transportation problems with type-2 fuzzy parameters. Unit transportation costs, fixed costs in the first problem and unit transportation costs, fixed costs, supplies and demands in the second problem are type-2 fuzzy variables. For the first problem, to get corresponding defuzzified values of the type-2 fuzzy cost parameters, first critical value (CV)-based reduction methods are applied to reduce type-2 fuzzy variables into type-1 fuzzy variables and then centroid method is used for complete defuzzification. Besides this, we also apply geometric defuzzification method to the type-2 fuzzy cost parameters in the first problem to provide a comparison of the results. Coming to the second problem, a chance-constrained programming model is formulated using generalized credibility measure for the objective function as well as the constraints with the CV-based reductions of corresponding type-2 fuzzy parameters. Next, the reduced model is turned into equivalent parametric programming problem. The deterministic problems so obtained are then solved by using the standard optimization solver – LINGO. We have provided numerical examples illustrating the proposed models and techniques. Some sensitivity analyzes for the second model are also presented.

A multi-item transportation problem with fuzzy tolerance

This paper presents the recently introduced modified subgradient method for optimization and its effectiveness in a fuzzy transportation model. Here a multi-item balanced transportation problem (MIBTP) is formulated where unit transportation costs are imprecise. Also available spaces and budgets at destinations are limited but imprecise. The objective is to find a shipment schedule for the items that minimizes the total cost subjected to imprecise warehouse and budget constraints at destinations. The proposed model is reduced to a multi-objective optimization problem using tolerances, then to a crisp single-objective one using fuzzy non-linear programming (FNLP) technique and Zimmermann's method. The above fuzzy MIBTP is also reduced to another form of deterministic one using modified sub-gradient method (MSM). These two crisp optimization problems are solved by Genetic Algorithm (GA). As an extension, fuzzy multi-item balanced solid transportation problems (STPs) with and without restrictions on some routes and items are formulated and reduced to deterministic ones following FNLP and Zimmermann's methods. These models are also solved by GA. Models are illustrated numerically, optimum results of fuzzy MIBTP from two deductions are compared. Results are also presented for different GA parameters.

Online retailers’ promotional pricing, free-shipping threshold, and inventory decisions: A simulation-based analysis

We consider a two-stage decision problem, in which an online retailer first makes optimal decisions on his profit margin and free-shipping threshold, and then determines his inventory level. We start by developing the retailer’s expected profit function. Then, we use publicly-available statistics to find the best-fitting distribution for consumers’ purchase amounts and the best-fitting function for conversion rate (i.e., probability that an arriving visitor places an online order with the retailer). We show that: (i) a reduction of the profit margin does not significantly affect the standard deviation of consumers’ order sizes (purchase amounts) but increases the average order size; whereas, (ii) variations in a positive finite free-shipping threshold affect both the average value and the standard deviation of the order sizes. We then use Arena to simulate the online retailing system and OptQuest to find the retailer’s optimal decisions and maximum profit. Next, we perform a sensitivity analysis to examine the impact of the ratio of the unit holding and salvage cost to the unit shipping cost on the retailer’s optimal decisions. We also draw some important managerial insights.

The impact of plant size and location on profitability of biogas plants in Germany under consideration of processing digestates

The production of bioenergy is considered to be a promising energy source for a sustainable energy mix and it is politically promoted in many countries. With the exception of Brazilian ethanol, bioenergy is not competitive with fossil energy sources, and therefore needs to be subsidised. Several types of bioenergy are based on bulky raw biomass with high per unit transport costs, importantly impacting on the plant's production costs and profitability. In addition, considerable quantities of digestates are released, causing disposal costs. Various studies in the past aimed primarily at analysing transport costs of inputs. In this paper we focus on disposal costs of fermentation digestates from biogas production in Germany and analyse different processing techniques and their impact on profitability for three plant size in three case study areas.Our results show that especially in regions with only a small amount of agricultural land and a large heterogeneity in its agricultural area, processing of digestates increases the profitability of biogas production. The same accounts for regions with high livestock density, where the area needed for disposal is comparatively large. The cost efficiency is enforced by a high share of animal excrements on input and the biogas plant size.

