Intermodal competition changes with changes in technology, economics, and environmental concerns. Trucks and airships are generally considered not to be competitors, but this depends on the distance of haul. The tonne...Intermodal competition changes with changes in technology, economics, and environmental concerns. Trucks and airships are generally considered not to be competitors, but this depends on the distance of haul. The tonne-kilometer cost of trucking rises much more quickly with distance than it does the cost of a cargo airship. At some distance, the two modes are direct substitutes. The costs of the Mexico-Canada refrigerated truck supply chain are compared with the costs of a 100t-lift, electrically-powered airship. The flight characteristics of the Hindenburg Zeppelin are used as a model for a modern cargo airship. The supply chain cost of trucking tomatoes is used to test the theorical proposition. The cost difference works out to about US10￠/kg (5￠/lb) advantage for trucking Mexican tomatoes to Canada. However, this cost disadvantage of the airship could be made up by their vibrationless ride, better air circulation and one-day service versus four days by truck. This alternative form of transportation could have a positive impact on worldwide north-south distribution of food. Airships can overcome trade barriers and distance to open new markets for perishable food exports. In addition, they would reduce the carbon emissions of transport. Canada imports 160,000 refrigerated truckloads of fruits and vegetables by from the southern US and Mexico. With an average driving distance of 3,000 km, these trucks emit 606,000 MT of CO<sub>2</sub> annually. Airships powered by hydrogen fuel cells would have zero-carbon emissions. Markets are not yet incorporating the environmental advantage of airships in any freight comparison, but inevitably this will be important.展开更多
The classical supply chain network(SCN)design problem is extended,where the candidate facilities are subject to failure and the products are prone to elapsed time deteriorion.First,the reliable SCN design problem is d...The classical supply chain network(SCN)design problem is extended,where the candidate facilities are subject to failure and the products are prone to elapsed time deteriorion.First,the reliable SCN design problem is defined by introducing the probability that a facility may be prone to inactivity based on the analysis of perishable product characteristics.The perishable product SCN design problem is formulated as a 0-1 integer programming model.The objective is to minimize the weighted sum of the operating cost(the fixed plus transportation cost)and the expected failure cost.And then,the perishable product SCN design model is discussed and solved using the genetic algorithm(GA).The results show how to generate the tradeoff curve between the operating costs and the expected failure costs.And these tradeoff curves demonstrate empirically that substantial improvements in reliability are often possible with minimal increase in the operating costs.展开更多
被引分析是最常见的科学计量学研究方法,主要用来证明作者或其成果在所属专业领域内的影响力。Publish or Perish是一种在线被引分析软件,依据Google Scholar数据库来查询作者或成果的被引次数,并提供相关的统计数据分析。文章主要介绍...被引分析是最常见的科学计量学研究方法,主要用来证明作者或其成果在所属专业领域内的影响力。Publish or Perish是一种在线被引分析软件,依据Google Scholar数据库来查询作者或成果的被引次数,并提供相关的统计数据分析。文章主要介绍了该工具的功能及使用方法,并结合实例探讨了其在外语教学研究中的应用。展开更多
There is still no effective means to analyze in depth and utilize domestic mass data about agricultural product quality safety tests in china now. The neural network algorithm, the classification regression tree algor...There is still no effective means to analyze in depth and utilize domestic mass data about agricultural product quality safety tests in china now. The neural network algorithm, the classification regression tree algorithm, the Bayesian network algorithm were selected according to the principle of selecting combination model and were used to build models respectively and then combined, innovatively establishing a combination model which has relatively high precision, strong robustness and better explanatory to predict the results of perishable food transportation meta-morphism monitoring. The relative optimal prediction model of the perishable food transportation metamorphism monitoring system could be got. The relative perfect prediction model can guide the actual sampling work about food quality and safety by prognosticating the occurrence of unqualified food to select the typical and effective samples for test, thus improving the efficiency and effectiveness of sampling work effectively, so as to avoid deteriorated perishable food’s approaching the market to ensure the quality and safety of perishable food transportation. A solid protective wall was built in the protection of general perishable food consumers’ health.展开更多
