Responding to supplier temporary price discounts in a supply chain through ordering and pricing decisions

This paper considers a one-retailer and one-supplier supply chain and addresses the question of how a retailer should use its ordering and pricing decisions to respond to its supplier’s temporary price discounts. The paper considers a hybrid environment – somewhere between deterministic and stochastic modelling approaches – that is, the retailer does not know when the next promotion from its supplier will occur but, once the promotion is announced, all its details are deterministic and often there is some time remaining before the promotion actually starts. We include in the objective function penalties on deviations from the original plan and explore the properties of the retailer’s ordering and pricing decisions under fixed and flexible set-up scenarios. We show that, when the set-up epochs are fixed, the retailer’s order quantities are monotonic and non-decreasing in situations where retail prices can be either fixed or flexible. When the set-up epochs are flexible, the ordering cycle is identical. Finally, we use some numerical examples to illustrate the proposed approach.     

Part selection policy for a flexible manufacturing cell feeding several production lines

Analysis of the part selection policy in the case of a flexible manufacturing cell producing different parts for several emanating lines is presented. The discrete response control problem is formulated as an undiscounted semi-Markovian decision problem whose decision epochs occur when the cell completes a part and must decide what type of part to fabricate next. Design objective is to minimize the expected shortage penalty per unit time incurred by the production lines when they run out of inputs. Optimal production policies are characterized, and a discussion of related industrial implementation issues is given.     

Production and maintenance integrated planning

This paper introduces an expert system for the planning and management of a multi-product and one-stage production system made up of flexible machines operating in parallel. The following characteristics of the production system were considered: production costs depending on the machine and on the job processed, setups depending on the machine and on the job-processing sequence, preventive maintenance, order portfolio defined by order quantities, release dates and due dates.

The system schedules both production and maintenance at the same time. It pursues three objectives: to meet release and due dates, to minimize the total cost of the plan (sum of the expected maintenance cost, the setup cost and the production cost) and to minimize the total plant utilization time (sum of the total job processing time, the total setup time, the total machine idle time and the total maintenance time).     

Material requirements planning with flexible bills-of-material

In conventional Material Requirements Planning (MRP), a Bills-of-Materials (BOM) for products is fixed. If time or quantity as stated in the Master Production Schedule (MPS) is not flexible for the final product, flexible BOM may be introduced to compensate for the inflexibility in the MPS. This paper addresses situations where a flexible BOM could be used to deal with unexpected shortages when using MRP to plan for requirements of dependent demand items. The requirements stated in the MPS are met in a timely manner by allowing the substitution of items for one another in the case of a shortage. A linear programming (LP) formulation is provided to help deal, if possible, with a shortage using the flexibility in the BOM. The LP model identifies a ‘mix’ of lower-level items that satisfy both the reality of shortages and ensure as small a deviation from the default BOM as possible. A detailed example in the food production environment is presented to explain how the flexible BOM concept may be applied.     

An S$$\ell _1$$LP-active set approach for feasibility restoration in power systems

We consider power networks in which it is not possible to satisfy all loads at the demand nodes, due to some attack or disturbance to the network. We formulate a model, based on AC power flow equations, to restore the network to feasibility by adjusting load at demand nodes or power production at generators, but doing so in a way that minimizes a weighted measure of the total power adjustment, and affects as few nodes as possible. Besides suggesting an optimal response to a given attack, our approach can be used to quantify disruption, thereby enabling “stress testing” to be performed and vulnerabilities to be identified. Optimization techniques including nonsmooth penalty functions, sequential linear programming, and active-set heuristics are used to solve this model. We describe an algorithmic framework and present convergence results, including a quadratic convergence result for the case in which the solution is fully determined by its constraints, a situation that arises frequently in the power systems application.     

