Pub Date : 2013-12-18DOI: 10.1504/IJIR.2013.058339
Tugce G. Martagan, B. Eksioglu
A game theoretic approach is used to analyse an inventory problem with two products, stochastic demand, and uncertain supply. The supply chain analysed includes two competing retailers selling two substitutable products and those retailer’ suppliers. Retailers face stochastic demand and replenish the inventory from the suppliers. However, both suppliers provide an indeterminate fraction of the quantity requested, due to randomness in capacity and quality. Some customers with unmet demand will substitute that product with one sold by the other retailer. We assume that the retailers are rational players with conflicting objectives. We model the retailers’ single period expected payoffs and identify the ordering decisions using Nash strategy. We prove the existence and uniqueness of the Nash solution, and provide results for numerical examples. We analyse the combined impact of product substitution and supply uncertainty on the retailers. Results suggest that supply uncertainties do not always hurt retailers’ expected payoffs.
{"title":"Game theoretic analysis of an inventory problem with substitution, stochastic demand, and uncertain supply","authors":"Tugce G. Martagan, B. Eksioglu","doi":"10.1504/IJIR.2013.058339","DOIUrl":"https://doi.org/10.1504/IJIR.2013.058339","url":null,"abstract":"A game theoretic approach is used to analyse an inventory problem with two products, stochastic demand, and uncertain supply. The supply chain analysed includes two competing retailers selling two substitutable products and those retailer’ suppliers. Retailers face stochastic demand and replenish the inventory from the suppliers. However, both suppliers provide an indeterminate fraction of the quantity requested, due to randomness in capacity and quality. Some customers with unmet demand will substitute that product with one sold by the other retailer. We assume that the retailers are rational players with conflicting objectives. We model the retailers’ single period expected payoffs and identify the ordering decisions using Nash strategy. We prove the existence and uniqueness of the Nash solution, and provide results for numerical examples. We analyse the combined impact of product substitution and supply uncertainty on the retailers. Results suggest that supply uncertainties do not always hurt retailers’ expected payoffs.","PeriodicalId":113309,"journal":{"name":"International Journal of Inventory Research","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131348732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-12-18DOI: 10.1504/IJIR.2013.058344
Adel Elomri, A. Ghaffari, Z. Jemai, Y. Dallery
In this paper we used principles of cooperative game theory to analyse the cooperation (inventory pooling) between multiple retailers replenishing their inventory by full truckload shipments to satisfy a deterministic and constant rate demand of final customers while minimising the associated total transportation and inventory costs. For this model we derive structural properties of the resulting cost function. We use these to prove not only that it is cost effective to consolidate the shipments between the retailers but also that this shipment consolidation strategy can be supported by a stable cost allocation i.e. the core of the associated cooperative game is non-empty. We further identify a stable cost allocation that is shown to give strong incentives for the retailers to cooperate. In the particular case of identical retailers this allocation coincide with Shapley value and lies at the centre of gravity of the core. In the general case of non-identical retailers Shapley value is not a core allocation and is compared to our allocation with regards of four criteria: stability complexity fairness and practical settings.
{"title":"Cost allocation in a full truckload shipment consolidation game","authors":"Adel Elomri, A. Ghaffari, Z. Jemai, Y. Dallery","doi":"10.1504/IJIR.2013.058344","DOIUrl":"https://doi.org/10.1504/IJIR.2013.058344","url":null,"abstract":"In this paper we used principles of cooperative game theory to analyse the cooperation (inventory pooling) between multiple retailers replenishing their inventory by full truckload shipments to satisfy a deterministic and constant rate demand of final customers while minimising the associated total transportation and inventory costs. For this model we derive structural properties of the resulting cost function. We use these to prove not only that it is cost effective to consolidate the shipments between the retailers but also that this shipment consolidation strategy can be supported by a stable cost allocation i.e. the core of the associated cooperative game is non-empty. We further identify a stable cost allocation that is shown to give strong incentives for the retailers to cooperate. In the particular case of identical retailers this allocation coincide with Shapley value and lies at the centre of gravity of the core. In the general case of non-identical retailers Shapley value is not a core allocation and is compared to our allocation with regards of four criteria: stability complexity fairness and practical settings.","PeriodicalId":113309,"journal":{"name":"International Journal of Inventory Research","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130548306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2010-02-08DOI: 10.1504/IJIR.2010.031460
Z. Jemai, Y. Dallery, N. Erkip
In this paper, we develop a two-stage supply chain model consisting of a supplier with uncertain capacity and a retailer facing an uncertain demand. We consider that the payment of the retailer to the supplier has two steps: a prepayment based on the quantity ordered by the retailer and a final payment based on the quantity actually delivered by the supplier. We first consider the centralised version of this model and determine the optimal policy analytically. We investigate the effects of the prepayment and capacity restriction. We then consider a decentralised version and characterise optimal decisions of both the supplier and the retailer in the framework of Stackelberg equilibrium. We analyse the efficiency loss of the described decentralised system compared to the centralised system. We discuss different contracting alternatives and propose a generalised contract structure that enables coordination of the decentralised system to achieve the performance of the centralised one.