This paper presents an economic lot-sizing problem with perishable inventory and general economies of scale cost functions. For the case with backlogging allowed, a mathematical model is formulated, and several proper...This paper presents an economic lot-sizing problem with perishable inventory and general economies of scale cost functions. For the case with backlogging allowed, a mathematical model is formulated, and several properties of the optimal solutions are explored. With the help of these optimality properties, a polynomial time approximation algorithm is developed by a new method. The new method adopts a shift technique to obtain a feasible solution of subproblem and takes the optimal solution of the subproblem as an approximation solution of our problem. The worst case performance for the approximation algorithm is proven to be （4√2 ＋ 5）/7. Finally, an instance illustrates that the bound is tight.展开更多
The amount of perishable products transported via the existing intermodal freight networks has significantly increased over the last years. Perishable products tend to decay due to a wide range of external factors. Su...The amount of perishable products transported via the existing intermodal freight networks has significantly increased over the last years. Perishable products tend to decay due to a wide range of external factors. Supply chain operations mismanagement causes waste of substantial volumes of perishable products every year. The heretofore proposed mathematical models optimize certain supply chain processes and reduce decay of perishable products, but primarily deal with local production, inventory, distribution, and retailing of perishable products. However, significant quantities of perishable products are delivered from different continents, which shall increase the total transportation time and decay potential of perishable products as compared to local deliveries. This paper proposes a novel optimization model to design the intermodal freight network for both local and long-haul deliveries of perishable products. The objective of the model aims to minimize the total cost associated with transportation and decay of perishable products. A set of piecewise approximations are applied to linearize the non-linear decay function for each perishable product type. CPLEX is used to solve the problem. Comprehensive numerical experiments are conducted using the intermodal freight network for import of the seafood perishable products to the United States to draw important managerial insights. Results demonstrate that increasing product decay cost may significantly change the design of intermodal freight network for transport of perishable products, cause modal shifts and affect the total transportation time and associated costs.展开更多
This paper considers the two-echelon supply chain system which consists of single agricultural producers and retailers,and analyzes the impact of sharing ratio on the option ordering quantity,and retailers and produce...This paper considers the two-echelon supply chain system which consists of single agricultural producers and retailers,and analyzes the impact of sharing ratio on the option ordering quantity,and retailers and producers' expected profits.Studies have shown that in the case of decentralization,when the revenue sharing ratio is between 0 and 0.3,the option ordering quantity of farm produce is a decreasing function of the sharing ratio; when the revenue sharing ratio is between 0.3 and 1,the option ordering quantity of farm produce is an increasing function of sharing ratio; when the revenue sharing ratio is between 0.421 and 1,the agricultural producers and retailers' expected profits are an increasing function of sharing ratio.Finally,through the numerical calculation,the applicability of the conclusions is verified,to provide a reference for the supply chain management practices.展开更多
In the classical inventory models, it is assumed that the retailer pays to the supplier as soon as he received the items and in such cases the supplier offers a cash discount or credit period (permis-sible delay) to t...In the classical inventory models, it is assumed that the retailer pays to the supplier as soon as he received the items and in such cases the supplier offers a cash discount or credit period (permis-sible delay) to the retailer. In this paper we presented an inventory model for perishable items with time varying stock dependent demand under inflation. It is assumed that the supplier offers a credit period to the retailer and the length of credit period is dependent on the order quantity. The purpose of our study is to minimize the present value of retailer’s total cost. Numerical examples are also given to demonstrate the presented mode.展开更多
Despite the government expanding PhD enrollment,students face limited mentorship and pressure to publish in order to graduate.As they struggle,many find their degrees losing value amid rising societal expectations for...Despite the government expanding PhD enrollment,students face limited mentorship and pressure to publish in order to graduate.As they struggle,many find their degrees losing value amid rising societal expectations for talent.展开更多
