An optimization model for the aggregate production planning of a Brazilian sugar and ethanol milling company

This work presents an optimization model to support decisions in the aggregate production planning of sugar and ethanol milling companies. The mixed integer programming formulation proposed is based on industrial process selection and production lot-sizing models. The aim is to help the decision makers in selecting the industrial processes used to produce sugar, ethanol and molasses, as well as in determining the quantities of sugarcane crushed, the selection of sugarcane suppliers and sugarcane transport suppliers, and the final product inventory strategy. The planning horizon is the whole sugarcane harvesting season and decisions are taken on a discrete fraction of time. A case study was developed in a Brazilian mill and the results highlight the applicability of the proposed approach.     

Multi-product production planning: A goal programming approach

Cost minimization multi-product production problems with static production resource usage and internal product flow requirements have been solved by linear programming (LP) with input/output analysis. If the problem is complicated by interval resource estimates, interval linear programming (ILP) can be used. The solution of realistic problems by the above method is cumbersome. This paper suggests that linear goal programming (LGP) can be used to model a multi-product production system. LGP's unique modeling capabilities are used to solve a production planning problem with variable resource parameters. Input/output analysis is used to determine the technological coefficients for the goal constraints and is also used to derive an information sub-model that is used to reduce the number of variable resource goal constraints. Preliminary findings suggest that the LGP approach is more cost-efficient (in terms of CPU time) and in addition provides valuable information for aggregate planning.     

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

Production planning (PP) is one of the most important issues carried out in manufacturing environments which seeks efficient planning, scheduling and coordination of all production activities that optimizes the company’s objectives. In this paper, we studied a two-stage real world capacitated production system with lead time and setup decisions in which some parameters such as production costs and customer demand are uncertain. A robust optimization model is developed to formulate the problem in which minimization of the total costs including the setup costs, production costs, labor costs, inventory costs, and workforce changing costs is considered as performance measure. The robust approach is used to reduce the effects of fluctuations of the uncertain parameters with regards to all the possible future scenarios. A mixed-integer programming (MIP) model is developed to formulate the related robust production planning problem. In fact the robust proposed model is presented to generate an initial robust schedule. The performance of this schedule could be improved against of any possible occurrences of uncertain parameters. A case from an Iran refrigerator factory is studied and the characteristics of factory and its products are discussed. The computational results display the robustness and effectiveness of the model and highlight the importance of using robust optimization approach in generating more robust production plans in the uncertain environments. The tradeoff between solution robustness and model robustness is also analyzed.     

Material compatibility constraints for make-to-order production planning

This paper defines a set of material compatibility constraints for use in order promising mixed integer programs. The constraints always represent a necessary condition for compatibility and, in certain cases, are both necessary and sufficient. The underlying analysis represents incompatibilities using bipartite graphs and applies results from the perfectly matchable subgraph polytope.     

A stochastic aggregate production planning model in a green supply chain: Considering flexible lead times,nonlinear purchase and shortage cost functions

In this paper we develop a stochastic programming approach to solve a multi-period multi-product multi-site aggregate production planning problem in a green supply chain for a medium-term planning horizon under the assumption of demand uncertainty. The proposed model has the following features: (i) the majority of supply chain cost parameters are considered; (ii) quantity discounts to encourage the producer to order more from the suppliers in one period, instead of splitting the order into periodical small quantities, are considered; (iii) the interrelationship between lead time and transportation cost is considered, as well as that between lead time and greenhouse gas emission level; (iv) demand uncertainty is assumed to follow a pre-specified distribution function; (v) shortages are penalized by a general multiple breakpoint function, to persuade producers to reduce backorders as much as possible; (vi) some indicators of a green supply chain, such as greenhouse gas emissions and waste management are also incorporated into the model. The proposed model is first a nonlinear mixed integer programming which is converted into a linear one by applying some theoretical and numerical techniques. Due to the convexity of the model, the local solution obtained from linear programming solvers is also the global solution. Finally, a numerical example is presented to demonstrate the validity of the proposed model.     

Linear programming with stochastic processes as parameters as applied to production planning

In formulating stochastic programming with recourse models, the parameters of the linear programs are usually assumed to be random variables with known distributions. In this paper, the requirement vector parameter is assumed to be a stochastic process { _i (t),tT,i=1,...,m}. The properties of the deterministic equivalents for the cases of the discrete and continuous index setT are derived. The results of the paper are applied to a multi-item production planning model with continuous (periodic) review of the stock on hand of various items.     

Solving certain singly constrained convex optimization problems in production planning

This paper considers the problem of minimizing a special convex function subject to one linear constraint. Based upon a theorem for lower and upper bounds on the Lagrange multiplier a fully polynomial time approximation scheme is proposed. The efficiency of the algorithm is demonstrated by a computational experiment.     

