The value chain for energy and other commodities entails physical conversions through refineries, power plants, storage facilities, and transportation and other capital-intensive infrastructure. When the operation of such commodity conversion assets occurs alongside liquid markets for the input and output commodities, the operating flexibility of conversion assets can be managed as real options on the underlying commodity prices. Merchant operations is an integrated trading and operations approach that (i) buys and sells commodities to support market-value maximizing operating policies and (ii) values conversion assets, for capital budgeting and trading purposes, based on the cash flows such policies produce. This monograph provides a unique integrated finance and operations perspective on the topic of merchant operations. In particular, this monograph introduces the concept of merchant operations; presents the basic principles of option valuation; surveys foundational models of commodity and energy price evolution; analyzes the structure of optimal operating policies for commodity conversions, focusing specifically on inventory and other intertemporal linkages in storage, inventory acquisition and disposal, and swing assets; considers a variety of heuristic storage operating policies; and discusses future trends in this multidisciplinary area of research and business applications.
{"title":"Real Options and Merchant Operations of Energy and Other Commodities","authors":"N. Secomandi, Duane J. Seppi","doi":"10.1561/0200000024","DOIUrl":"https://doi.org/10.1561/0200000024","url":null,"abstract":"The value chain for energy and other commodities entails physical conversions through refineries, power plants, storage facilities, and transportation and other capital-intensive infrastructure. When the operation of such commodity conversion assets occurs alongside liquid markets for the input and output commodities, the operating flexibility of conversion assets can be managed as real options on the underlying commodity prices. Merchant operations is an integrated trading and operations approach that (i) buys and sells commodities to support market-value maximizing operating policies and (ii) values conversion assets, for capital budgeting and trading purposes, based on the cash flows such policies produce. This monograph provides a unique integrated finance and operations perspective on the topic of merchant operations. In particular, this monograph introduces the concept of merchant operations; presents the basic principles of option valuation; surveys foundational models of commodity and energy price evolution; analyzes the structure of optimal operating policies for commodity conversions, focusing specifically on inventory and other intertemporal linkages in storage, inventory acquisition and disposal, and swing assets; considers a variety of heuristic storage operating policies; and discusses future trends in this multidisciplinary area of research and business applications.","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"160 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122471933","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}
We investigate a game of singular control and strategic exit in a model of competitive market share control. In the model, each player can make irreversible investments to increase his market share, which is modeled as a diffusion process. In addition, each player has an option to exit the market at any point in time. We formulate a verification theorem for best responses of the game and characterize Markov perfect equilibria (MPE) under a set of verifiable assumptions. We find a class of MPEs with a rich structure. In particular, each player maintains up to two disconnected intervals of singular control regions, one of which plays a defensive role, and the other plays an offensive role. We also identify a set of conditions under which the outcome of the game may be unique despite the multiplicity of the equilibria.
{"title":"Game of Singular Stochastic Control and Strategic Exit","authors":"H. D. Kwon, Hongzhong Zhang","doi":"10.2139/ssrn.2446209","DOIUrl":"https://doi.org/10.2139/ssrn.2446209","url":null,"abstract":"We investigate a game of singular control and strategic exit in a model of competitive market share control. In the model, each player can make irreversible investments to increase his market share, which is modeled as a diffusion process. In addition, each player has an option to exit the market at any point in time. We formulate a verification theorem for best responses of the game and characterize Markov perfect equilibria (MPE) under a set of verifiable assumptions. We find a class of MPEs with a rich structure. In particular, each player maintains up to two disconnected intervals of singular control regions, one of which plays a defensive role, and the other plays an offensive role. We also identify a set of conditions under which the outcome of the game may be unique despite the multiplicity of the equilibria.","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114898069","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}
In a multi-armed bandit (MAB) problem a gambler needs to choose at each round of play one of K arms, each characterized by an unknown reward distribution. Reward realizations are only observed when an arm is selected, and the gambler's objective is to maximize his cumulative expected earnings over some given horizon of play T. To do this, the gambler needs to acquire information about arms (exploration) while simultaneously optimizing immediate rewards (exploitation); the price paid due to this trade off is often referred to as the regret, and the main question is how small can this price be as a function of the horizon length T. This problem has been studied extensively when the reward distributions do not change over time; an assumption that supports a sharp characterization of the regret, yet is often violated in practical settings. In this paper, we focus on a MAB formulation which allows for a broad range of temporal uncertainties in the rewards, while still maintaining mathematical tractability. We fully characterize the (regret) complexity of this class of MAB problems by establishing a direct link between the extent of allowable reward "variation" and the minimal achievable regret. Our analysis draws some connections between two rather disparate strands of literature: the adversarial and the stochastic MAB frameworks.