{"title":"Contracting under uncertain capacity: a generalisation","authors":"Z. Jemai, Y. Dallery, N. Erkip","doi":"10.1504/IJIR.2010.031460","DOIUrl":"https://doi.org/10.1504/IJIR.2010.031460","url":null,"abstract":"In this paper, we develop a two-stage supply chain model consisting of a supplier with uncertain capacity and a retailer facing an uncertain demand. We consider that the payment of the retailer to the supplier has two steps: a prepayment based on the quantity ordered by the retailer and a final payment based on the quantity actually delivered by the supplier. We first consider the centralised version of this model and determine the optimal policy analytically. We investigate the effects of the prepayment and capacity restriction. We then consider a decentralised version and characterise optimal decisions of both the supplier and the retailer in the framework of Stackelberg equilibrium. We analyse the efficiency loss of the described decentralised system compared to the centralised system. We discuss different contracting alternatives and propose a generalised contract structure that enables coordination of the decentralised system to achieve the performance of the centralised one.","PeriodicalId":113309,"journal":{"name":"International Journal of Inventory Research","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129827516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2010-02-08DOI: 10.1504/IJIR.2010.031459
Dmitriy S Shaltayev, C. R. Sox
This research studies the impact of market state information on the long run average cost of a single item inventory system facing dynamic, random demand. The probability distribution of the demand in any time period is determined by the current market state in that period which is modelled as a Markov chain. The inventory manager must infer the market state from the demand observations and a market state signal that is not necessarily accurate. The proposed model accommodates a range of different levels of accuracy for this market state information. The computational results indicate that the value of the market information increases at an increasing rate as the accuracy increases suggesting a strong, persistent value from increasing the information accuracy. The computational results also characterise the effects of lead time, the difference between the market state distributions, autocorrelation, and service level on the value of the market state information.
{"title":"The impact of market state information on inventory performance","authors":"Dmitriy S Shaltayev, C. R. Sox","doi":"10.1504/IJIR.2010.031459","DOIUrl":"https://doi.org/10.1504/IJIR.2010.031459","url":null,"abstract":"This research studies the impact of market state information on the long run average cost of a single item inventory system facing dynamic, random demand. The probability distribution of the demand in any time period is determined by the current market state in that period which is modelled as a Markov chain. The inventory manager must infer the market state from the demand observations and a market state signal that is not necessarily accurate. The proposed model accommodates a range of different levels of accuracy for this market state information. The computational results indicate that the value of the market information increases at an increasing rate as the accuracy increases suggesting a strong, persistent value from increasing the information accuracy. The computational results also characterise the effects of lead time, the difference between the market state distributions, autocorrelation, and service level on the value of the market state information.","PeriodicalId":113309,"journal":{"name":"International Journal of Inventory Research","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117180109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2010-02-08DOI: 10.1504/IJIR.2010.031462
M. Rossetti, N. Buyurgan, A. Bhonsle, Seda Gumrukcu, Kiran Chittoori
This paper examines the effect of inventory record inaccuracy within the context of a two-echelon supply chain. The system consists of an external supplier, a distribution centre, and a retail level. Each location operates under an (R, Q) reorder point reorder quantity inventory control policy with backordering permitted. The model introduces count-based discrepancies into the inventory records and measures the effect on system performance at the locations and throughout the supply chain. A set of simulation experiments examines two fundamental methods to mitigate the effect of inaccurate inventory records: carrying extra inventory to protect against the errors and using cycle counting procedures to correct the records over time. In addition, the effect of learning through the use of cycle counting procedures and error reduction methods and the effect of non-compliance (not correcting records) within the system are explored. The results indicate that cycle counting can have significant positive effects within the entire supply chain. In addition, the experiments show that the learning effect has benefits both locally and throughout the supply chain. The results also show that non-compliance to the cycle counting procedure by locations within the chain can have significant detrimental effects on supply chain partners and overall supply chain performance.
