Multi-period Setting Research Articles

Multiobjective Optimization for Multiperiod Reverse Logistics Network Design

In recent years, the ever-rising return streams for repair service have forced the electronics manufacturers to expand their reverse logistics capacities. However, most existing papers on the reverse logistics network design neglected the time sensitivity of the return flows. Moreover, most of these investigations were primarily concerned with the single objective problems of either minimizing the total cost or maximizing the profit. In this paper, we propose a biobjective mixed-integer linear programming model for the multiperiod design problem of a reverse logistics network for repair service. A multiperiod setting is taken into account to make the reverse logistics network flexible to accommodate the gradual changes in the capacity of the facilities and the network configuration. To solve the NP-hard problem with biobjective, we develop a hybrid evolutionary algorithm that combines nondominated sorting genetic algorithm II (NSGA-II) with a local search method. We compare the hybrid evolutionary algorithm with NSGA-II and ϵ-constraint method using numerical examples. The comparison results indicate that the hybrid evolutionary algorithm outperforms the NSGA-II in most cases. The ϵ-constraint method performs best for the small instances, but it cannot solve large instances within reasonable time. Finally, an extensive parametric analysis is conducted and several managerial insights are derived.

Recursive expected conditional value at risk in the fleet renewal problem with alternative fuel vehicles

We study the fleet portfolio management problem faced by a firm deciding which alternative fuel vehicles (AFVs) to choose for its fleet to minimise the weighted average of cost and risk, in a stochastic multi-period setting. We consider different types of technology and vehicles with heterogeneous capabilities. We propose a new time consistent recursive risk measure, the Recursive Expected Conditional Value at Risk (RECVaR), which we prove to be coherent. We then solve the problem for a large UK based company, reporting how the optimal policies are affected by risk aversion and by the clustering for each type of vehicle.

How does wholesale price depend on initial inventory at retailer?

In a decentralised supply chain, the presence of initial inventory at the retailer is believed to cause the manufacturer to set a lower wholesale price than otherwise. But is such always the case? The importance of that question also derives from a multi-period setting where the manufacturer chooses a wholesale price in each period based on initial inventory at retailer. As the wholesale price is decreasing in inventory level, goes the argument, the retailer will 'overstock', referred to as holding 'strategic inventory'. We show that the optimal wholesale price may increase in initial inventory. We initially assume fixed retail price, and later consider a model with price-sensitive demand. We then outline other price-sensitive models based on different demand functions.

How does wholesale price depend on initial inventory at retailer?

In a decentralised supply chain, the presence of initial inventory at the retailer is believed to cause the manufacturer to set a lower wholesale price than otherwise. But is such always the case? The importance of that question also derives from a multi-period setting where the manufacturer chooses a wholesale price in each period based on initial inventory at retailer. As the wholesale price is decreasing in inventory level, goes the argument, the retailer will 'overstock', referred to as holding 'strategic inventory'. We show that the optimal wholesale price may increase in initial inventory. We initially assume fixed retail price, and later consider a model with price-sensitive demand. We then outline other price-sensitive models based on different demand functions.

Acquisition Pricing and Inventory Decisions on Dual-Source Spare-Part System with Final Production and Remanufacturing

The life spans of durable goods are longer than their warranty periods. To satisfy the service demand of spare parts and keep the market competition advantage, enterprises have to maintain the longer inventory planning of spare parts. However, how to obtain a valid number of spare parts is difficult for those enterprises. In this paper, we consider a spare-part inventory problem, where the inventory can be replenished by two ways including the final production order and the remanufacturing way. Especially for the remanufacturing way, we consider the acquisition management problem of used products concerning an acquisition pricing decision. In a multiperiod setting, we formulate the problem into a dynamic optimization problem, where the system decisions include the final production order and acquisition price of used products at each period. By stochastic dynamic programming, we obtain the optimal policy of the acquisition pricing at each period and give the optimal policy structure of the optimization problem at the first period. Then, a recursion algorithm is designed to calculate the optimal decisions and the critical points in the policy. Finally, the numerical analyses show the effects of demand information and customer’s sensitive degree on the related decisions and the optimal cost.

Strategic Corporate Hedging

We consider a dynamic multi-period framework of a Cournot duopoly and introduce a simultaneous hedging and a storage opportunity to allow players to manage risk before and after demand uncertainty is realized. Decision makers face a strategic dilemma: they must weigh the advantages of dealing with their risk exposure and the disadvantages of higher competition. Due to the storage opportunity, our multi-period setting differs from a repetition of the single-shot interaction. In equilibrium, firms consider the strategic impact of the hedging component, which increases competition. We provide supportive evidence of this theory in a laboratory experiment. Our experimental results suggest that the simultaneous hedging device significantly increases competition and negates duopoly profits.