Determining optimal resource recycling boundary at regional level: A case study on Tokyo Metropolitan Area in Japan

Conventionally, material inputs to industries come from either natural resources or intermediate products. With the increasing attention on greening the industrial process, municipal solid waste (MSW) can be separated and utilized as inputs to large-scale industries. As such, waste flows need to be managed to meet the requirements of industries by considering both quality and scale. Small scales of municipal recycling centers (MRCs) for pre-treating recyclable wastes often lead to higher pre-treatment cost and lower recycling efficiencies. Theoretically, appropriate facility scale and recycling boundary should be based upon a balanced consideration between economies of scale and transportation costs. However, only a few empirical studies on recycling boundaries have been conducted. Existing modeling studies are mostly case studies for planning purposes and do not theoretically examine the mechanisms and factors that determine recycling boundary. Under such a circumstance, this paper fills such a gap by quantitatively seeking the determinants for recycling boundaries and the related mechanism. An optimization model applying on the recycling of waste plastics is developed and tested in the Tokyo Metropolitan Region (TMR) in Japan. The results indicate two determinants for recycling boundary at the regional level: spatial density of separated wastes and the ratio of unit transportation cost to unit treatment cost. Separated wastes that are collected in low spatial density and have a low ratio of unit transportation cost to unit treatment cost should be better recycled in a large region. The finding implies that regional recycling networks should have multiple layers designed for different types of wastes due to the differences in their spatial density, unit transportation cost and unit treatment cost.

Port Privatization in an International Oligopoly

We investigate how port privatization affects port charges, firm profits, and welfare. Our model consists of an international duopoly with two ports and two markets. When the unit transport cost is large, privatization of ports decreases the prices for port usage, although neither government has an incentive to privatize its port. The equilibrium governmental decisions are inconsistent with the desirable outcome if the unit transport cost is not large enough. The smaller country’s government is more likely to privatize its port, although the larger country’s government is more likely to nationalize its port to protect its domestic market.

Product quality and Firm Heterogeneity in International Trade

I develop and implement a methodology for obtaining plant-level estimates of product quality from revenue and physical output data. Intuitively, firms that sell large quantities of output conditional on price are classified as high quality producers. I use this method to decompose cross-plant variation in price and export status into a quality and an efficiency margin. The empirical results show that prices are increasing in quality and decreasing in efficiency. However, selection into exporting is driven mainly by quality. The finding that changes in quality and efficiency have different impact on the firm's export decision is shown to be inconsistent with the traditional iceberg trade cost formulation and points to the importance of per unit transport costs.

An Inverse Capacitated Transportation Problem

This paper deal with the inverse version of capacitated transportation problem, in which the unit transportation cost of some cells in the original problem are adjusted as little as possible so that the given feasible solution become an optimal one. In our proposed method, first we reduce the capacitated transportation problem into linear programming problem and then obtained its inverse problem using dual and the optimality conditions. The method has been illustrated by a numerical example also.

Selection of ore transport system for a metalliferous underground mine / Dobór systemu transportu rud w kopalni podziemnej rud metalu

Abstract The conditions of increasing competition in today’s mining industry, deepening of mines and also decreasing ore reserve and quality parameters (grade, calorie, ppm, etc.) compels to reduce unit cost for maximum benefit. In this context, optimization of machinery and equipment in technical and economical sense is required in terms of economic mining. In underground mining, as ore transport operation significantly affects profitability, optimization of the system gains importance technically and economically. In this paper, the authors studied production capacities up to 1,000,000 ton/year and orebody depths up to 1,000 m according to different haulage systems; conventional shaft hoisting, declined mine truck haulage and flexowell vertical belt applications. In model study, unit transport costs of each alternative depending on the production capacity and mine depth have been calculated.