An effective approach to multi-item capacitated dynamic lot-sizing problems

In this study we solve the multi-item capacitated dynamic lot-sizing problem, where each item faces a series of dynamic demands, and in each period multiple items share limited production resources. The objective is to find the optimal production plan so as to minimise the total cost, including production cost, inventory holding cost, and fixed setup cost. We consider both single-level and multi-level cases. In the multi-level case, some items are consumed in order to produce some other items and therefore items face internally generated demand in addition to external demands. We propose a simple three-stage approach that is applicable to both classes of problems. In the first stage we perform preprocessing, which is designed to deal with the difficulty due to the joint setup cost (a fixed cost incurred whenever production occurs in a period). In the second stage we adopt a period-by-period heuristic to construct a feasible solution, and in the final stage we further improve the solution by solving a series of subproblems. Extensive experiments show that the approach exhibits very good performance. We then analyse how the superior performance is achieved. In addition to its performance, one appealing feature of our method is its simplicity and general applicability.     

Batch process schedule optimization under parameter volatility

A general strategy to treat the uncertainties in parameters of batch process scheduling has been developed. The strategy consists of three algorithms: flexible planning, flexible scheduling and reactive schedule adaptation. In this paper, we introduce the flexible scheduling and the reactive schedule adaptation algorithms. The flexible scheduling algorithm is based on both a Monte Carlo simulation and a simulated annealing. It can deal with multiple uncertain parameters and any type of probability density function for the uncertain parameter. We seek the flexible schedule that maximizes the expected profit, including net present values of products less raw material and processing costs, as well as due date penalties, inventory costs and setup costs. In reality, the values of uncertain parameters always change after the batch process schedule and plan are set up. Since the flexible schedule has periods of free time that can be used to accommodate uncertainties during the actual production, the reactive schedule adaptation algorithm can modify the flexible schedule in response to any change in an uncertain parameter with little or no penalty. This algorithm finds a new optimal or suboptimal solution under the new condition by using a combination of different local search methods, which are described.     

Coordinating production quantities and demand forecasts through penalty schemes

In this paper, we study coordination mechanisms through penalty schemes between manufacturing and marketing departments which enable organizations to match demand forecasts with production quantities. This research was motivated by our interactions with a leading electronics and computer manufacturer. We consider two possible organizational structures - centralized and decentralized. In the decentralized case we model a single period problem where demand is uncertain and the marketing department provides a forecast to manufacturing which in turn produces a quantity based on the forecast and the demand distribution. In the centralized case, marketing and manufacturing jointly decide on the production quantity. Among other results we show that by setting suitable penalties one can generate the same result in a decentralized system as that obtained from a centralized system. We also show that setting the correct penalty for marketing is essential for coordination. Subsequently, we analyze models where the marketing department has the ability to change the distribution of demand based on efforts (through promotion, advertising and personal relationship with customers). An interesting result indicates that ii. is possible to set penalties so that a coordinated decentralized system outperforms a centralized system when there are no tangible costs to the firm for the efforts expended by the marketing department.     

连锁经营企业集中订货与支援调拨策略及模型

根据连锁经营企业的特点,提出了各分店和配送中心集中订货和相互之间在商品上的支援调拨策略。在理论上证明了集中订货和支援调拨策略可以降低总体订货量,通过模拟实验验证了该策略能够降低总体订货量的波动。建立了集中订货和支援调拨策略的数学模型。使用实际案例验证了该策略和模型能够带来显著的订货和库存量的下降和服务水平的提高。     

Automatic derivation of positivity conditions inside boundary elements with the help of the REDLOG computer logic package

The very well-known shape functions are used in classical boundary element analysis for the construction of the polynomial interpolation function p for the approximation to the unknown field quantity u. In this note, we show the usefulness of the recent REDLOG Reduce computer logic package of Dolzmann and Sturm for the construction of positivity and analogous parametric feasibility conditions, based on the nodal values of the polynomial p, inside the whole boundary element. A simple one-dimensional case, based on the classical quadratic element, and a more difficult two-dimensional case, based on a quadratic triangular element, are used for the illustration of the approach, whereas several related conclusions are also drawn. The present results are applicable to cases where the positivity or the negativity or just the boundedness of the unknown quantity is required (such as the case of the pressure distribution in contact problems and the opening displacement in crack problems) and significantly extend the already available recent related computational quantifier elimination research results.     