A Marathon, a Series of Sprints, or Both? Tournament Horizon and Dynamic Task Complexity in Multi-Period Settings

ABSTRACTWhen using a tournament in multi-period settings, firms have discretion in selecting the tournament horizon. For example, firms can use a single tournament (a grand tournament) or a sequence of multiple tournaments, each with a shorter horizon than a grand tournament (a repeated tournament). Firms have also begun to use a combination of both in which a repeated tournament is embedded within a grand tournament (a hybrid tournament). Using an experiment, we investigate whether the effect of tournament horizon on performance depends on the dynamic complexity of the task, which reflects the potential for effort in one period to influence the link between effort and performance in future periods. When dynamic task complexity is low, we find that performance is greatest in the hybrid tournament, followed by the repeated and then the grand tournament. In contrast, when dynamic task complexity is high, we find that performance is greatest in the repeated tournament, followed by the grand and hybrid tournaments, with similar performance in the latter two tournaments. More generally, the results of our experiment suggest that the effect of tournament horizon on performance depends on dynamic task complexity. These results can help firms make better decisions when designing their tournaments by reinforcing the need to align the tournament horizon with the task.

Deductibility of Provisions under the CCCTB Proposal and Its Effects on Companies: The Case of Poland

The aim of the paper is to empirically examine the scale and the distribution of the tax advantage which emerges when provisions for future liabilities are deductible from taxable earnings, as proposed in the CCCTB concept. The paper concentrates on Poland - a country for which the expected economic effects of this proposal are still controversial and ambiguous. The results are also relevant for other European countries in which provisions are currently treated in a different way for financial and for tax accounting purposes. The analysis is based on the information from financial statements of 250 companies from the period 2007 - 2012. The microsimulation method in a multi-period setting is implemented. The results show that in case provisions are deductible for tax purposes the tax due decreases by 5,6 % or and by 9,8 % on average, depending on the liquidity situation of companies. The tax advantage is distributed differently among companies. The majority of taxpayers is expected to gain from the reform. Only for single companies there is an increase in tax, induced by the existing, restricted tax loss carry forward rules. The median change in CIT amounts to -1 % and -2 %.

A Marathon, a Series of Sprints, or Both? Tournament Horizon and Task Complexity in Multi-Period Settings

When using a tournament in multi-period settings, firms have discretion in selecting the tournament horizon. For example, firms can use a single tournament (a grand tournament) or a sequence of multiple tournaments each with a shorter horizon than a grand tournament (a repeated tournament). Firms have also begun to use a combination of both in which a repeated tournament is embedded within a grand tournament (a hybrid tournament). Using an experiment, we investigate whether the effect of tournament horizon on performance depends on the dynamic complexity of the task, which reflects the potential for effort in one period to influence the link between effort and performance in future periods. When dynamic task complexity is low, we find performance is greatest in the hybrid tournament, followed by the repeated and then the grand tournament. In contrast, when dynamic task complexity is high, we find performance is greatest in the repeated tournament, followed by the grand and hybrid tournaments, with similar performance in the latter two tournaments. More generally, the results of our experiment suggest the effect of tournament horizon on performance depends on dynamic task complexity. These results can help firms make better decisions when designing their tournaments by reinforcing the need to align the tournament horizon with the task.

Reconsidering the appropriate discount rate for tax shield valuation

This paper aims at identifying the appropriate discount rate for tax shield valuation in a setting where a partial default is possible and either principal or interest payments are prioritized in default. As a general valuation framework we use the stochastic discount factor. We assume a tax framework with corporate taxes, tax-deductible interest payments of the firm, no taxes on the cancellation of debt and no personal taxes. We strictly decompose the payments owed to the debtholders into interest and principal payments and analyze discount rates of those claims for the different priorities. As a result of the single-period analysis we find that the discount rate for tax savings, i.e., the conditional expected return on tax savings, is always equal to the discount rate of debt only for a proportional loss distribution on interest and principal payments. If losses are distributed according to one of the priority assumptions, the discount rate of tax savings behaves different from the discount rate of debt and both discount rates are equal only in very special cases. Furthermore, we derive qualitative statements for the relation between the discount rate of debt and the discount rate of tax savings assuming certain correlations between the stochastic discount factor and the debt repayments. Finally, we show how the prioritization assumptions can be implemented in a multi-period setting. We obtain for the presented set of assumptions a pricing equation equivalent to the one by Miles and Ezzell (J Finance 40:1485–1492, 1985).