Consumers pay more and more attention to the quality of perishable roods, which is mainly affected by storage temperature. This paper presents a dynamic pricing model for perishable foods under temperature control. To...Consumers pay more and more attention to the quality of perishable roods, which is mainly affected by storage temperature. This paper presents a dynamic pricing model for perishable foods under temperature control. To maximize the total profit, the optimal price and storage temperature are obtained using Pontryagin＇s maximum principle. A static pricing model is provided to compare with the dynamic one. It is shown by a numerical example that the dynamic policy can make more revenue than the static one. Moreover, the managerial implications are analyzed and the effectiveness of the proposed method is demonstrated.展开更多
Numerous empirical studies show that advertising effort can stimulate demand in both current and future periods, and there is an interaction between pricing, advertising and ordering decisions. How do these decisions ...Numerous empirical studies show that advertising effort can stimulate demand in both current and future periods, and there is an interaction between pricing, advertising and ordering decisions. How do these decisions interact with each other and what is the effect of advertising on pricing and ordering decisions？ To understand this interaction, we consider a newsvendor-type firm that sells a perishable product in a stable market and dynamically determines the joint ordering, pricing and advertising strategies. The problem is modeled as an infmite horizon newsvendor problem with an advertising carryover effect and price-sensitive demand. We characterize the optimal pricing, advertising and inventory strategies and their comparative statics, and consider how this policy differs from the traditional approach without the advertising effect. We show that the optimal effective advertising level is monotonically increasing with the effective advertising level in the previous period, and hence the optimal strategies （advertising, pricing, inventory level） globally converge to the steady states in the long run. We numerically show that the optimal policy can reap significant profit, which underscores the importance of the advertising-driven ordering and pricing strategies.展开更多
This study investigated an economic order quantity (EOQ) model with completebackorder for fixed lifetime perishable items under multiple advance and delayedpayments policies. Here, a new type of business policy is con...This study investigated an economic order quantity (EOQ) model with completebackorder for fixed lifetime perishable items under multiple advance and delayedpayments policies. Here, a new type of business policy is consideredwhere supplieroffers the retailer to pay a fraction of the purchasing cost before the order deliverybymultiple equal installments starting from the ordering time and the rest amountafter the delivery by multiple equal installments. Here, some theoretical results areillustrated to determine the conditions of existence and uniqueness of the optimalsolutions. A closed form solution is determined to solve the proposed model underapproximation. Some numerical examples are provided to examine the validity ofthe proposed model. Finally, sensitivity analyses are presented to obtain the effectof optimal policy and provide some managerial insights of the model.展开更多
The supply chain of perishable products is a combination of information organization,sharing and integration.The information modeling of supply chain is constructed to abstract key quality information including enviro...The supply chain of perishable products is a combination of information organization,sharing and integration.The information modeling of supply chain is constructed to abstract key quality information including environment information,processing procedures and product quality assessments based on principle of quality safety factors and property of decay rate.The coloured Petri Net is applied for integrated description of independent information classification,aiming at risk identification and risk management framework.Well,according to the quality deterioration tendency,risk grades management and decision-making system are established.Practically,the circulation system of aquatic products is studied in this paper for full processing description.The simulation experiments are manipulated on environmental information,processing information and product quality information by the coloured Petri Net.Eventually,the conclusion turns out precisely as such that the coloured Petri Net conclusive for information classification and information transmission while integrated information management is available of efficient risk identification and decision-making system in supply chain of perishable products.Meanwhile,the validity of evaluating management and shelf-life estimation of perishable products are technically feasible.展开更多