基于应力约束全局化策略的板壳结构强度拓扑优化

应力约束下板壳结构的拓扑优化设计由于应力约束难以显式化和约束条件数量庞大等问题,存在建模和求解的困难。为了解决这些困难,首先,该文通过类比独立连续映射(Independent Continuous and Mapping, ICM)方法中的过滤函数,在实体各向同性材料惩罚(Solid Isotropic Material Penalization, SIMP)方法中引进了单元重量惩罚函数和材料许用应力惩罚函数,实现了对SIMP方法惩罚函数概念的拓广。然后,该文移植了ICM方法中行之有效的应力约束全局化策略,基于拓广后的SIMP方法,构造了代替应力约束后的结构畸变能约束的近似显式化函数,建立了多工况下板壳结构拓扑优化模型。最后,采用对偶序列二次规划算法求解该优化模型,并基于Python语言在ABAQUS软件平台进行了程序实现。数值算例都取得了很好的结果,这表明该文提出的方法是可行而有 效的。     

Design for Line Flexibility

Capacity planning for a manufacturing line is often difficult because of changes in production demands. If the line is set up at a fixed capacity during the entire product lifetime, it is likely to have either insufficient capacity or overinvestment situations. On the other hand, any change made in capacity by adding or deleting work stations may cause line disruption and waste space. This paper presents a simple method to resolve such problems, using a direct-access material-handling system. Such a system allows construction of a flexible line that can be dynamically expanded or contracted.     

A sequential quadratically constrained quadratic programming technique for a multi-objective optimization problem

In this article a line search algorithm is proposed for solving constrained multi-objective optimization problems. At every iteration of the proposed method, a subproblem is formulated using quadratic approximation of all functions. A feasible descent direction is obtained as a solution of this subproblem. This scheme takes care some ideas of the sequential quadratically constrained quadratic programming technique for single objective optimization problems. A non-differentiable penalty function is used to restrict constraint violations at every iterating point. Convergence of the scheme is justified under the Slater constraint qualification along with some reasonable assumptions. The proposed algorithm is verified and compared with existing methods with a set of test problems. It is observed that this algorithm provides better results in most of the test problems.     

Capacitated, finish-to-order production planning with customer ordering day assignments

We examine the production and ordering fulfillment system of a firm offering a large variety of products to time-sensitive customers. The firm wants to combine a finish-to-order strategy with an existing customer ordering system. The finish-to-order policy guarantees significant inventory savings due to the large number of end-product offerings, but it may also increase setup costs due to a short delivery commitment. The ordering system assigns periodic ordering dates to customers, encourages them to place their orders only on these dates, and promises them the same short delivery time irrespective of their geographic locations. The ordering system facilitates a smooth capacity load as well as transportation economies by allowing shipments to each location once during each ordering cycle. We propose a formulation for the combinatorial problem of choosing an ordering-day assignment and a finish-to-order production schedule that minimizes setup costs and maintains a balanced capacity load. We examine a Lagrangian relaxation of this formulation and heuristic solutions based on our relaxation. Our numerical work demonstrates that our best heuristic differs from the optimal solution by 5% on average for small problems (with up to 10 products and 10 customers). Moreover, we show that the difference between the objective value of the relaxation and that of the best heuristic decreases significantly as the problem size increases, being as low as 4% on average for problems with 30 products and 30 customers.     