{"title":"An analysis of the effect of inventory record inaccuracy in a two-echelon supply chain","authors":"M. Rossetti, N. Buyurgan, A. Bhonsle, Seda Gumrukcu, Kiran Chittoori","doi":"10.1504/IJIR.2010.031462","DOIUrl":"https://doi.org/10.1504/IJIR.2010.031462","url":null,"abstract":"This paper examines the effect of inventory record inaccuracy within the context of a two-echelon supply chain. The system consists of an external supplier, a distribution centre, and a retail level. Each location operates under an (R, Q) reorder point reorder quantity inventory control policy with backordering permitted. The model introduces count-based discrepancies into the inventory records and measures the effect on system performance at the locations and throughout the supply chain. A set of simulation experiments examines two fundamental methods to mitigate the effect of inaccurate inventory records: carrying extra inventory to protect against the errors and using cycle counting procedures to correct the records over time. In addition, the effect of learning through the use of cycle counting procedures and error reduction methods and the effect of non-compliance (not correcting records) within the system are explored. The results indicate that cycle counting can have significant positive effects within the entire supply chain. In addition, the experiments show that the learning effect has benefits both locally and throughout the supply chain. The results also show that non-compliance to the cycle counting procedure by locations within the chain can have significant detrimental effects on supply chain partners and overall supply chain performance.","PeriodicalId":113309,"journal":{"name":"International Journal of Inventory Research","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114196924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2010-02-08DOI: 10.1504/IJIR.2010.031461
D. Gupta, H. Gurnani, Haoya Chen
Many retailers offer to special order out-of-stock items at no additional cost to the customers. This practice is based on an implicit assumption that by increasing sales and reducing stockouts, special orders increase retailers' profits. We study the relative benefit of special ordering to the retailer and show that this assumption may not hold. Our model reveals two counter-intuitive results. First, the retailer's expected profit is higher when the manufacturer has additional pricing flexibility, i.e., the manufacturer offers two prices, a base price for the primary order and a different price for the special order, as compared to a single price for all items. Second, higher demand variability may increase retailer's profits.
{"title":"When do retailers benefit from special ordering","authors":"D. Gupta, H. Gurnani, Haoya Chen","doi":"10.1504/IJIR.2010.031461","DOIUrl":"https://doi.org/10.1504/IJIR.2010.031461","url":null,"abstract":"Many retailers offer to special order out-of-stock items at no additional cost to the customers. This practice is based on an implicit assumption that by increasing sales and reducing stockouts, special orders increase retailers' profits. We study the relative benefit of special ordering to the retailer and show that this assumption may not hold. Our model reveals two counter-intuitive results. First, the retailer's expected profit is higher when the manufacturer has additional pricing flexibility, i.e., the manufacturer offers two prices, a base price for the primary order and a different price for the special order, as compared to a single price for all items. Second, higher demand variability may increase retailer's profits.","PeriodicalId":113309,"journal":{"name":"International Journal of Inventory Research","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123231553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2010-02-08DOI: 10.1504/IJIR.2010.031463
Mingming Leng, M. Parlar
For an assemble-to-order …rm operating in a single period, we …nd that, for the multiplicative demand case the optimal riskless price may or may not be higher than the optimal risk price. However, for the additive demand case, the optimal riskless price is always greater than the optimal risk price.