Many crops in China have two or more harvesting methods;however,little research has focused on this phenomenon.The current study proposes an operational model that looks to maximize grower profits.This model considers...Many crops in China have two or more harvesting methods;however,little research has focused on this phenomenon.The current study proposes an operational model that looks to maximize grower profits.This model considers a production plan for a perishable crop that has two harvesting methods:harvesting unripe produce at a lower operational cost but with a long lead time,and harvesting ripe crops at a higher operational cost but with quick turnaround.This study proposes a heuristic algorithm by which to pinpoint the optimal plan for the model;the model results indicate that for a crop with two harvesting methods,significant savings can be obtained by applying an optimal production plan.The current study’s main contribution is a production model for crops that feature two harvesting methods and for which the market poses varying demands.展开更多
This work considers a long-term Perishable Inventory Routing Problem with multiple products,static demand,and single vehicle,in the setting of Vendor Managed Inventory.By analyzing the optimal solutions of long-term c...This work considers a long-term Perishable Inventory Routing Problem with multiple products,static demand,and single vehicle,in the setting of Vendor Managed Inventory.By analyzing the optimal solutions of long-term cases that can be solved in Python+Gurobi within 2 h,we capture some patterns of optimal solutions.Utilizing these patterns,experiments show that under certain conditions,the mathematical models of multi-product problems could be simplified to single-product problems,which have the same optimal solutions while taking less time to solve.Managerial insights were generated that for products with static demand in the long term,delivery should be arranged at the store level rather than at the product level.Products in the same store should have the same delivery pattern,no matter how different the unit holding costs are.By further analyzing the optimal solutions of the simplified models,we find that optimal value will stabilize in the long term,and the optimal solution is very close to the solution point where total inventory holding cost and transportation cost are close.Based on these findings,we have developed a heuristic that always provides optimal or close-to-optimal solutions with far less computational time,compared with Python+Gurobi.展开更多
We study the equipment sharing problem where a group of food&beverage companies share the same equipment of a contractor and wish to have their processing tasks coordinated such that the total cost is minimized.Th...We study the equipment sharing problem where a group of food&beverage companies share the same equipment of a contractor and wish to have their processing tasks coordinated such that the total cost is minimized.The raw materials to be processed are perishable,which incur a decay cost as time goes.One key issue of this equipment sharing problem is how to allocate the total cost among the participants.We apply cooperative game theory to tackle this issue and formulate the problem as an equipment sharing game.First,we study the 1-equipment sharing game in which all participants share one equipment.We show that the 1-equipment sharing game is quasi-concave when the fixed operation cost is larger than a certain value.We then discuss the special case where the processing time for all participants is equal.For this case,we further investigate the properties of the 1-equipment sharing game and the multi-equipment sharing game.We identify the conditions under which the Shapely value and the T-value can be easily calculated for the 1-equipment and multi-equipment sharing games.展开更多
文摘Intermodal competition changes with changes in technology, economics, and environmental concerns. Trucks and airships are generally considered not to be competitors, but this depends on the distance of haul. The tonne-kilometer cost of trucking rises much more quickly with distance than it does the cost of a cargo airship. At some distance, the two modes are direct substitutes. The costs of the Mexico-Canada refrigerated truck supply chain are compared with the costs of a 100t-lift, electrically-powered airship. The flight characteristics of the Hindenburg Zeppelin are used as a model for a modern cargo airship. The supply chain cost of trucking tomatoes is used to test the theorical proposition. The cost difference works out to about US10￠/kg (5￠/lb) advantage for trucking Mexican tomatoes to Canada. However, this cost disadvantage of the airship could be made up by their vibrationless ride, better air circulation and one-day service versus four days by truck. This alternative form of transportation could have a positive impact on worldwide north-south distribution of food. Airships can overcome trade barriers and distance to open new markets for perishable food exports. In addition, they would reduce the carbon emissions of transport. Canada imports 160,000 refrigerated truckloads of fruits and vegetables by from the southern US and Mexico. With an average driving distance of 3,000 km, these trucks emit 606,000 MT of CO<sub>2</sub> annually. Airships powered by hydrogen fuel cells would have zero-carbon emissions. Markets are not yet incorporating the environmental advantage of airships in any freight comparison, but inevitably this will be important.
