A linear programming model for integrated steel production and distribution planning

This study developed an extended stochastic programming model for the deterministic approach proposed by Chen, Chen and Liou [1]. Capacity planning, which plays a role in production planning, is a challenging problem for the semiconductor manufacturing industry. This study dealt with the uncertain demands of customers for a foundry industry in Taiwan. Through three scenarios, the stochastic programming model was exploited to solve the optimal medium-term capacity planning problem. The data collected from a real wafer foundry in Taiwan were treated as a fundamental scenario to demonstrate the value of the proposed stochastic programming model. The forecast demand variations in other scenarios complied with a normal distribution. The effect of the different probability distributions of demand scenarios on capacity allocation was considered. Changes in the customer order fulfillment rate or capacity utilization rate were analyzed from a series of capacity planning tests with varying demands of the initial customer. Based on different demand scenarios, the numerical results in this study revealed the concordance between the deterministic model and the proposed stochastic programming model. This stochastic programming model also expressed the flexible consideration of auxiliary tools and the increasing number of certified fabrication to the capacity planning problem in the wafer foundry.

The aim of every manufacturing organization is to fulfil the demand of their customers at minimum total cost or at maximum profit. To fulfil the demand of geographically dispersed customers, manufacturing organizations need to produce products at multiple manufacturing sites located close to the customer. Although planning function in such a scenario becomes very complex, this multi-site environment has been found to improve efficiency and provide better services to customers. It involves interlinked decisions involving procurement, production and distribution at different plants and distribution sites. Production and distribution planning are very important aspects of planning in multi-site manufacturing. To compete in this globalized market, enterprises should focus on optimizing and integrating production and distribution functions simultaneously. The authors in the research work present an integrated production and distribution planning problem for a two-level supply chain consisting of multiple manufacturing sites serving multiple selling locations. The problem is formulated as a multi-objective mixed-integer programming model considering three important aspects of production and distribution planning, viz. set-up, backorder and transportation capacity. Total cost, delivery time and backlog level are the three conflicting objectives that need to be minimized. The proposed multi-objective mathematical problem is solved using pre-emptive goal programming method. The performance of the proposed model is illustrated through an example problem instance. Further analysis is conducted to visualize the effect of changing priority level on objective function and deviation variable values.

Production planning and control is an absolute must for companies that produce goods or services. This is considered very important because it is the core of the entire production process. Every company may not carry out a production activity if it does not conduct production planning and control activities. Production plan at PT. Krakatau Wajatama on capacity planning and production of profile steel products requires a production plan based on demand that might come so that it needs an appropriate plan so that there is no overproduction. Therefore, integration between production plans and capacity plans needs to be done in order to obtain a realistic production plan. The method used is forecasting, capacity planning using RCCP can be done with the conversion process of the Production Plan or MPS based on order requests in bales in the period January 2019 to December 2019 into the time requirement of the production machine. Estimated results of 2019 demand for profile steel production are IWF-Flange, U-Chanal, L-Angels. In January 2019 it was 250836,713 minutes, February 2019 was 225731.5425 minutes, March 2019, and for IWF-Flange, U-Chanal, L-Angels products. In January 2019 it was 298080 minutes, February 2019 was 259200 minutes, March 2019 was 298080 minutes. company capacity planning needs on profile steel products namely IWF-Flange, U-Chanal, L-Angels using machine capacity that is used multiplied by hours per shift at times of shifts per day multiplied by workdays per period by converting production plans or MPS into capacity by using the RCCP concept with the Capacity Planning Using Overall Factors (CPOF) method.

Chapter 8 Mathematical programming models and methods for production planning and scheduling

Robust production planning and capacity control for flexible assembly lines

This paper proposes an integrated approach for optimizing production, inventory and distribution in a multi-period, multi-item and less-than-truckload configuration. The value of coordinating production with distribution is investigated. The objective is to minimize the sum of setup production costs, holding costs and distribution costs on the planning horizon. An iterative approach is developed for this NP-hard problem. A first production plan is obtained using integer linear programming and the distribution plan (set of vehicle trips in each period) is built using a tabu search metaheuristic that does not change the production plan. In the following iteration, an improved production plan is first determined considering the distribution plan of the previous interation as a constraint. Then, a new distribution plan is computed given the new production plan. This iterative process stops when the two plans become stable. The iterative method is evaluated on a set of randomly generated instances. The impact of various parameters are evaluated. A comparison with a classical two-phase method shows significant savings ranging from 3.50% to 27.73%. These results underline the relevance of integrating distribution and production planning decisions.

