Abstract Accepted by: Konstantinos Nikolopoulos This paper develops a new stochastic volatility model for the average daily temperature. It is a natural extension of a Gaussian model in which the temperature returns to a seasonal trend with a deterministic time-dependent volatility. The new model allows to be more conservative regarding extreme events while keeping tractability. We give a method based on conditional least squares to estimate the parameters on daily data and estimate our model on eight major European cities. We then show how to calculate efficiently the average payoff of weather derivatives both by Monte-Carlo and Fourier transform techniques. This new model allows to better assess the risk related to temperature volatility.

Abstract Accepted by: M. Zied Babai Deep reinforcement learning (DRL) can solve complex inventory problems with a multi-dimensional state space. However, most approaches use a discrete action representation and do not scale well to problems with multi-dimensional action spaces. We use DRL with a continuous action representation for inventory problems with a large (multi-dimensional) discrete action space. To obtain feasible discrete actions from a continuous action representation, we add a tailored mapping function to the policy network that maps the continuous outputs of the policy network to a feasible integer solution. We demonstrate our approach to multi-product inventory control. We show how a continuous action representation solves larger problem instances and requires much less training time than a discrete action representation. Moreover, we show its performance matches state-of-the-art heuristic replenishment policies. This promising research avenue might pave the way for applying DRL in inventory control at scale and in practice.

Abstract Accepted by: M. Zied Babai The clustered and generalized vehicle routing problem (CGVRP) extends the well-known vehicle routing problem by grouping the demand points into multiple distinct zones, and within each zone, further separation is made by forming clusters. The objective of the CGVRP is to determine the optimal routes for a fleet of vehicles dispatched from a depot, visiting all zones within each cluster. This requires making two simultaneous optimization decisions. Firstly, each zone must be visited by exactly one node, and secondly, all zones within a cluster must be visited by the same vehicle. In this paper, we introduce two mixed-integer linear programming formulations for the CGVRP, aimed at solving a joint order batching and picker routing problem with alternative locations in a warehouse environment featuring mixed-shelves configuration. Both formulations are tested on three scenarios of randomly generated small- and medium-sized instances. Additionally, we propose a general rule approach for calculating a cost matrix in a rectangular environment. The results demonstrate the effectiveness of the proposed mathematical formulations in efficiently solving problems with up to 180 nodes.

Abstract Assembly line balancing by workload smoothing is very common; it aims to appropriately assign tasks to the stations of an assembly line, to ensure as similar as possible workloads for the stations. A shortcoming of the mathematical models developed in the literature is the optimization of workload smoothing when only all potential stations are considered. Therefore, the obtained solution may not be the global optimal solution and also may not be effective for real world cases. To overcome this shortcoming, some new workload smoothing criteria and their related mixed integer linear mathematical models are developed for three different settings: (1) workload smoothing optimization, when all potential stations are considered, (2) workload smoothing and minimization of the number of stations are optimized simultaneously, (3) global workload smoothing optimization regardless of the number of considered stations. The proposed formulations are associated with fewer variables and constraints compared with models previously presented in the literature and lead to better results according to an extensive numerical study. The proposed models can be applied in practice for designing the assembly lines of, inter alia, automobile and electronic equipment production systems.

Abstract We present a novel general inverse data envelopment analysis model for assessing the restructuring of decision-making units (DMUs) while observing predetermined value efficiency targets, under two distinct scenarios: merger and acquisitions and split. By considering the set of efficient DMUs as the Decision Maker’s set of Most Preferred Solutions, virtual new units with desired targets for value efficiency scores and input and output levels can be computed. The innovations of this paper are threefold. First, a comparison between the proposed value efficiency and previous technical efficiency approaches reveals improvement in the estimation of restructured input/output levels. Second, the proposed approach is capable of handling the decision-maker’s preferences during restructuring. Third, an algorithm to determine the worst case-scenario for restructuring is presented. An applied case study in banking operations is presented to illustrate the validity and applicability of the proposed method.