Improving Risk Sharing and Borrower Incentives in Mortgage Design

In a traditional fixed rate mortgage, the borrower pays a fixed amount each period regardless of the value of the mortgaged property. One problem with this contract is that the borrower is less willing to pay when the house value falls. This was clearly seen in the 2008 financial crisis and its aftermath when mortgage default rates and foreclosures skyrocketed as the housing market crashed. A more efficient contract design should link payments to house prices so that the borrower's incentive to pay is not undermined by a decline in property value. In addition this design can save the lender the deadweight foreclosure costs. In this paper we examine two proposed index linked mortgages which have this risk sharing feature. We analyze the effect of both designs on borrower incentives in a multi-period setting.

Assessing Systemic Risk Using Interbank Exposures in the Global Banking System

This paper contributes to the literature on systemic risk by examining the network structure of bilateral exposures in the global banking system. The global interbank market constitutes a major part of the global banking system. The market has a hierarchical network structure, composed of the national or jurisdictional area's local markets and the cross-border interbank market. First, we estimate the bilateral exposures matrix using aggregate financial data on loans and deposits from Bankscope and analyze the interconnectedness in the market using network centrality measures. Subsequently, for the model analysis, we apply the Eisenberg–Noe framework to a multi-period setting. In this framework, bank defaults are classified into stand-alone defaults and contagious defaults. The banks in our sample (i.e., the top 202 banks with more than $50 billion in total assets) comprise a major part of this global banking system. The main findings are as follows: The theoretical network analysis using network centrality measures showed that most of the banks designated as global systemically important banks (G-SIBs) play a central role in the global interbank market. The theoretical default analysis showed a few contagious defaults triggered by the basic defaults during and after the global financial crisis. Our stress test proved that many G-SIBs theoretically caused 1–6 contagious defaults. Our methodology would assist in the development of a monitoring system by the respective supervisory authorities as well as in the implementation of bank-internal stress tests of default contagion.

Assessing systemic risk using interbank exposures in the global banking system

This paper contributes to the literature on systemic risk by examining the network structure of bilateral exposures in the global banking system. The global interbank market constitutes a major part of the global banking system. The market has a hierarchical network structure, composed of the national or jurisdictional area's local markets and the cross-border interbank market. First, we estimate the bilateral exposures matrix using aggregate financial data on loans and deposits from Bankscope and analyze the interconnectedness in the market using network centrality measures. Subsequently, for the model analysis, we apply the Eisenberg–Noe framework to a multi-period setting. In this framework, bank defaults are classified into stand-alone defaults and contagious defaults. The banks in our sample (i.e., the top 202 banks with more than $50 billion in total assets) comprise a major part of this global banking system. The main findings are as follows: The theoretical network analysis using network centrality measures showed that most of the banks designated as global systemically important banks (G-SIBs) play a central role in the global interbank market. The theoretical default analysis showed a few contagious defaults triggered by the basic defaults during and after the global financial crisis. Our stress test proved that many G-SIBs theoretically caused 1–6 contagious defaults. Our methodology would assist in the development of a monitoring system by the respective supervisory authorities as well as in the implementation of bank-internal stress tests of default contagion.

Tight Approximations of Dynamic Risk Measures

This paper compares two frameworks for measuring risk in a multiperiod setting. The first corresponds to applying a single coherent risk measure to the cumulative future costs, and the second involves applying a composition of one-step coherent risk mappings. We characterize several necessary and sufficient conditions under which one measurement always dominates the other and introduce a metric to quantify how close the two measures are. Using this notion, we address the question of how tightly a given coherent measure can be approximated by lower or upper bounding compositional measures. We exhibit an interesting asymmetry between the two cases: the tightest upper bound can be exactly characterized and corresponds to a popular construction in the literature, whereas the tightest lower bound is not readily available. We show that testing domination and computing the approximation factors are generally NP-hard, even when the risk measures are comonotonic and law-invariant. However, we characterize conditions and discuss examples where polynomial-time algorithms are possible. One such case is the well-known conditional value-at-risk measure, which we explore in more detail. Our theoretical and algorithmic constructions exploit interesting connections between the study of risk measures and the theory of submodularity and combinatorial optimization, which may be of independent interest.

Demystifying Rebalancing Premium: A Methodological Path to Risk Premia Engineering

Volatility is usually considered as a synonym for risk. Mainstream financial theory states that higher portfolio volatility is translated into higher expected returns while diversification helps eliminate idiosyncratic risks. This leaves us with an apparent anomaly as low-risk (low-beta) stocks out-perform high-risk (high-beta) stocks over the long term. Is this really an anomaly? What about high conviction investing? Should we dismiss stock-picking as a futile exercise even if such an approach is used by one of the most successful investors of our times? In this paper we answer these questions and propose a framework that encompasses various investment styles and portfolio construction methodologies. Modern Portfolio Theory is a one period approach relating expected returns and volatilities as two independent variables estimated from time averages. Here we focus on a multi-period setting, which is more relevant for the task of maximizing investor's wealth in the long run. Contrary to previous studies based on maximizing log returns, we find no contradictions with the results of modern portfolio theory. We show that Markowitz portfolios and Warren Buffett's investment style are valid special cases of optimal growth portfolios. In addition, we provide insights on rebalancing bonus, showing how and when it is possible to add value from volatility in active portfolio management. As fire can be either dangerous, if uncontrolled, or useful to run a mechanical engine if controlled, in the very same way it should be possible to put volatility to work in a controlled manner in order to produce growth.