{"title":"A note on optimal 'riskless' and 'risk' prices for the newsvendor problem with an assembly cost","authors":"Mingming Leng, M. Parlar","doi":"10.1504/IJIR.2010.031463","DOIUrl":"https://doi.org/10.1504/IJIR.2010.031463","url":null,"abstract":"For an assemble-to-order …rm operating in a single period, we …nd that, for the multiplicative demand case the optimal riskless price may or may not be higher than the optimal risk price. However, for the additive demand case, the optimal riskless price is always greater than the optimal risk price.","PeriodicalId":113309,"journal":{"name":"International Journal of Inventory Research","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133297394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-07-03DOI: 10.1504/IJIR.2008.019207
S. Johansen, Anders Thorstenson
We show that well-known textbook formulae for determining the optimal base stock of the inventory system with continuous review and constant lead time can easily be extended to the case with periodic review and stochastic, sequential lead times. The provided performance measures and conditions for optimality are exact
{"title":"Optimal base-stock policy for the inventory system with periodic review, backorders and sequential lead times","authors":"S. Johansen, Anders Thorstenson","doi":"10.1504/IJIR.2008.019207","DOIUrl":"https://doi.org/10.1504/IJIR.2008.019207","url":null,"abstract":"We show that well-known textbook formulae for determining the optimal base stock of the inventory system with continuous review and constant lead time can easily be extended to the case with periodic review and stochastic, sequential lead times. The provided performance measures and conditions for optimality are exact","PeriodicalId":113309,"journal":{"name":"International Journal of Inventory Research","volume":"539 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127057260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-07-03DOI: 10.1504/IJIR.2008.019209
H. Lau, Huawei Song
Classical multi-echelon repairable item inventory models are based either on steady-state analysis or infinite repair capacity, which may not work well in situations when the demand is nonstationary, or repair capacity is limited. In this paper, we propose an analytical model for evaluating system performance that works well under limited repair capacity and nonstationary demands. Following the METRIC methodology, we then develop an optimisation algorithm to solve the corrective maintenance problem in military logistics. Experimental results show that our approach yields good solutions efficiently. This work has also resulted in a software that has been field-tested by a military organisation.
{"title":"Multi-Echelon Repairable Item Inventory System with Limited Repair Capacity under Nonstationary Demands","authors":"H. Lau, Huawei Song","doi":"10.1504/IJIR.2008.019209","DOIUrl":"https://doi.org/10.1504/IJIR.2008.019209","url":null,"abstract":"Classical multi-echelon repairable item inventory models are based either on steady-state analysis or infinite repair capacity, which may not work well in situations when the demand is nonstationary, or repair capacity is limited. In this paper, we propose an analytical model for evaluating system performance that works well under limited repair capacity and nonstationary demands. Following the METRIC methodology, we then develop an optimisation algorithm to solve the corrective maintenance problem in military logistics. Experimental results show that our approach yields good solutions efficiently. This work has also resulted in a software that has been field-tested by a military organisation.","PeriodicalId":113309,"journal":{"name":"International Journal of Inventory Research","volume":"276 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131764857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-07-03DOI: 10.1504/IJIR.2008.019205
O. Berman, D. Perry, W. Stadje
We consider an EOQ model in which the content level is modelled by a Brownian Motion (BM) with state-dependent drift and diffusion parameters. There are either one or two prespecified switchover threshold values (cases 1 and 2) such that the drift and the volatility change whenever the critical threshold is reached (in case 1) or whenever the upper threshold is reached from below or the lower one from above (in case 2). The controller places an order of fixed size every time the content level reaches 0. We derive all the relevant cost functionals for the discounted case with infinite horizon and for the long-run average case. These explicit results are used for finding the optimal replenishment level in the long-run average case.
{"title":"Optimal replenishment in a Brownian Motion EOQ model with hysteretic parameter changes","authors":"O. Berman, D. Perry, W. Stadje","doi":"10.1504/IJIR.2008.019205","DOIUrl":"https://doi.org/10.1504/IJIR.2008.019205","url":null,"abstract":"We consider an EOQ model in which the content level is modelled by a Brownian Motion (BM) with state-dependent drift and diffusion parameters. There are either one or two prespecified switchover threshold values (cases 1 and 2) such that the drift and the volatility change whenever the critical threshold is reached (in case 1) or whenever the upper threshold is reached from below or the lower one from above (in case 2). The controller places an order of fixed size every time the content level reaches 0. We derive all the relevant cost functionals for the discounted case with infinite horizon and for the long-run average case. These explicit results are used for finding the optimal replenishment level in the long-run average case.","PeriodicalId":113309,"journal":{"name":"International Journal of Inventory Research","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131641443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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