The Impact of Unilateral Climate Policy with Endogenous Plant Location and Market Size Asymmetry

AbstractThis paper analyses the impact of unilateral climate policy on firms' international location strategies in emission‐intensive sectors, when countries differ in terms of market size. The cases of both partial and total relocation via foreign direct investment are separately considered. A simple international duopoly model highlights the differences between short‐term and long‐term effects. In the short‐term no change in location is a likely outcome in very capital‐intensive sectors and, when there is a strategy shift, this takes the form of partial rather than total relocation. In the long‐run total relocation becomes a feasible outcome. However, when tighter mitigation measures are introduced by the larger country and unit transport cost is high, with a pronounced market asymmetry, the probability of firms not relocating abroad is high even in the long‐term. The welfare implications of unilateral environmental measures are assessed considering global industrial pollution and accounting for shifts in location strategy.

Taguchi method for parameter design in ACO algorithm for distribution–allocation in a two-stage supply chain

In a distribution–allocation problem, when fixed cost for a transportation route is also taken into account in addition to the unit transportation cost, the problem is known as fixed charge transportation problem (FCTP). It is not possible to solve an FCTP optimally in polynomial time. This forces the researchers and practitioners to develop efficient non-traditional optimisation techniques that can provide near-optimal solutions in lesser time. This paper presents a solution methodology using ant colony optimisation (ACO) for a distribution–allocation problem in a two-stage supply chain with fixed cost for a transportation route. Taguchi method for robust design is adopted for finding the optimum combination of parameters of the ACO algorithm. A comparative analysis between the predicted signal-to-noise (S/N) ratio and the actual S/N ratio reveals that the error deviation in the experiment is minimal. From the confirmation tests, a good agreement between the predicted S/N ratio and the actual S/N ratio is observed. This validates the proposed experiment based on Taguchi method for parameter design.

Agility and Proximity Considerations in Supply Chain Design - An Analytical Approach

Strategic supply chain design decisions are critical to the long-term success of a business. Traditional facility location models for supply chain design focus on the trade-offs between the costs and benefits of proximity, i.e., the distance between facilities and customers. These strategic-focused models do not consider the supply chain's agility, i.e., its ability to quickly respond to unexpected fluctuations in customer needs. In this paper, we study the problem of designing a supply chain distribution network under demand uncertainty and analyze how the optimal design characteristics of proximity and agility depend on various input parameters. We are able to draw managerial insights on how agility considerations may invalidate well-established and widely-accepted qualitative results derived from traditional models. In particular, we show that it is optimal to increase the density of DCs when the shortage penalty cost increases, and to decrease the density of DCs when a certain unit transportation cost parameter increases. Through these findings, our work conveys the message that traditional, proximity-based facility location models can be inadequate for designing modern responsive supply chains, and calls for the need to develop a new class of models for the task.

Multi-Dimensional Product Differentiation

We analyze product differentiation in a multi-dimensional model with non-uniform consumer distribution. The level of product differentiation is measured by both unit transport costs and firm locations. Our analysis concerns both measures. First, fixing firms' locations, we show that equilibrium prices can increase or decrease with unit transport cost. The overall result depends on the interplay of a shifting effect and a rotating effect -- the latter exists only in multi-dimensional models. Second, fixing unit transport costs, we find that under non-uniform distribution, there may exist no equilibrium where firms maximize differentiation on one dimension but minimize differentiation on other dimensions. Instead, there may exist equilibrium where firms choose intermediate locations, contrary to the common findings in existing studies which assume uniform distribution.

Economic evaluation of CO 2 pipeline transport in China

Carbon capture and sequestration (CCS) is an important option for CO 2 mitigation and an optimized CO 2 pipeline transport system is necessary for large scale CCS implementation. In the present work, a hydrodynamic model for CO 2 pipeline transport was built up and the hydrodynamic performances of CO 2 pipeline as well as the impacts of multiple factors on pressure drop behavior along the pipeline were studied. Based on the model, an economic model was established to optimize the CO 2 pipeline transport system economically and to evaluate the unit transport cost of CO 2 pipeline in China. The hydrodynamic model results show that pipe diameter, soil temperature, and pipeline elevation change have significant influence on the pressure drop behavior of CO 2 in the pipeline. The design of pipeline system, including pipeline diameter and number of boosters etc., was optimized to achieve a lowest unit CO 2 transport cost. In regarding to the unit cost, when the transport flow rate and distance are between 1–5 MtCO 2/year and 100–500 km, respectively, the unit CO 2 transport cost mainly lies between 0.1–0.6 RMB/(tCO 2 km) and electricity consumption cost of the pipeline inlet compressor was found to take more than 60% of the total cost. The present work provides reference for CO 2 transport pipeline design and for feasibility evaluation of potential CCS projects in China.