基金The National Key Technology R&D Program of China during the 11th Five-Year Plan Period(No.2006BAH02A06)
文摘The classical supply chain network(SCN)design problem is extended,where the candidate facilities are subject to failure and the products are prone to elapsed time deteriorion.First,the reliable SCN design problem is defined by introducing the probability that a facility may be prone to inactivity based on the analysis of perishable product characteristics.The perishable product SCN design problem is formulated as a 0-1 integer programming model.The objective is to minimize the weighted sum of the operating cost(the fixed plus transportation cost)and the expected failure cost.And then,the perishable product SCN design model is discussed and solved using the genetic algorithm(GA).The results show how to generate the tradeoff curve between the operating costs and the expected failure costs.And these tradeoff curves demonstrate empirically that substantial improvements in reliability are often possible with minimal increase in the operating costs.
文摘被引分析是最常见的科学计量学研究方法,主要用来证明作者或其成果在所属专业领域内的影响力。Publish or Perish是一种在线被引分析软件,依据Google Scholar数据库来查询作者或成果的被引次数,并提供相关的统计数据分析。文章主要介绍了该工具的功能及使用方法,并结合实例探讨了其在外语教学研究中的应用。
文摘There is still no effective means to analyze in depth and utilize domestic mass data about agricultural product quality safety tests in china now. The neural network algorithm, the classification regression tree algorithm, the Bayesian network algorithm were selected according to the principle of selecting combination model and were used to build models respectively and then combined, innovatively establishing a combination model which has relatively high precision, strong robustness and better explanatory to predict the results of perishable food transportation meta-morphism monitoring. The relative optimal prediction model of the perishable food transportation metamorphism monitoring system could be got. The relative perfect prediction model can guide the actual sampling work about food quality and safety by prognosticating the occurrence of unqualified food to select the typical and effective samples for test, thus improving the efficiency and effectiveness of sampling work effectively, so as to avoid deteriorated perishable food’s approaching the market to ensure the quality and safety of perishable food transportation. A solid protective wall was built in the protection of general perishable food consumers’ health.
基金supported by National Natural Science Foundation of China (No. 10671108 and 70971076)Found for the Doctoral Program of Higher Education of Ministry of Education of China (No. 20070446001)+1 种基金Innovation Planning Project of Shandong Province (No. SDYY06034)Foundation of Qufu Normal University (No. XJZ200849)
文摘This paper presents an economic lot-sizing problem with perishable inventory and general economies of scale cost functions. For the case with backlogging allowed, a mathematical model is formulated, and several properties of the optimal solutions are explored. With the help of these optimality properties, a polynomial time approximation algorithm is developed by a new method. The new method adopts a shift technique to obtain a feasible solution of subproblem and takes the optimal solution of the subproblem as an approximation solution of our problem. The worst case performance for the approximation algorithm is proven to be （4√2 ＋ 5）/7. Finally, an instance illustrates that the bound is tight.
文摘The amount of perishable products transported via the existing intermodal freight networks has significantly increased over the last years. Perishable products tend to decay due to a wide range of external factors. Supply chain operations mismanagement causes waste of substantial volumes of perishable products every year. The heretofore proposed mathematical models optimize certain supply chain processes and reduce decay of perishable products, but primarily deal with local production, inventory, distribution, and retailing of perishable products. However, significant quantities of perishable products are delivered from different continents, which shall increase the total transportation time and decay potential of perishable products as compared to local deliveries. This paper proposes a novel optimization model to design the intermodal freight network for both local and long-haul deliveries of perishable products. The objective of the model aims to minimize the total cost associated with transportation and decay of perishable products. A set of piecewise approximations are applied to linearize the non-linear decay function for each perishable product type. CPLEX is used to solve the problem. Comprehensive numerical experiments are conducted using the intermodal freight network for import of the seafood perishable products to the United States to draw important managerial insights. Results demonstrate that increasing product decay cost may significantly change the design of intermodal freight network for transport of perishable products, cause modal shifts and affect the total transportation time and associated costs.
