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The roughness and uncertainty are important parameters of surface morphology. The least square middle line method is often used to estimate the roughness and its uncertainty. However, the roughness and its uncertainty obtained by the least square middle line method are inaccurate. This paper proposes a method to calculate exactly the roughness and its uncertainty by piecewise fitting the smooth B-spline filter assessment middle lines. A B-spline smoothing filter is selected to determine the assessment middle line of roughness. The B-spline filter can not only give the accurate roughness, but also obtain the smooth assessment middle line. The model of roughness uncertainty is proposed by piecewise fitting B-spline filter middle lines as the quadratic curves. The S-shaped test part is used to verify the model of roughness uncertainty.

Supply disruption may cause strong complaints of customers, which is a cost loss for the firms in the supply chain. Obviously, if realizing that there is the disruption risk, the members in a supply chain will adjust their decisions. For analyzing the influence, we consider a popular supply chain mode with dual channels, where one manufacturer has its direct sales channel and one traditional retailer channel. The manufacturer may suffer a supply disruption so that all ordered products by the retailer or the direct retail channel will be lost, and the members in supply chain will bear the corresponding disruption penalty from the customers. By considering four structures with different market power relations, the closed-form optimal price decisions of the four models are given. We found that the disruption factor improves the sales prices for any member structure as compared to the supply chain without the disruption. And the direct retail prices in the different modes are the same as each other, but the price of the traditional channel is influenced by the market share. And the sorts of the sales prices under different structures are given. We also conduct some extensive numerical analysis and compare the results under different structures. We observe that the expected optimal profits of considering the external penalty are smaller than those of no external penalty, and we give a sort of the optimal expected profits. And we also provide the effects of some parameters on the optimal decisions and the optimal expected profits.

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.

This paper studies the coordination issue of a supply chain consisting of one retailer and two suppliers, a main supplier and a backup supplier. The main supplier’s yield is subject to disruption and the retailer faces a random demand. We determine the retailer’s optimal ordering policy and the main supplier’s production quantity that maximize expected profit of the centralized supply chain. We also analyze the decentralized scenario, and a combination of overproduction risk sharing and buy-back contracts with a side payment from/to the backup supplier is provided to coordinate the supply chain. Numerical examples are given to gain some qualitative insights.

As an effective way of decreasing production cost, remanufacturing has attracted more and more attention from firms. However, it also brings many difficulties to firms, especial when firms remanufacture products which they produce. A primary problem for the case is how to acquire the used product sold by the firm itself. In this paper, we consider a return compensation policy for acquiring used product from customers. Under this policy, the return quantity of used product is a proportion of demand. We study an inventory replenishment and production planning problem for a two-period inventory system with dependent return and demand. We formulate the problem into a three-stage stochastic programming problem, where the firm needs to make decisions on the replenishment quantity of new raw material inventory in each period and the production quantities of manufacturing and remanufacturing ways. We give the optimal production policy of manufacturing and remanufacturing ways for the realized demand and prove the objective function for each stage to be concave in the inventory replenishment quantity. Moreover, we prove that the basic inventory policy is still optimal for each period and give the analytical conditions of the optimal inventory levels which are unrelated to acquisition price. Finally, we investigate numerical studies to analyze managerial insights.

Discrete and dynamic optimization is a significant methodology that has been widely applied to operation management fields.This issue on discrete and dynamic optimization problems in operationmanagement aims at an all-around research and the state-of-the-art theoretical, numerical, and practical achievements that contribute to this field. This issue contains 21 papers, with the following features.