A branch-and-cut framework for the consistent traveling salesman problem

We develop an exact solution framework for the Consistent Traveling Salesman Problem. This problem calls for identifying the minimum-cost set of routes that a single vehicle should follow during the multiple time periods of a planning horizon, in order to provide consistent service to a given set of customers. Each customer may require service in one or multiple time periods and the requirement for consistent service applies at each customer location that requires service in more than one time period. This requirement corresponds to restricting the difference between the earliest and latest vehicle arrival-times, across the multiple periods, to not exceed some given allowable limit. We present three mixed-integer linear programming formulations for this problem and introduce a new class of valid inequalities to strengthen these formulations. The new inequalities are used in conjunction with traditional traveling salesman inequalities in a branch-and-cut framework. We test our framework on a comprehensive set of benchmark instances, which we compiled by extending traveling salesman instances from the well-known TSPLIB library into multiple periods, and show that instances with up to 50 customers, requiring service over a 5-period horizon, can be solved to guaranteed optimality. Our computational experience suggests that enforcing arrival-time consistency in a multi-period setting can be achieved with merely a small increase in total routing costs.

Incentive Contracting with an Independent Underwriter: Does It Benefit Insurers?

Abstract In this article, we propose a model consisting of an insurance distribution channel compensation scheme, paying special attention to the insurer’s choice of distribution system in both single-period and multi-period settings. We find that the risk factor is the key element in both the insurer’s choice of distribution channel and the distribution channel compensation scheme. The advantage of having an independent underwriter is mainly manifested in lines of business that are more risky. Our analysis suggests that a profit-sharing contingent-commission scheme serves as a risk-sharing mechanism and is especially effective with risky business lines.

Learning and coordination with dispersed information

We analyse adaptive learning in a model of incomplete and dispersed information, with externalities and strategic interactions. We build on the framework proposed by Angeletos and Pavan (2007a) and extend it to a dynamic multi-period setting where agents need to learn to coordinate. We derive conditions under which adaptive learning obtains in such setting and show that, when actions are strategic substitutes, the information structure affects the speed of convergence: while more precise private information is beneficial, better public information has negative effects. We also show that adaptive learning dynamics converge to the Bayesian Nash equilibrium, which means that agents can learn to act strategically by relying only on observable (exogenous) information.

Microsimulation as an instrument for tax policy analyses

The paper deals with microsimulation – an increasingly popular instrument used for policy analysis, especially in the field of individual and corporate income taxation. The aim of the paper is twofold. First, it discusses some key aspects of microsimulation with a particular focus on its types and implementations in tax policy research. Secondly, it presents a microsimulation analysis of the effects of unlimited inter-period loss offset in corporate income tax. The investigation is based on a panel of 222 corporations active in Poland, which was derived from the InfoCredit database. The microsimulation is carried out in a multi-period setting (2007-2012). It considers a perspective of taxpayers with a particular focus on individual tax burden and distributional effects of taxation. The analysis shows that the expected overall consequences of the tax reform in question would be rather moderate, however the size of the effects would vary strongly across firms.

Optimal selection of energy efficiency measures for energy sustainability of existing buildings

This study is motivated by the need to increase energy efficiency in existing buildings. Around 33% of the energy used in the world is consumed in the buildings. Identifying and investing in the right energy saving technologies within a given budget helps the adoption of energy efficiency measures in existing buildings. We use a mathematical programming approach to select the right energy efficiency measures among all the available ones to optimize financial or environmental benefits subject to budgetary and other logical constraints in single- and multi-period settings. We also present a business model to offer energy efficiency measures as a service. By using a real case study of a university campus, all the relevant energy efficiency measures are identified and their effects are determined by using engineering measurements and modelling. Through numerical experiments using the case data, we investigate and quantify the effects of using environmental or financial savings as the main objective, the magnitude of benefit of using a multi-period planning approach instead of a single-period approach, and also feasibility of offering energy saving technologies as a service. We show that substantial environmental and financial savings can be obtained by using the proposed method to select and invest in technologies in a multi-period setting. We also show that offering energy efficient technologies as a service can be a win–win–win arrangement for a service provider, its client, and also for the environment.