{"title":"Optimal Exploration-Exploitation in a Multi-Armed-Bandit Problem with Non-Stationary Rewards","authors":"Omar Besbes, Y. Gur, A. Zeevi","doi":"10.2139/ssrn.2436629","DOIUrl":"https://doi.org/10.2139/ssrn.2436629","url":null,"abstract":"In a multi-armed bandit (MAB) problem a gambler needs to choose at each round of play one of K arms, each characterized by an unknown reward distribution. Reward realizations are only observed when an arm is selected, and the gambler's objective is to maximize his cumulative expected earnings over some given horizon of play T. To do this, the gambler needs to acquire information about arms (exploration) while simultaneously optimizing immediate rewards (exploitation); the price paid due to this trade off is often referred to as the regret, and the main question is how small can this price be as a function of the horizon length T. This problem has been studied extensively when the reward distributions do not change over time; an assumption that supports a sharp characterization of the regret, yet is often violated in practical settings. In this paper, we focus on a MAB formulation which allows for a broad range of temporal uncertainties in the rewards, while still maintaining mathematical tractability. We fully characterize the (regret) complexity of this class of MAB problems by establishing a direct link between the extent of allowable reward \"variation\" and the minimal achievable regret. Our analysis draws some connections between two rather disparate strands of literature: the adversarial and the stochastic MAB frameworks.","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126335739","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}
Despite linear programming and duality have correctly been incorporated in algorithms to compute the nucleolus, we have found mistakes in how these have been used in a broad range of applications. Overlooking the fact that a linear program can have multiple optimal solutions and neglecting the relevance of duality appear to be crucial sources of mistakes in computing the nucleolus. We discuss these issues and illustrate them in mistaken examples collected from a variety of literature sources. The purpose of this note is to prevent these mistakes propagate longer by clarifying how linear programming and duality can be correctly used for computing the nucleolus.
{"title":"Common Mistakes in Computing the Nucleolus","authors":"M. Guajardo, K. Jörnsten","doi":"10.2139/ssrn.2425596","DOIUrl":"https://doi.org/10.2139/ssrn.2425596","url":null,"abstract":"Despite linear programming and duality have correctly been incorporated in algorithms to compute the nucleolus, we have found mistakes in how these have been used in a broad range of applications. Overlooking the fact that a linear program can have multiple optimal solutions and neglecting the relevance of duality appear to be crucial sources of mistakes in computing the nucleolus. We discuss these issues and illustrate them in mistaken examples collected from a variety of literature sources. The purpose of this note is to prevent these mistakes propagate longer by clarifying how linear programming and duality can be correctly used for computing the nucleolus.","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116554304","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}
We study the effects of learning by doing resulting from the production of a final good on economic growth in a region that is creative in the sense of Richard Florida. Firms in this region use creative and physical capital to produce output. We model learning by doing formally and our analysis of the working of this creative region leads to four results. First, we derive analytic expressions for the growth rates of physical capital and technology. Second, we draw phase diagrams and show that in the steady state, the preceding two growth rates must be equal. Third, we show that the economy of our creative region converges to a balanced growth path (BGP) in which the growth rates of physical capital, technology, and the output of the final good are identical. Finally, we investigate the impact that an increase in the savings rate has on the economic growth of our creative region in the long run.
{"title":"Goods Production, Learning by Doing, and Growth in a Region with Creative and Physical Capital","authors":"Umer Usman, A. Batabyal","doi":"10.2139/ssrn.2410493","DOIUrl":"https://doi.org/10.2139/ssrn.2410493","url":null,"abstract":"We study the effects of learning by doing resulting from the production of a final good on economic growth in a region that is creative in the sense of Richard Florida. Firms in this region use creative and physical capital to produce output. We model learning by doing formally and our analysis of the working of this creative region leads to four results. First, we derive analytic expressions for the growth rates of physical capital and technology. Second, we draw phase diagrams and show that in the steady state, the preceding two growth rates must be equal. Third, we show that the economy of our creative region converges to a balanced growth path (BGP) in which the growth rates of physical capital, technology, and the output of the final good are identical. Finally, we investigate the impact that an increase in the savings rate has on the economic growth of our creative region in the long run.","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121134785","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}
We present an improved SPFA algorithm for the single source shortest path problem. For a random graph, the empirical average time complexity is O(|E|), where |E| is the number of edges of the input network. SPFA maintains a queue of candidate vertices and add a vertex to the queue only if that vertex is relaxed. In the improved SPFA, MinPoP principle is employed to improve the quality of the queue. We theoretically analyze the advantage of this new algorithm and experimentally demonstrate that the algorithm is efficient.