Modelling regional input markets with numerous processing plants: The case of green maize for biogas production in Germany

The location of first generation processing plants for biogas using bulky inputs is a prominent example of locational decisions of plants that face high per unit transport costs of feedstock and simultaneously depend to a large extent on feedstock availability. Modelling the resulting regional feedstock markets then requires a spatially explicit representation of demand. With production capacities of plants small in comparison to market size, large numbers of possible type-location combinations need to be considered, requiring considerable computation time under existing integer programming-based approaches. Therefore, in this paper we aim to present an alternative, faster and more flexible iterative solution approach to simulate location decisions for processing plants. And with greater flexibility, this approach is able to take into account spatially heterogeneous transport costs depending on total demand. The approach is implemented in a modelling framework for biogas production from green maize in Germany, which currently accounts for ca. five per cent of Germany’s agricultural area. By modifying green maize prices, demand functions are derived and intersected with regional supply functions from an agricultural model to simulate market clearing prices and quantities. The application illustrates that our approach efficiently simulates markets characterised by small-scale demand units and high, spatially heterogeneous transport costs.

Foreign Direct Investment and Environmental Policy: Have Location Factors Been Neglected?

This paper analyzes the effect of asymmetric environmental policies on firms' international location strategies in pollution-intensive sectors, when countries differ in terms of market size. The model shows that, when the tighter mitigation measures are introduced by the larger country and unit transport cost is high, the probability of firms not relocating abroad via foreign direct investment increases with market asymmetry. Furthermore, in some key scenarios, the total relocation outcome predicted by the pollution haven hypothesis is never an optimal strategy. The analysis suggests that international environmental rules should take account of differences in countries' market size and thus ability to attract production.

Modelling supply chain decision problem with fixed charge – a review

In the recent past, distribution activity in a supply chain is considered as a major function. The basic version of a transportation problem is linear, single objective, balanced and planar problem. Generally, the unit transportation cost is used to find optimal distribution schedule and this unit transportation cost is directly proportional to the transported load. In real life situations, there is another cost associated with the distribution which is known as fixed cost. In the presence of fixed cost, the model becomes a fixed charge transportation problem which is an extension of transportation problem. This paper presents the state-of-the-art review of the research on the fixed charge transportation problem. Directions for further research are also highlighted.

Economies of size of large containerships based on internal and external costs

Economies and diseconomies of ship size express the change of shipping costs as a function of ship size. In an earlier publication by one of the authors the impact of increasing containership size on unit shipping costs up to 20,000 TEU was elaborated. This paper expands in two directions. The first is to include ship design parameters to support statements on future containership particulars with respect to size, dimensions, speed and engine power, rather than just extrapolating them either explicitly or implicitly. The second is to include external costs related to the effects of CO 2 emissions on climate change. Discussions on the monetary value of these emissions are in full swing. This paper therefore applies a plausible bandwidth. Results of the analysis show that economies of ships size continue to exist for ships up to 25,000 TEU, but those technical limitations with respect to propulsion, engine power and cavitations put the maximum size of a single propeller ship at a lower level.

Game Equilibrium of Agricultural Biomass Material Competition -Its Assumptions, Conditions and Probability

Abstract This research aims to shed light on the mechanism of agricultural biomass material competition between the power generation and straw pulp industries in a local area. A two-stage game model is set up based on the assumptions on biomass distribution and structure of collection cost to analyze parameters of equilibrium, such as unit transportation cost, and profit spaces. The condition and probability is derived from the solutions of game equilibrium. The results show that raw material competition will hardly bring about the sustainable development of the two industries based on agricultural residues in the assumed circular collection area