考虑生产计划的多周期切割问题优化研究

切割生产广泛存在于工业企业,是原材料加工的重要环节。已有文献主要关注单周期切割问题,但是切割计划也是生产计划的一部分,切割计划和生产计划应该协调优化,达到全局最优。本文研究考虑生产计划的多周期切割问题,目标是最小化运营成本,包括准备成本、切割成本、库存成本以及母材消耗成本。首先建立混合整数规划模型;提出动态规划启发式算法;最后对算例在多种情境下测试,分析成本因子变化对最优结果的影响。算法结果与CPLEX最优结果比较,平均误差为1.85%,表明算法是有效的。     

A Cutting Stock and Scheduling Problem in the Copper Industry

This case study was carried out for Thomas Bolton Ltd, a copper component manufacturer. The focus was on the first major production operation that is carried out in the foundry. This operation consists of three processes — melting scrap metal, casting it as ‘logs’ and cutting logs into ‘billets’. The timely production of the billets is essential as these feed a bottleneck process. The objective of the study was to investigate alternative methods of generating a production plan for the foundry that minimized costs whilst meeting the demand for billets at the bottleneck. The production plan was required to include a daily production schedule and a list of the cutting patterns to use when cutting the logs into billets. Thus, both the scheduling and cutting stock problems were addressed. A two-stage solution procedure was proposed. Alternative heuristic methods were investigated at the first stage and an optimal solution using Integer Programming (IP) was proposed for the second stage. It is shown that current performance could be improved using all of the heuristics considered at the first stage, but that using an IP-based heuristic method gives the best results.     

The Cutting Stock Problem in the Flat Glass Industry

The cutting stock problem occurs where large rectangles of some material require cutting into smaller rectangles, in the most appropriate way, to satisfy an order book. A linear programming approach to the problem has been suggested by P. C. Gilmore and R. E. Gomory. An application of this approach in the glass industry is described which is shown to be inadequate since it only satisfies a wastage criterion. In practice, multiple criteria must be satisfied and two alternative approaches using linear programming and heuristic scheduling are proposed.     

The Cutting Stock Problem in the Flat Glass Industry -- Selection of Stock Sizes

In the glass industry holding good stock sizes appears to have at least as big an impact on trim loss as cutting up the stock plates efficiently. In this paper two tech niques are described for determining "optimal" stock sizes, one a heuristic method and the other an integer programming algorithm. Several actual applications within the glass industry are described, and illustrative results of the improvements in wastage that have been achieved are given.     

Production Planning in the New Zealand Dairy Industry

From 1977 onwards, D.S.I.R. has been developing an L.P. model to help the largest N.Z. dairy company plan its medium-term production. This time-staged model finds the most profitable daily production schedule of the various powder, casein, cheese and butter products. Computer reports and graphics show Company management how to allocate the milk available in the various farming regions to the Company's factories, and where to send the by-products for further processing.The L.P. models seasonal fluctuations in wholemilk availability and quality, as well as transport costs, factory capacities and costs, and product-yields and prices. Comparison runs have shown that the L.P. increases the profitability of the manual plan by over $5000 per day (because the computer can handle changing yields, factory costs and by-product processing). The model gives management the ability to adjust production plans quickly in response to improved information, new market opportunities and emergencies like plant breakdown.     

基于质量控制的供应链计划问题研究

为了研究基于质量控制的供应链计划问题,采用了优化建模的方法,分析了易腐物品生命周期函数的选用及拟合原则,建立起了质量衰减成本与时间之间的关系,考虑了涉及交通及天气情况的运输风险,最终建立了优化模型,以实现供应链运行总成本最小。最后,提出了动态规划的求解方法,并通过仿真实验证明了算法的有效性。     

An Interactive Production Planning System in the Chemical Industry

This paper offers an example of a practical production planning system as used routinely by BP Chemicals Ltd. It is based on the interactive control of a linear programming model embedded in a system for data collection and report production. The model solves a "product mix" type of problem with a multi-criteria objective function.     

The Commonality Problem in Stock Control for Complex Assemblies

A method is described for maintaining overall inventories close to the minimum level, in the situation of keeping stocks of parts to be issued for assemblies.Simulation results show that the minimum total inventory level is reached when approximately 80 per cent of the assemblies can be commenced at the scheduled time. Furthermore, by additional simulations it is shown that this performance figure can only be attained by a 30 per cent increase of inventory if inferior strategies are used.The power of the method is directly related to the wide ranges of item values and item commonalities which are present.     

Production Planning and Inventory Control on a Chemical Plant

In this paper formulae are derived to give the optimum run lengths on a plant producing two products alternately. The general case of n runs of one product to one run of the other is considered. The work is applied to a chemical plant and the difficulties of determining certain costs are discussed. It is estimated that appreciable savings can be made.An empirical method of calculating buffer stocks is then described, together with a method of planning production before an annual shut-down. This part of the work does not lead to any substantial savings in cost, but reduces the danger of running out of stock.     

A Production Problem in Phosphate Mining

A model to determine the method of mining phosphates and its scheduling was developed. A heuristic algorithm was constructed to demonstrate how this model can increase the discounted profits of Israeli firms producing phosphoric acid.     

A Nomogram for Stock Control

A well-known replenishment policy for an inventory subject to probabilistic demand gives rise to the problem of determining an order quantity and a reorder level which minimize the average cost of keeping inventory. If the problem can be expressed in terms of a simple approximative model which includes a restriction on back-orders and represents demand in the replenishment lead time as normally distributed, it is possible to construct a "set-square index" nomogram which accomplishes a major part of the necessary computations. The procedure for using the nomogram and the principles of its construction are described.     

A Partitioned Cutting-stock Problem Applied in the Meat Industry

The paper reports on a linear programming application in the meat industry. The problem is formulated as a variant of the cutting-stock or trim problem, where the objective is to maximize the return from selling products yielded from cutting patterns applied to animal carcasses. One feature of the formulation is the partitioning of cutting patterns among carcass sections. Since the sections are relatively independent, this partitioning vastly reduces the number of cutting patterns in the formulation. Implementation is on a personal computer, and the system is used by a meat company for market planning. The system uses a commercial database to handle data entry and solution reporting, and has been found to be extremely user-friendly.     

A Simple Allocation Algorithm in Production Planning

A set of practical production planning procedures is outlined, and the algorithmic aspects of the production allocation procedure is presented is some detail. It is suggested that the algorithm's properties of ease of use and speed might make it a candidate for inclusion in more complex planning processes. A formal statement of the logic employed in the algorithm is included as an Appendix.     

On the Use of Pseudo Shadow Prices in a Multiperiod Formulation of the Production Planning Problem

A multiperiod linear programming model of the production planning problem is used to argue for a different costing, profit and resource-evaluation procedure in manufacturing. This procedure is based on the concept of ‘pseudo shadow prices’, and it avoids many of the pitfalls associated with the more traditional accounting methodologies. Conclusions are drawn which question the profit objectives used by many firms, as well as by those in academia.