{"title":"An Improved SPFA Algorithm for Single-Source Shortest Path Problem Using Forward Star Data Structure","authors":"Xin Zhou","doi":"10.5121/IJMIT.2014.6402","DOIUrl":"https://doi.org/10.5121/IJMIT.2014.6402","url":null,"abstract":"We present an improved SPFA algorithm for the single source shortest path problem. For a random graph, the empirical average time complexity is O(|E|), where |E| is the number of edges of the input network. SPFA maintains a queue of candidate vertices and add a vertex to the queue only if that vertex is relaxed. In the improved SPFA, MinPoP principle is employed to improve the quality of the queue. We theoretically analyze the advantage of this new algorithm and experimentally demonstrate that the algorithm is efficient. <br>","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"109 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116047883","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}
Complementary to the axiomatic and mechanism design studies on queueing problems, this paper proposes a strategic bargaining approach to resolve queueing conflicts. Given a situation where players with different waiting costs have to form a queue in order to be served, they firstly compete with each other for a specific position in the queue. Then, the winner can decide to take up the position or sell it to the others. In the former case, the rest of the players will proceed to compete for the remaining positions in the same manner; whereas for the latter case the seller can propose a queue with corresponding payments to the others which can be accepted or rejected. In this paper we show that, when the players are competing for the first position in the queue, then the subgame perfect equilibrium outcome of the corresponding mechanism coincides with the well-known maximal transfer rule, while an efficient queue is always formed in equilibrium. We also argue that changing the mechanism so that the players compete for the last position implements the minimal transfer rule. The analysis discovers a striking relationship between pessimism and optimism in this type of decision making.
{"title":"Auctioning and Selling Positions: A Non-Cooperative Approach to Queuing Conflicts","authors":"Yuan Ju, Y. Chun, R. Brink","doi":"10.2139/ssrn.2388060","DOIUrl":"https://doi.org/10.2139/ssrn.2388060","url":null,"abstract":"Complementary to the axiomatic and mechanism design studies on queueing problems, this paper proposes a strategic bargaining approach to resolve queueing conflicts. Given a situation where players with different waiting costs have to form a queue in order to be served, they firstly compete with each other for a specific position in the queue. Then, the winner can decide to take up the position or sell it to the others. In the former case, the rest of the players will proceed to compete for the remaining positions in the same manner; whereas for the latter case the seller can propose a queue with corresponding payments to the others which can be accepted or rejected. In this paper we show that, when the players are competing for the first position in the queue, then the subgame perfect equilibrium outcome of the corresponding mechanism coincides with the well-known maximal transfer rule, while an efficient queue is always formed in equilibrium. We also argue that changing the mechanism so that the players compete for the last position implements the minimal transfer rule. The analysis discovers a striking relationship between pessimism and optimism in this type of decision making.","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126977542","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}
We examine the strategy-proof allocation of multiple divisible and indivisible resources; an application is the assignment of packages of tasks, workloads, and compensations among the members of an organization. We find that any allocation mechanism obtained by maximizing a separably concave function over a polyhedral extension of the set of Pareto-efficient allocations is strategy-proof. Moreover, these are the only strategy-proof and unanimous mechanisms satisfying a coherence property and responding well to changes in the availability of resources. These mechanisms generalize the parametric rationing mechanisms (Young, 1987), some of which date back to the Babylonian Talmud.
{"title":"Strategy-Proof Package Assignment","authors":"Albin Erlanson, Karol Szwagrzak","doi":"10.2139/ssrn.2406879","DOIUrl":"https://doi.org/10.2139/ssrn.2406879","url":null,"abstract":"We examine the strategy-proof allocation of multiple divisible and indivisible resources; an application is the assignment of packages of tasks, workloads, and compensations among the members of an organization. We find that any allocation mechanism obtained by maximizing a separably concave function over a polyhedral extension of the set of Pareto-efficient allocations is strategy-proof. Moreover, these are the only strategy-proof and unanimous mechanisms satisfying a coherence property and responding well to changes in the availability of resources. These mechanisms generalize the parametric rationing mechanisms (Young, 1987), some of which date back to the Babylonian Talmud.","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"91 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122237404","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}
This note briefly presents the GAMS matrix adjustment program GPCEMA.gms (GPCEMA stands for General Purpose Cross-Entropy Matrix Adjustment). The matrix adjustment problem tackled in GPCEMA.gms is to adjust an existing matrix (called the prior matrix) so that the adjusted matrix (the posterior matrix) has row and column sums that conform to known marginal totals. GPCEMA.gms is based on the minimum information-gain principle (also known as minimum cross-entropy), as it has been extended to deal with negative entries by Junius and Oosterhaven (2003). The program automatically deals with situations where row sums, column sums, or both are constrained to zero.
{"title":"GPCEMA.GMS: A General Purpose Cross-Entropy Matrix Adjustment Program (Quick User Guide)","authors":"A. Lemelin","doi":"10.2139/ssrn.2439905","DOIUrl":"https://doi.org/10.2139/ssrn.2439905","url":null,"abstract":"This note briefly presents the GAMS matrix adjustment program GPCEMA.gms (GPCEMA stands for General Purpose Cross-Entropy Matrix Adjustment). The matrix adjustment problem tackled in GPCEMA.gms is to adjust an existing matrix (called the prior matrix) so that the adjusted matrix (the posterior matrix) has row and column sums that conform to known marginal totals. GPCEMA.gms is based on the minimum information-gain principle (also known as minimum cross-entropy), as it has been extended to deal with negative entries by Junius and Oosterhaven (2003). The program automatically deals with situations where row sums, column sums, or both are constrained to zero.","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129227652","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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