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Multi-focus image fusion (MFIF) is an image-processing method that aims to generate fully focused images by integrating source images from different focal planes. However, the defocus spread effect (DSE) often leads to blurred or jagged focus/defocus boundaries in fused images, which affects the quality of the image. To address this issue, this paper proposes a novel model that embeds the Kolmogorov–Arnold network with convolutional layers in parallel within the U-Net architecture (KCUNet). This model keeps the spatial dimensions of the feature map constant to maintain high-resolution details while progressively increasing the number of channels to capture multi-level features at the encoding stage. In addition, KCUNet incorporates a content-guided attention mechanism to enhance edge information processing, which is crucial for DSE reduction and edge preservation. The model’s performance is optimized through a hybrid loss function that evaluates in several aspects, including edge alignment, mask prediction, and image quality. Finally, comparative evaluations against 15 state-of-the-art methods demonstrate KCUNet’s superior performance in both qualitative and quantitative analyses.

Network externality arises when the utility of a product depends not only on its attributes but also on the number of consumers who purchase the same product. In this paper, we study consumer choice models that endogenize such network externality. We first characterize the choice probabilities under such models and conduct studies on comparative statics. Then we investigate the assortment optimization problem under such choice models. Although the problem is generally NP-hard, we show that a new class of assortments, called quasi-revenue-ordered assortments , which consist of a revenue-ordered assortment plus at most one additional item, are optimal under mild conditions. We also propose an iterative estimation method to calibrate such choice models, for both uncensored and censored data cases. An empirical study on a mobile game data set shows that our proposed model can provide better fits for the data, increase the prediction accuracy for consumer choices, and potentially increase revenue. This paper was accepted by Noah Gans, stochastic models and simulation .

We study firms that sell multiple substitutable products and customers whose purchase behavior follows a nested logit model, of which the multinomial logit model is a special case. Customers make purchasing decisions sequentially under the nested logit model: they first select a nest of products and subsequently purchase one within the selected nest. We consider the multiproduct pricing problem under the general nested logit model with product-differentiated price sensitivities and arbitrary nest coefficients. We show that the adjusted markup , defined as price minus cost minus the reciprocal of price sensitivity, is constant for all the products within a nest at optimality. This reduces the problem's dimension to a single variable per nest. We also show that the adjusted nest-level markup is nest invariant for all the nests, which further reduces the problem to maximizing a single-variable unimodal function under mild conditions. We also use this result to simplify the oligopolistic multiproduct price competition and characterize the Nash equilibrium. We also consider more general attraction functions that include the linear utility and the multiplicative competitive interaction models as special cases, and we show that similar techniques can be used to significantly simplify the corresponding pricing problems.

Consumers search for product information to resolve valuation uncertainties before purchase. We incorporate search cost into consumer choice models and study the two-stage consider-then-choose policy. In the first stage, a consumer forms her consideration set by balancing utility uncertainty and search cost. In the second stage, she evaluates all products in her consideration set and chooses the one with the highest net utility. We show that the revenue-ordered assortment (i.e., the offer set that includes products in the revenue-decreasing order) fails to be optimal, although it can obtain at least half the optimal revenue. We propose a k -quasi-attractiveness-ordered assortment and show that it can be arbitrarily near optimal for the market share maximization problem. The assortment problems with search cost are generally NP-hard, so we develop efficient approximation or relatively fast exact algorithms for a variety of assortment problems under the consider-then-choose models with search cost. For the joint assortment planning and pricing problem with homogeneous consumers, we show that the intrinsic-utility-ordered assortment and the quasi-same-price policy, which charges the same price for all products except at most one, are optimal. The online appendix is available at https://doi.org/10.1287/mnsc.2017.2790 . This paper was accepted by Gad Allon, operations management.

Biogas production in the cold regions of China is hindered by low temperatures, which led to slow lignocellulose biotransformation. Cold-adapted lignocellulose degrading microbial complex community LTF-27 was used to investigate the influence of hydrolysis on biogas production. After 5 days of hydrolysis at 15 ± 1 °C, the hydrolysis conversion rate of the corn straw went up to 22.64%, and the concentration of acetic acid increased to 2596.56 mg/L. The methane production rates of total solids (TS) inoculated by LTF-27 reached 204.72 mL/g, which was higher than the biogas (161.34 mL/g), and the control group (CK) inoculated with cultural solution (121.19 mL/g), the methane production rate of volatile solids (VS) increased by 26.88% and 68.92%, respectively. Parabacteroides , Lysinibacillus , and Citrobacter were the main organisms that were responsible for hydrolysis. While numerous other bacteria genera in the gas-producing phase, Macellibacteroides were the most commonly occurring one. Methanosarcina and Methanobacteriaceae contributed 86.25% and 11.80% of the total Archaea abundance during this phase. This study proves the psychrotrophic LTF-27’s applicability in hydrolysis and biomass gas production in low temperatures.

We investigate heterogeneous customer choice behavior in the presence of main products —ancillary services with options of pay-per-use and subscription— and outside option. The willingness to pay for a service subscription is derived as a closed-form expression, which enables us to characterize the optimal pricing strategy and the impact of service subscriptions on customer surplus. Analytical results and numerical experiments show that offering service subscriptions may result in “win-win,” “win-win-win,” “win-win-lose,” or “lose-lose-win” scenarios or in other situations for the firm, competitors, and customers in a variety of monopolistic and duopolistic scenarios. The advantages of service subscription still remain with heterogeneous customers differing on multiple dimensions including the nominal utility, uncertainty in the need of ancillary service, and purchase frequency. We find that if the product quality for both firms, measured by nominal utility, is not significantly different, more fierce price competition by offering a service subscription may result in a higher customer surplus, compared with that without a service subscription. Ancillary service subscription can help firms to better price-discriminate heterogeneous customers through different subscription decisions and subsequent purchase behavior. This paper was accepted by Gad Allon, operations management.