基金Supported by National Natural Science Foundation of China(7093200571102055)+1 种基金Youth Fund Project of Sichuan Provincial Department of Education(13ZB003514ZA0304)
文摘This paper considers the two-echelon supply chain system which consists of single agricultural producers and retailers,and analyzes the impact of sharing ratio on the option ordering quantity,and retailers and producers' expected profits.Studies have shown that in the case of decentralization,when the revenue sharing ratio is between 0 and 0.3,the option ordering quantity of farm produce is a decreasing function of the sharing ratio; when the revenue sharing ratio is between 0.3 and 1,the option ordering quantity of farm produce is an increasing function of sharing ratio; when the revenue sharing ratio is between 0.421 and 1,the agricultural producers and retailers' expected profits are an increasing function of sharing ratio.Finally,through the numerical calculation,the applicability of the conclusions is verified,to provide a reference for the supply chain management practices.
文摘In the classical inventory models, it is assumed that the retailer pays to the supplier as soon as he received the items and in such cases the supplier offers a cash discount or credit period (permis-sible delay) to the retailer. In this paper we presented an inventory model for perishable items with time varying stock dependent demand under inflation. It is assumed that the supplier offers a credit period to the retailer and the length of credit period is dependent on the order quantity. The purpose of our study is to minimize the present value of retailer’s total cost. Numerical examples are also given to demonstrate the presented mode.
文摘Despite the government expanding PhD enrollment,students face limited mentorship and pressure to publish in order to graduate.As they struggle,many find their degrees losing value amid rising societal expectations for talent.
基金supported by the National Natural Science Foundation of China No.71371133,No.61004015,No.61473204the Program for New Century Excellent Talents in Universities of China(NCET11-0377)
文摘Consumers pay more and more attention to the quality of perishable roods, which is mainly affected by storage temperature. This paper presents a dynamic pricing model for perishable foods under temperature control. To maximize the total profit, the optimal price and storage temperature are obtained using Pontryagin＇s maximum principle. A static pricing model is provided to compare with the dynamic one. It is shown by a numerical example that the dynamic policy can make more revenue than the static one. Moreover, the managerial implications are analyzed and the effectiveness of the proposed method is demonstrated.
文摘Numerous empirical studies show that advertising effort can stimulate demand in both current and future periods, and there is an interaction between pricing, advertising and ordering decisions. How do these decisions interact with each other and what is the effect of advertising on pricing and ordering decisions？ To understand this interaction, we consider a newsvendor-type firm that sells a perishable product in a stable market and dynamically determines the joint ordering, pricing and advertising strategies. The problem is modeled as an infmite horizon newsvendor problem with an advertising carryover effect and price-sensitive demand. We characterize the optimal pricing, advertising and inventory strategies and their comparative statics, and consider how this policy differs from the traditional approach without the advertising effect. We show that the optimal effective advertising level is monotonically increasing with the effective advertising level in the previous period, and hence the optimal strategies （advertising, pricing, inventory level） globally converge to the steady states in the long run. We numerically show that the optimal policy can reap significant profit, which underscores the importance of the advertising-driven ordering and pricing strategies.
文摘This study investigated an economic order quantity (EOQ) model with completebackorder for fixed lifetime perishable items under multiple advance and delayedpayments policies. Here, a new type of business policy is consideredwhere supplieroffers the retailer to pay a fraction of the purchasing cost before the order deliverybymultiple equal installments starting from the ordering time and the rest amountafter the delivery by multiple equal installments. Here, some theoretical results areillustrated to determine the conditions of existence and uniqueness of the optimalsolutions. A closed form solution is determined to solve the proposed model underapproximation. Some numerical examples are provided to examine the validity ofthe proposed model. Finally, sensitivity analyses are presented to obtain the effectof optimal policy and provide some managerial insights of the model.
基金This work was supported by the National Natural Science Foundation of China(No.61201432)Colleges and universities of Shandong Province science and technology plan projects(No.J16LE16)the Natural Science Foundation of Shandong Province(ZR2017BG016).