Abstract In this paper, we present a routing heuristic for the Flying Sidekick Traveling Salesman Problem. This problem combines a single truck with a single drone. The drone may be launched from the truck from a customer location and can make a single package delivery before being recovered by the truck. While the drone is in flight, the truck can deliver packages independently. The problem is one of simultaneously assigning the customers to each vehicle and determining the synchronized routes for both vehicles to satisfy all customer demands in the shortest time possible. The problem is NP-hard. Our main contribution lies in developing a novel split algorithm that utilizes a shortest path approach for determining the optimal routing solution to a given order of customer locations. This split algorithm has polynomial complexity. We develop a heuristic solution to the problem by combining the split algorithm with local search techniques. This overall heuristic is shown to be accurate and computationally scalable to large, realistically sized problems applicable in last-mile logistics.

Abstract To examine the familiar tradeoff between risk and return in financial investments, we use a rolling two-stage stochastic program to compare mean-risk optimization models with time series momentum strategies. In a backtest of allocating investment between a market index and a risk-free asset, we generate scenarios of future return according to a momentum-based stochastic process model. A new hybrid approach, time series momentum strategy controlling downside risk (TSMDR), frequently dominates traditional approaches by generating trading signals according to a modified momentum measure while setting the risky asset position to control the conditional value-at-risk (CVaR) of return. For insight into the outperformance of TSMDR, we decompose each strategy into two aspects, the trading signal and the asset allocation model that determines the risky asset position. We find that 1) weighted moving average can better capture the trend of the stock market than time series momentum computed as past 12-month excess return, 2) mean-risk strategies generally provide better returns whereas risk parity strategies have less investment risk and 3) controlling CVaR limits the investment risk better than controlling variance does.

Sports have been always a fertile area of application of mathematics with a wide range of potential problems, ranging from simple examples which can be effectively used to teach students fundamental ideas about mathematics, probability and statistics (see, e.g. Kvam & Sokol, 2004), up to complicated models that can be utilized to study space creation in soccer (see, e.g. Bornn et al., 2018). Students are extremely motivated to study mathematics and statistics when real-life sports examples are involved in a relevant course or lecture. For example, early in 1950s, Moroney (1951) examined whether goals in football were ruled by pure chance. In such case, the distribution should have been one like a Poisson distribution. But what happens if other factors enter the scene? How can we move away from such a simplistic assumption? The debate whether pure chance solely drives football is still present but the advance in...

Abstract The existing literature on make-to-order firms typically supposes that the unit production cost is a constant. In contrast, in this study, this cost is a variable that depends on the lead time. Under this assumption, we investigate the pricing problem for both a monopoly firm and two competing firms. Specifically, we develop a queueing-game-theoretic model to capture the interaction between customers and the firm’s manager and further solve the pricing problem. The results illustrate that, for a monopoly firm, there exists a service rate threshold, and for two homogeneous firms, there is a unique symmetric equilibrium. However, for two heterogeneous firms, the equilibrium may not exist, and if it does, it may not be unique. In this case, the equilibrium is characterized analytically if it is unique and explored numerically if not. Finally, a specific cost function is adopted to analyse the sensitivity of the optimal decisions. When the firms have this variable cost, compared with those with constant unit production cost, customers’ waiting time might be shorter, and the competition between firms might be fiercer. Also, for these firms, increasing the service rate or decreasing the cost parameter does not always help to increase their market share or profit.

Abstract Advance selling activities are becoming more popular, especially in online retailing of new products. During the advance selling process, consumers may be loss averse. This influences the pricing strategy of the members of the supply chain. Using prospect theory and game theory, and considering consumers’ loss aversion, this paper studies the pricing strategy of advance selling in a supply chain consisting of a manufacturer and an e-retailer under a resale contract or an agency contract. The study finds that as consumers’ loss aversion increases, supply chain members set lower prices. Consumers’ loss aversion has a positive impact on the member who directly prices to consumers, but it has a negative impact on the indirect member. Advance selling under an agency contract makes it easier to achieve a Pareto improvement than that under the resale contract. When the unit order fulfilment cost is low, the e-retailer prefers the agency contract.