We consider an assortment optimization problem where a retailer chooses a set of substitutable products to maximize the total expected revenue or profit subject to a capacity constraint. The customer purchase behavior follows the generalized attraction model (GAM), of which the multinomial logit model and the independent demand model are special cases. We visualize the efficient assortments and propose a nonrecursive polynomial-time algorithm to find the optimal one for the static problem. We then connect it with the concept of efficient set in the context of revenue management and show that the efficient sets, the only candidates for the optimal assortments under the capacitated GAM formulation, are of polynomial size. Moreover, the efficient sets significantly reduce the computational complexity in the dynamic assortment management and the optimal policy has a time-threshold structure.

We study the joint inventory and sales effort management problems of a retailer in a broad context and investigate the optimal policies for a single item, periodic-review system. In each period, the demand is uncertain depending on the sales effort level exerted by the retailer, which incurs an associated cost. The retailer’s objective is to find a joint optimal inventory replenishment and sales effort policy to maximize the discounted profit over a finite horizon. We first consider a basic setting with zero setup cost and no batch ordering, under which the base stock list sales effort policy is optimal. Two extensions are then investigated: (1) the case with nonzero setup cost, under which we show that (s,S,e) policy is optimal; and (2) the case with batch ordering, under which we prove the optimality of the (r,Nq,e) policy. Finally, we conduct numerical studies to provide additional managerial insights.

Low temperature is a major factor limiting the bio-sustainable and efficient conversion of cellulose-based resources in cold regions. In this study, a low-temperature resistant cellulose-degrading fungus with high cellulase production was screened from samples found in a primitive forest in Daqing by straw using the enrichment-restricted culture technique. The fungus was identified as genus Trichoderma harzianum, strain L-8 by morphological and molecular biological analysis. The enzyme production conditions were optimized via response surface methodology, and the optimal conditions for the enzyme production of Trichoderma harzianum L-8 were as follows: a CMC-Na addition of 10.63 g·L-1, an ammonium sulfate addition of 2.22 g·L-1, an initial pH of 5.29, and a lecithin addition of 5.18 g·L-1 when the CMCase reached 53.40 IU·mL-1. The leading enzyme families of Trichoderma harzianum L-8 were identified via proteomic analysis. Proteases including glycosyl hydrolase family 3-4 and cellobiohydrolase play important roles in cellulose degradation. The strain Trichoderma harzianum L-8 showed a strong cellulose degradation ability under low temperatures, providing strain resources for cellulose resource biotransformation technology in cold regions.

In this thesis, we study price optimization and competition of multiple differentiated substitutable products under the general Nested Logit model and also consider the designing and pricing of new service products, e.g., flexible warranty and refundable warranty, under customers' strategic claim behavior. Chapter 2 considers firms that sell multiple differentiated substitutable products and customers whose purchase behavior follows the Nested Logit model, of which the Multinomial Logit model is a special case. In the Nested Logit model, customers make product selection decision sequentially: they first select a class or a nest of products and subsequently choose a product within the selected class. We consider the general Nested Logit model with product-differentiated price coefficients and general nest-heterogenous degrees. We show that the adjusted markup, which is defined as price minus cost minus the reciprocal of the price coefficient, is constant across all the products in each nest. When optimizing multiple nests of products, the adjusted nested markup is also constant within a nest. By using this result, the multi-product optimization problem can be reduced to a single-dimensional problem in a bounded interval, which is easy to solve. We also use this result to simplify the oligopolistic price competition and characterize the Nash equilibrium. Furthermore, we investigate its application to dynamic pricing and revenue management. In Chapter 3, we investigate the flexible monthly warranty, which offers flexibility to customers and allow them to cancel it at anytime without any penalty. Frequent technological innovations and price declines severely affect sales of extended warranties as product replacement upon failure becomes an increasingly attractive alternative. To increase sales and profitability, we propose offering flexible-duration extended warranties. These warranties can appeal to customers who are uncertain about how long they will keep the product as well as to customers who are uncertain about the product's reliability. Flexibility may be added to existing services in the form of monthly-billing with month-by-month commitments, or by making existing warranties easier to cancel, with pro-rated refunds. This thesis studies flexible warranties from the perspectives of both the customer and the provider. We present a model of the customer's optimal coverage decisions under the objective of minimizing expected support costs over a random planning horizon. We show that under some mild conditions the customer's optimal coverage policy has a threshold structure. We also show through an analytical study and through numerical examples how flexible warranties can result in higher profits and higher attach rates. Chapter 4 examines the designing and pricing of residual value warranty that refunds customers at the end of warranty period based on customers' claim history. Traditional extended warranties for IT products do not differentiate customers according to their usage rates or operating environment. These warranties are priced to cover the costs of high-usage customers who tend to experience more failures and are therefore more costly to support. This makes traditional warranties economically unattractive to low-usage customers. In this chapter, we introduce, design and price residual value warranties. These warranties refund a part of the upfront price to customers who have zero or few claims according to a pre-determined refund schedule. By design, the net cost of these warranties is lower for light users than for heavy users. As a result, a residual value warranty can enable the provider to price-discriminate based on usage rates or operating conditions without the need to monitor individual customers' usage. Theoretic results and numerical experiments demonstrate how residual value warranties can appeal to a broader range of customers and significantly increase the provider's profits.