Integrated planning of transportation and recycling for multiple plants based on process simulation

By-products accrue in all stages of industrial production networks. Legal requirements, shortening of primary resources and their increasing prices make their recycling more and more important. For the re-integration into the economic cycle the scope of common supply chain management is enlarged and so-called closed-loop supply chains with adapted and new planning tasks are developed. In process industries this requires a detailed modelling of the recycling processes. This is of special relevance for operational planning tasks in which an optimal usage of a given production system is envisaged. This contribution presents an integrated planning approach for a real-world case study from the zinc industry to achieve such an adequate process modelling. We consider the planning problem of a company that operates four metallurgical recycling plants and has to allocate residues from different sources to these recycling sites. The allocation determines the raw material mix used in the plants. This blending has an effect on the transportation costs and the costs and revenues of the individual technical processes in the recycling plants. Therefore in this problem transportation and recycling planning for multiple sites have to be regarded in an integrated way. The necessary detailed process modelling is achieved by the use of a flowsheet process simulation system to model each recycling plant individually. The models are used to derive linear input–output functions by multiple linear regression analyses. These are used in an integrated planning model to calculate the decision-relevant input and output flows that are dependent upon the allocation of the residues to the recycling sites. The model is embedded in a decision support system for the operational use. An example application and sensitivity analyses demonstrate and validate the approach and its potentials. The approach is transferable to other recycling processes as well as to other processes in process industries.     

Industrial petrochemical production planning and expansion: A multi-objective linear programming approach

This paper considers a strategic model planning for the petrochemical industry. It concerns with the expansion in a firm producing multiple products in several regions of a country. The expansion of the existing facilities and the new ones are considered. It also exists a large amount of interdependencies among the firm’s products, because the output of one particular plant can be used as an input to the production of another plant in the same or different regions and to satisfy the final demand. The decision makers involved in the planning process should identify several objectives. Then, multiple objective programming is used for making trade-offs among the economic and operational factors considered. To define the interval criteria weights into the model we utilized the Analytic Hierarchy Process to bring them closer to the decision makers preferences. This work was sponsored by the Institut National Polytechnique de Toulouse, France, when the author was Associate Professor at the Département Génie des Systèmes Industriels.     

Tactical planning of offshore petroleum production

This paper describes a model for tactical planning of Norwegian petroleum production. The problem involves regulation of production levels from wells, splitting of production flows into oil and gas products, further processing of gas and transportation in a pipeline network. Blending and processing of gas is necessary to satisfy quality requirements in the markets. The problem is formulated with multi-component flows, regulation alternatives in production, non-linear splitting for chemical processing and linear quality constraints on composite products. Production and splitting are modelled with integer requirements. The model is implemented in Xpress^MP with a Visual Basic supported user interface in Excel. It is constructed in cooperation with the major Norwegian oil company, Statoil and can identify optimal production patterns and assist in planning of possible shut-downs, demonstrate system robustness to customers and aid in contract negotiations.     

Efficient algorithms for combined heat and power production planning under the deregulated electricity market

Combined heat and power (CHP) production is an important energy production technology that can yield much higher total energy efficiency than separate heat and power generation. In CHP production, the heat and power production follows a joint characteristic, which means that the production planning must be done in coordination. Cost-efficient operation of a CHP system can be planned by using an optimization model. A long-term planning model decomposes into thousands of hourly models. Earlier, in the regulated electric power market, the planning problem was symmetrically driven by heat and power demand. The liberalization of the power market has created an asymmetrical planning problem, where heat production responds to the demand and power production to the volatile market price. In this paper, we utilize this asymmetry to develop novel envelope-based dual algorithms for solving the hourly CHP models efficiently. The basic idea is to transform the three-dimensional characteristic operating region for heat and power production of each CHP plant into a two-dimensional envelope by taking the power price as a parameter. Then the envelopes of each plant are used for looking up the optimal solution rapidly. We propose two versions of the algorithm: the on-line envelope construction algorithm (ECON) where the envelopes are constructed for each hour based on the power price and the off-line envelope construction algorithm (ECOFF) where envelopes are pre-computed for all different power price ranges. We derive the theoretical time complexity of the two algorithms and compare their performance empirically with realistic test models against the ILOG CPLEX solver and the Power Simplex (PS) algorithm. PS is an extremely efficient specialized primal algorithm developed for the symmetrical CHP planning problem under the regulated market. On average, when reusing previous basic solutions, ECON is 603 times faster than CPLEX and 1.3 times faster than PS. ECOFF is 1860 times faster than CPLEX and four times faster than PS.     

Hierarchical production planning and scheduling with random demand and production failure

A multiple-objective hierarchical production planning and scheduling model is developed that integrates aggregate type decisions, family disaggregate decisions, lotsizing and scheduling of the jobs. It is assumed that demand and production failure are subject to uncertainties. Stochastic programming with recourse using a constraint sample approximation method is used to incorporate random demand and production failure into the model. The model evaluates final production plans, updates the demand forecasts and proceeds on a rolling horizon manner. Experimental results show that it is sufficient to generate and incorporate into the aggregate type model a small sample of the stochastic constraints from an infinite set of scenarios. A heuristic scheduling algorithm provides detailed information regarding the progress of jobs through work centers. This information is extremely useful in resolving infeasibilities during the production process. Other features of the model are also reported.     