Production plans based on Material Requirement Planning (MRP) frequently fall short in reflecting actual customer demand and coping with demand fluctuations, mainly due to the rising complexity of the production environment and the challenge of making precise predictions. At the same time, MRP is deficient in effective adjustment strategies and has inadequate operability in plan optimization. To address material management challenges in a volatile supply-demand environment, this paper creates a make-to-stock (MTS) material production planning model that is based on customer demand and the demand-driven production planning and control framework. The objective of the model is to optimize material planning output under resource constraints (capacity and storage space constraints) to meet the fluctuating demand of customers. To solve constrained optimization problems, the demand-driven material requirements planning (DDMRP) management concept is integrated with the grey wolf optimization (GWO) algorithm and proposed the DDMRP-GWO algorithm. The proposed DDMRP-GWO algorithm is used to optimize the inventory levels, shortage rates, and production line capacity utilization simultaneously. To validate the effectiveness of the proposed approach, two sets of customer demand data with different levels of volatility are used in experiments. The results demonstrate that the DDMRP-GWO algorithm can optimize the production capacity allocation of different types of parts under the resource constraints, enhance the material supply level, reduce the shortage rate, and maintain a stable production process.

Decision making has become a part of our everyday lives. The main apprehension is that almost all decision difficulties include certain criteria, which usually can be multiple or conflicting. Certainly, the production planning and production capacity development includes several parameters uncertainty such as fuzzy resource capacity, fuzzy demand and fuzzy production rate. This situation makes decision maker challenging to describe the objective crisply and at the end the real optimum solution cannot attained correctly. The Fuzzy model for multi-objective linear programming should be an suitable approach for dealing with the production planning and production capacity (PP& PC) problems. The PP& PC problem based on the fuzzy environment becomes even more sophisticated as decision makers try to consider multi-objectives, Therefore, this study attempts to propose a novel scheme which is capable of dealing with these obstacles in PP& PC problem. Intuitionistic Fuzzy Optimization (1FO) by implementing the optimization problem in an Intuitionistic Fuzzy Set (IFS) environment and considered the degrees of rejection of objective(s) and of constraints as the complement of satisfaction degrees. The aim of the research is to propose a new method capable of dealing with these obstacles in the PP & PC problem. It takes into account uncertainty and makes trade-offs between multiple conflicting goals simultaneously. To verify the validity of the proposed method, a case study of the fuzzy multi-objective model of the PP&PC is used. This research takes into account uncertainty and makes a comparison between multiple conflicting goals at the same time. Therefore, this study attempts to propose a new scheme which is the modified Angelov’s approach.

A robust optimization model for multi-product two-stage capacitated production planning under uncertainty

A mathematical programming model is reported that can be used to support a key decision associated with production planning and control of surface mount technology production lines in certain environments. After a brief introduction on the nature of surface mount technology products and processes, a hierarchical view of surface mount technology production planning and control is presented, which in turn is used to organize a brief review of other published work on surface mount technology optimization. Following this, a mathematical programming model to support the making of decisions at one of the levels in the hierarchy, that concerned with allocating production lots to surface mount technology lines, is described in detail. Example results from using the model are given as well as conclusions about its value and future extensions.

Sustainable Optimization of Agricultural Production

Stochastic programming models have been proposed for capacity planning problems in different environments, including energy, telecommunication networks, distribution networks, and manufacturing systems. In this chapter we give an introductory tutorial to stochastic linear programming models, with emphasis on modeling techniques, rather than specialized solution methods. We consider two-stage and multi-stage stochastic programming models with recourse for manufacturing related applications, such as production planning and capacity planning with uncertainty on demand. We stress the importance of proper model formulation from two points of view: the first one is building strong mixed-integer formulations; the second one is generating scenario trees in order to suitably represent uncertainty while keeping them to a manageable size. We also compare the stochastic programming approach to traditional dynamic programming and to robust optimization.

A mathematical programming approach to optimize process plant performance subject to equipment failure is presented. The optimal production planning and scheduling in multipurpose process plants involves the efficient utilization of assets and resources to produce a number of products so as to satisfy market demands while optimizing a performance criterion. However, the degree of utilization of process plant components, within the time horizon of operation, critically depends on the level of equipment availability. The interactions between production and maintenance planning as well as the necessary links to quantify the strong interactions between them are studied. The preventive maintenance planning and crew allocation problem are used to demonstrate the effectiveness of the proposed approach. The overall problem is first formulated as an optimal control problem by integrating an aggregate production planning model with a continuous time Markov chain maintenance model. The resulting problem is then transformed into a mixed-integer linear programming model by using an Euler discretization scheme and appropriate linearizations of bilinear terms. Finally, extensions to include design aspects are also discussed. The applicability of the proposed approach is demonstrated by a number of illustrative examples.

A flexible production planning for rolling-horizons

We develop a decision support system in Microsoft Excel that integrates production and distribution for a manufacturer of natural fiber-based products in North America. The production and distribution of the company’s products were optimized using a linear programming model, implemented in Excel. The spreadsheet dynamically adjusts the formulation to reflect the user’s current requirements, solves the optimization model in the background, and generates detailed managerial reports. In addition, it allows users to conduct what-if analyses by varying the number of plants and warehouses. It demonstrates the ability of a Linear Programming Model run on an Excel platform to provide the firm with an optimized production plan resulting in significant, cost savings since implementation.