文摘The supply chain of perishable products is a combination of information organization,sharing and integration.The information modeling of supply chain is constructed to abstract key quality information including environment information,processing procedures and product quality assessments based on principle of quality safety factors and property of decay rate.The coloured Petri Net is applied for integrated description of independent information classification,aiming at risk identification and risk management framework.Well,according to the quality deterioration tendency,risk grades management and decision-making system are established.Practically,the circulation system of aquatic products is studied in this paper for full processing description.The simulation experiments are manipulated on environmental information,processing information and product quality information by the coloured Petri Net.Eventually,the conclusion turns out precisely as such that the coloured Petri Net conclusive for information classification and information transmission while integrated information management is available of efficient risk identification and decision-making system in supply chain of perishable products.Meanwhile,the validity of evaluating management and shelf-life estimation of perishable products are technically feasible.
基金This researchwas supported by:(i)MOE(Ministry of Education in China)Liberal Arts and Social Sciences Foundation(18YJC630070)(ii)Nanjing Agricultural University Fundamental Research Funds for the Central Universities(SKYZ2018031).
文摘Many crops in China have two or more harvesting methods;however,little research has focused on this phenomenon.The current study proposes an operational model that looks to maximize grower profits.This model considers a production plan for a perishable crop that has two harvesting methods:harvesting unripe produce at a lower operational cost but with a long lead time,and harvesting ripe crops at a higher operational cost but with quick turnaround.This study proposes a heuristic algorithm by which to pinpoint the optimal plan for the model;the model results indicate that for a crop with two harvesting methods,significant savings can be obtained by applying an optimal production plan.The current study’s main contribution is a production model for crops that feature two harvesting methods and for which the market poses varying demands.
基金supported by the European Union's Horizon 2020 Research and Innovation Programme RISE(No.823759)(REMESH).
文摘This work considers a long-term Perishable Inventory Routing Problem with multiple products,static demand,and single vehicle,in the setting of Vendor Managed Inventory.By analyzing the optimal solutions of long-term cases that can be solved in Python+Gurobi within 2 h,we capture some patterns of optimal solutions.Utilizing these patterns,experiments show that under certain conditions,the mathematical models of multi-product problems could be simplified to single-product problems,which have the same optimal solutions while taking less time to solve.Managerial insights were generated that for products with static demand in the long term,delivery should be arranged at the store level rather than at the product level.Products in the same store should have the same delivery pattern,no matter how different the unit holding costs are.By further analyzing the optimal solutions of the simplified models,we find that optimal value will stabilize in the long term,and the optimal solution is very close to the solution point where total inventory holding cost and transportation cost are close.Based on these findings,we have developed a heuristic that always provides optimal or close-to-optimal solutions with far less computational time,compared with Python+Gurobi.
基金This work has been supported in part by the National Natural Science Foundation of China(NSFC),under grant No.71671146the Leading Talent Program of Guangdong Province under Grant No.2016LJ06D703+1 种基金the Shenzhen Science and Technology Innovation Committee under Grant No.JCYJ20210324115604012National Social Science Foundation of China under Grant No.19XGL015.
文摘We study the equipment sharing problem where a group of food&beverage companies share the same equipment of a contractor and wish to have their processing tasks coordinated such that the total cost is minimized.The raw materials to be processed are perishable,which incur a decay cost as time goes.One key issue of this equipment sharing problem is how to allocate the total cost among the participants.We apply cooperative game theory to tackle this issue and formulate the problem as an equipment sharing game.First,we study the 1-equipment sharing game in which all participants share one equipment.We show that the 1-equipment sharing game is quasi-concave when the fixed operation cost is larger than a certain value.We then discuss the special case where the processing time for all participants is equal.For this case,we further investigate the properties of the 1-equipment sharing game and the multi-equipment sharing game.We identify the conditions under which the Shapely value and the T-value can be easily calculated for the 1-equipment and multi-equipment sharing games.
