This paper presents a dynamic production planning and scheduling algorithm for two products processed on one line over a fixed time horizon. Production rates are assumed fixed, and restrictions are placed or inventory levels and production run lengths. The resulting problem is a nonlinear binary program, which is solved using an implicit enumeration strategy. The algorithm focuses on the run changeover period while developing tighter bounds on the length of the upcoming run to improve computational efficiency. About 99% pf 297 randomly generated problems with varying demand patterns are solved in less than 15 seconds of CPU time on a CDC Cyber 172 Computer. A mixed integer programming formulation of the generalized multi-product case under no-backlogging of demand is also given. 相似文献
The main purpose of this paper is to present a crop planning problem for agricultural management under uncertainty. It is significant that agricultural managers assign their limited farmlands to cultivation of which crops in a season. This planning is called the crop planning problem and influences their incomes for the season. Usually, the crop planning problem is formulated as a linear programming problem. But there are many uncertain factors in agricultural problems, so future profits for crops are not certain values. A linear programming model with constant profit coefficients may not reflect the environment of decision making properly. Therefore, we propose a model of crop planning with fuzzy profit coefficients, and an effective solution procedure for the model. Furthermore, we extend this fuzzy model, setting the profit coefficients as discrete randomized fuzzy numbers. We show concrete optimal solutions for each models. 相似文献
The role of optimization is central to economic analysis, particularly in its “neoclassical” phase, since about 1870, and is therefore highly compatible with the impulse behind linear programming (LP), as developed by Dantzig. LP’s stress on alternative activities fits very well with modern economic analysis. The concept of economic equilibrium, properly understood, required the central notion of complementary slackness. so central in LP.
LP was seen as a tool for actual implementation of neoclassical principles precisely at a time when the market was under attack from several directions. The economists Koopmans and Hurwicz played an important role both in stimulating the crucial development of the simplex method and in relating LP to the world of economics.
LP became widely used in national economic planning, particularly for developing countries, and for the study of individual industries, especially the energy sector. The works of Chenery and of Manne are central in these fields.
As respect for the usefulness of the market increased, the emphasis on national planning diminished and was replaced by an emphasis on equilibrium analysis, in which LP still plays a large part in the study of individual sectors, particularly energy. 相似文献
We address a multi-item capacitated lot-sizing problem with setup times and shortage costs that arises in real-world production planning problems. Demand cannot be backlogged, but can be totally or partially lost. The problem is NP-hard. A mixed integer mathematical formulation is presented. Our approach in this paper is to propose some classes of valid inequalities based on a generalization of Miller et al. [A.J. Miller, G.L. Nemhauser, M.W.P. Savelsbergh, On the polyhedral structure of a multi-item production planning model with setup times, Mathematical Programming 94 (2003) 375–405] and Marchand and Wolsey [H. Marchand, L.A. Wolsey, The 0–1 knapsack problem with a single continuous variable, Mathematical Programming 85 (1999) 15–33] results. We also describe fast combinatorial separation algorithms for these new inequalities. We use them in a branch-and-cut framework to solve the problem. Some experimental results showing the effectiveness of the approach are reported. 相似文献
Efficient workforce scheduling has an important impact on store profit and customer service. Standard scheduling problems do not recognize the effect of staff availability on customer sales, however, even though the latter is an important factor in the retail sector. In this paper a two-stage model is proposed for this purpose. In the first stage a sales response model is used to specify hourly staff requirements. The output of the sales response model is then used as the input of a mixed integer optimization model, which finds an optimum assignment of the staff to daily shifts. Simulations are used to validate the sales response function, and to revise the model for more accurate results. In the simulations, customer arrivals and sales response error values are generated using appropriate distribution functions. As a case study the proposed model is applied to a Turkish retailer in the apparel sector. 相似文献
We consider the robust surgery loading problem for a hospital’s operating theatre department, which concerns assigning surgeries and sufficient planned slack to operating room days. The objective is to maximize capacity utilization and minimize the risk of overtime, and thus cancelled patients. This research was performed in collaboration with the Erasmus MC, a large academic hospital in the Netherlands, which has also provided historical data for the experiments. We propose various constructive heuristics and local search methods that use statistical information on surgery durations to exploit the portfolio effect, and thereby to minimize the required slack. We demonstrate that our approach frees a lot of operating room capacity, which may be used to perform additional surgeries. Furthermore, we show that by combining advanced optimization techniques with extensive historical statistical records on surgery durations can significantly improve the operating room department utilization. 相似文献
In a sustained development scenario, it is often the case that an investment is to be made over time in facilities that generate benefits. The benefits result from joint synergies between the facilities expressed as positive utilities specific to some subsets of facilities. As incremental budgets to finance fixed facility costs become available over time, additional facilities can be opened. The question is which facilities should be opened in order to guarantee that the overall benefit return over time is on the highest possible trajectory. This problem is common in situations such as ramping up a communication or transportation network where the facilities are hubs or service stations, or when introducing new technologies such as alternative fuels for cars and the facilities are fueling stations, or when expanding the production capacity with new machines, or when facilities are functions in a developing organization that is forced to make choices of where to invest limited funding. 相似文献
Bahl and Zionts [H.C. Bahl, S. Zionts, A noniterative multiproduct multiperiod production planning method, Operations Research Letters 1 (1982) 219-221] formulated a problem for planning multiproduct multiperiod production on a single facility. They developed a column-minima noniterative method and claimed that it gave an optimal solution. We show that the claim is incorrect. 相似文献