Joint inventory-and-pricing strategy for a stochastic continuous-review system

We analyze an infinite-horizon continuous-review stochastic inventory system in which the selling price and inventory replenishment are determined simultaneously. The demand process is Poisson with a price-dependent arrival rate. The ordering cost includes a fixed setup cost and a variable cost proportional to the order quantity. We obtain closed-form solutions for the optimal inventory control strategy and optimal pricing strategy, which provide managerial insights as well as quantitative and qualitative relationships between decision rules and system parameters. We show that the optimal price is a unimodal function of the inventory level. We also develop efficient algorithms to compute the optimal strategies and present numerical examples.     

Optimal production and inventory decisions under demand and production disruptions

Unanticipated events may take place and disrupt demand and/or production in a supply chain. Conditional on the type, magnitude and duration of disruptions, changes may be called to revise the original production plan. We analyse different disruption scenarios and propose optimal production–inventory models for products facing demand and production disruptions. To lower the cost, we optimise the production run time, purchasing times and order quantity for the manufacturer. Numerical experiments are conducted to examine the influences of disruption time and magnitude on optimal production and purchasing decisions.     

On optimal emergency orders with updated demand forecast and limited supply

This study analyses a two-stage newsvendor system with a regular and an emergency order. The emergency order can be placed at a later time based on a more accurate demand forecast. However, the unit cost for the emergency order is higher, and the quantity is limited. To maximise the expected profit, a retailer should determine both regular and emergency order quantities by considering the demand forecast updating, ordering cost and quantity constraint. Using dynamic programming, optimal ordering quantities are derived, and properties of the optimal solutions are obtained. Numerical experiments are carried out to illustrate the effect of the emergency order on the ordering decisions and expected profit. Some managerial insights are gained from the numerical results.     

Joint production and shipment lot sizing for a delivery price-based production facility

A joint economic production quantity (EPQ) and delivery quantity model for a production system is investigated in this paper. More specifically, an EPQ policy is implemented in the production system, while a smaller shipping quantity is periodically dispatched to the customer. The production system is also responsible for the shipment cost, i.e. a delivery price-based procurement from the customer. The considered cost includes setup cost to launch the batch production, inventory carrying cost, and transportation cost, where the transportation cost is a function of the delivery quantity. A per unit time cost model is developed and analysed to determine the optimal production and delivery quantities. Under some mild conditions, it can be shown that the joint cost function is convex with respect to the production quantity; and the number of delivery is an integer in each replenishment cycle. Computational study has demonstrated the significant impact of the joint decision model on the operating cost. In particular, the reduction in total cost can be more than 15% when inventory carrying costs, and/or transportation costs, are high.     

Impact of sequence-dependent setup time on job shop scheduling performance

In a production system using multi-purpose and flexible machines, reducing setup time is an important task for better shop performance. Numerous cases were reported about successful reduction of setup times by standardization of setup procedures. However, setup times have not been eliminated and remain an important element of real production problems for production systems such as commercial printing, plastics manufacturing, metal processing, etc. It is especially critical when the setup time is sequence dependent. In this situation, shop performance cannot be effectively improved without the aid of an appropriate scheduling procedure. Review of the past studies shows that there has not been a significant amount of research done on the scheduling procedure for a dynamic job shop with sequence dependent setup times. This paper investigates the job shop scheduling problems that are complicated by sequence-dependent setup times. The study classifies and tests scheduling rules by considering whether setup time and/or due date information is employed. These scheduling rules are evaluated in dynamic scheduling environments defined by due date tightness, setup times and cost structure. A simulation model of a nine machine job shop is used for the experiment. A hypothetical, asymmetric, setup time matrix is applied to the nine machines.     

《工程制图》电子教案的设计与开发

提出了以AutoCAD为平台开发电子教案的方法，利用AutoCAD绘图软件强大的绘图和编辑功能以及AutoLSP语言，通过界面设计，各种自定义函数的定义及大量绘图程序的编写和素材库的建立，使所开发的电子教案图文并茂，操作简单，交互功能强，是一个完全开放的授课平台。该电子教案在教学中得到广泛的运用，并收到了良好的教学效果。