Service level robustness in stochastic production planning under random machine breakdowns

In this paper, we consider a multi-period, multi-product production planning problem where the production rate and the customer service level are random variables due to machine breakdowns. In order to determine robust production plans, constraints are introduced in the stochastic capacitated lot-sizing problem to ensure that a pre-specified customer service level is met with high probability. The probability of meeting a service level is evaluated by using the first passage time theory of a Wiener process to a boundary. A two-step optimization approach is proposed to solve the developed model. In the first step, the mean-value deterministic model is solved. Then, a method is proposed in the second step to improve the probability of meeting service level. The resulting approach has the advantage of not being a scenario-based one. It is shown that substantial improvements in service level robustness are often possible with minimal increases in expected cost.     

A heuristic approach for big bucket multi-level production planning problems

Multi-level production planning problems in which multiple items compete for the same resources frequently occur in practice, yet remain daunting in their difficulty to solve. In this paper, we propose a heuristic framework that can generate high quality feasible solutions quickly for various kinds of lot-sizing problems. In addition, unlike many other heuristics, it generates high quality lower bounds using strong formulations, and its simple scheme allows it to be easily implemented in the Xpress-Mosel modeling language. Extensive computational results from widely used test sets that include a variety of problems demonstrate the efficiency of the heuristic, particularly for challenging problems.     

Collaborative production planning of supply chain under price and demand uncertainty

This research is motivated by an automobile manufacturing supply chain network. It involves a multi-echelon production system with material supply, component fabrication, manufacturing, and final product distribution activities. We address the production planning issue by considering bill of materials and the trade-offs between inventories, production costs and customer service level. Due to its complexity, an integrated solution framework which combines scatter evolutionary algorithm, fuzzy programming and stochastic chance-constrained programming are combined to jointly take up the issue. We conduct a computational study to evaluate the model. Numerical results using the proposed algorithm confirm the advantage of the integrated planning approach. Compared with other solution methodologies, the supply chain profits from the proposed approach consistently outperform, in some cases up to 13% better. The impacts of uncertainty in demand, material price, and other parameters on the performance of the supply chain are studied through sensitivity analysis. We found the proposed model is effective in developing robust production plans under various market conditions.     

An analytical model for reverse automotive production planning and pricing

Automotive shredders need a reverse production planning strategy that includes determining at what price to purchase vehicle hulks from different sources. In this paper, we formulate the automotive reverse production planning and pricing problem in a nonlinear programming model, develop an approximate supply function for hulks when adjacent shredders price independently, and compare two hulk pricing strategies in three trends for ferrous metal and hulk prices: constant, increasing and decreasing. The case study results indicate that adjusting purchase price based on hulk composition in coordination with planning for purchasing, storing and processing can increase net revenue by 7–15%.     

On the noniterative multiproduct multiperiod production planning method

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.     

A detailed workforce planning model including non-linear dependence of capacity on the size of the staff and cash management

This paper introduces an original planning model which integrates production, human resources and cash management decisions, taking into account the consequences that decisions in one area may have on other areas and allowing all these areas to be coordinated. The most relevant characteristics of the planning problem are: (1) production capacity is a non-linear function of the size of the staff; (2) firing costs may depend on the worker who is fired; (3) working time is managed under a working time account (WTA) scheme, so positive balances must be paid to workers who leave the company; (4) there is a learning period for hired workers; and (5) cash management is included. A mixed integer linear program is designed to solve the problem. Despite the size and complexity of the model, it can be solved in a reasonable time. A numerical example, the main results of a computational experiment and a sensibility analysis illustrate the performance and benefits of the model.     

A polyhedral approach to a production planning problem

Production planning in manufacturing industries is concerned with the determination of the production quantities (lot sizes) of some items over a time horizon, in order to satisfy the demand with minimum cost, subject to some production constraints. In general, production planning problems become harder when different types of constraints are present, such as capacity constraints, minimum lot sizes, changeover times, among others. Models incorporating some of these constraints yield, in general, NP-hard problems. We consider a single-machine, multi-item lot-sizing problem, with those difficult characteristics. There is a natural mixed integer programming formulation for this problem. However, the bounds given by linear relaxation are in general weak, so solving this problem by LP based branch and bound is inefficient. In order to improve the LP bounds, we strengthen the formulation by adding cutting planes. Several families of valid inequalities for the set of feasible solutions are derived, and the corresponding separation problems are addressed. The result is a branch and cut algorithm, which is able to solve some real life instances with 5 items and up to 36 periods. This revised version was published online in June 2006 with corrections to the Cover Date.     

A clone-based graphical modeler and mathematical model generator for optimal production planning in process industries

This paper outlines a visually interactive graphical modeling approach for process type production systems, with hidden generation of complex optimization models for production planning. The proposed system lets the users build a graphical model of the production system with one-to-one clones of its production units through its interactive visual interface, accepts production-specific data for its components, and finally, internally generates and solves its mathematical programming model without any interaction from the user. This “clone-based” modeling approach allows the continued use of optimization models with minimal mathematical programming understanding, as generation of mathematical model by clones is hidden and automatic, therefore maintenance-free: Updating graphical production system models is enough for renewing internal optimization models. The concept is demonstrated in this paper with a linear programming prototype developed for a petroleum refinery.