Master production scheduling make-to-stock products: a framework for analysis

Excessive changes in MRP system schedules, commonly referred to as 'nervousness’, is frequently an obstacle in implementing an effective MRP based manufacturing planning and control system. This paper is concerned with the design of methods for freezing the master production schedule (MPS) as a way of controlling MPS stability under rolling planning conditions for make-to-stock products. It presents a framework for the design of MPS freezing methods and compares their performance when the design parameters of these methods are varied. Simulation experiments are reported that demonstrate important differences in performance considering criteria involving both the cost of lot-sizing the MPS and the stability of the master production schedule.     

SMT production scheduling: a generalized transportation approach

A generalized transportation model is first formulated for the scheduling of Surface Mount Technology (SMT) production. Its dual form is next discussed. By specially coding the SMT scheduling problem, it is unnecessary to develop the constraint matrix for the dual. The simplex method is not applicable for this problem due to its sparse data structure. An efficient algorithm for the dual model is then developed from the idea of the revised simplex method. To illustrate the algorithm, a numeric example is presented.     

Parallel machine scheduling with tool loading: a constraint programming approach

This paper presents constraint programming models that aim to solve scheduling and tool assignment problems in parallel machine environments. There are a number of jobs to be processed on parallel machines. Each job requires a set of tools, but limited number of tools are available in the system due to economic restrictions. The problem is to assign the jobs and the required tools to machines and to determine the schedule so that the makespan is minimised. Three constraint programming models are developed and compared with existing methods described in the literature.     

Production scheduling in a market-driven foundry: a mathematical programming approach versus a project scheduling metaheuristic algorithm

This paper describes a real problem in a market-driven medium sized foundry delivering a wide range of castings to different markets. The problem consists of finding an efficient production plan to schedule the different processes (moulding, furnacing, cutting, tooling, etc.) needed to the manufacture of the pieces. Different objectives and resources and technical constraints must be taken into account. To solve this problem we have first developed a more classical integer linear programming approach based on a rolling horizon strategy. The most innovative contribution of the paper is that it models the problem as a project scheduling problem. Based on this model we present a metaheuristic algorithm that adapts techniques from the area. Computational experiments comparing both approaches are provided on instances created by a generator simulating real instances.     

Master production scheduling in capacitated sequence-dependent process industries

Traditional approaches to planning and control of manufacturing (MRPII) focus on discrete parts manufacturing industries (e.g. automotive). The chemical industry, however, presents unique challenges. Cross-contamination of production is a key issue among some chemical facilities. A considerable amount of capacity is lost as a result of changeovers which involve performing thorough clean-ups to wash away the impurities which may contaminate the next product to be produced. Therefore, planning for sequence-dependent changeovers becomes crucial and complicates the master production scheduling process. This paper shows how improved master production scheduling performance can be obtained by using a two-level master production schedule (MPS) to focus on key plant processes, and by incorporating a scheduling heuristic which considers sequence-dependent changeovers and capacity constraints. This approach is illustrated using actual operating data from a chemical firm typical of many process industry operations. Simulation experiments are reported that test the performance of the proposed master scheduling method in a single-stage sequence-dependent process. The experimental factors include both the introduction of the two-level MPS with the scheduling heuristic, and the effect of changes in the MPS batch size. The results demonstrate that important simultaneous improvements in process changeover time and delivery performance can be achieved using the proposed MPS scheduling approach against a more traditional (single-level) MPS approach which does not consider sequence-dependent changeovers. Further, we find that delivery performance is relatively insensitive to adjustments in the MPS batch size when using the two-level MPS approach.     

Value function approximation via linear programming for FMS scheduling

In this paper, we develop a linear programming framework for computing a quadratic approximation to the value function, which constitutes the off-line computation of a hierarchical FMS scheduling approach previously developed by us. In contrast to previous work, where relatively crude value functions were used, we develop a quadratic approximation that is a prior fit. We consider the multiple part multiple machine discounted cost case and illustrate the approach via a simulation example in the context of an industrial setting.     

Dynamic programming approach to the bilateral contract scheduling

Bilateral forward contracts are generally used in electricity markets to stabilise prices and hedge electricity shortage risks. A contract party is able to draw electricity from the contract and resell it to the dayahead wholesale and retail markets. Contract parties schedule electricity deliveries over contract period to obtain the highest profit and estimate the acceptable contract price. Two types of contracts are introduced as a way to coordinate interests of the contract parties. The study formulates optimisation problems for contract scheduling. The stochastic dynamic programming technique is proposed as a numerical method for the problem solving. An algorithm based on preliminary construction of revenue functions is developed. A numerical example demonstrates the efficiency of the algorithm.     

An integer programming approach to elective surgery scheduling

The scope of this work covers a real case of elective surgery planning in a Lisbon hospital. The aim is to employ more efficiently the resources installed in the surgical suite of the hospital in question besides improving the functioning of its surgical service. Such a planning sets out to schedule elective surgeries from the waiting list on a weekly time horizon with the objective of maximizing the use of the surgical suite. For this purpose, the authors develop an integer linear programming model. The model is tested using real data obtained from the hospital’s record. The non-optimal solutions are further improved by developing a custom-made, simple and efficient improvement heuristic. Application of this heuristic effectively improves almost all non-optimal solutions. The results are analyzed and compared with the actual performance of the surgical suite. This analysis reveals that the solutions obtained using this approach comply with the conditions imposed by the hospital and improve the use of the surgical suite. It also shows that in this case study the plans obtained from the proposed approach may be implemented in real life.     

Energetic reasoning and mixed-integer linear programming for scheduling with a continuous resource and linear efficiency functions

This paper addresses a scheduling problem with a continuously divisible, cumulative and renewable resource with limited capacity. During its processing, each task consumes a part of this resource, which lies between a minimum and a maximum requirement. A task is finished when a certain amount of energy is received by it within its time window. This energy is received via the resource and an amount of resource is converted into an amount of energy with a non-decreasing and continuous function. The goal is to find a feasible schedule, which is already NP-complete, and then to minimize the resource consumption. For the case where all functions are linear, we present two new mixed-integer linear programs (MILP), as well as improvements of an existing formulation. We also present a detailed version of the adaptation of the well-known “left-shift/right-shift” satisfiability test for the cumulative constraint and the associated time-window adjustments to our problem. For this test, three ways of computing relevant intervals are described. Finally, a hybrid branch-and-bound using both the satisfiability test and the MILP is presented with a new heuristic for choosing the variable on which the branching is done. Computational experiments on randomly generated instances are reported in order to compare all of these solution methods.     

Optimal design of stochastic production lines: a dynamic programming approach

We consider the problem of choosing the number and type of machines for each station in a new production line where the sequence of processes (i.e., manufacturing recipe) has already been established. We formulate a model to minimize cost (investment plus operating) subject to constraints on throughput and cycle time. Using queueing network approximations within a dynamic programming framework, we develop a line design algorithm that works in station-wise fashion. For computational tractability, we must discretize a continuous state space. However, we are able to compute bounds on the error in the cost function as a guide to the appropriate choice of grid size. We conclude by applying our algorithm to an industrial problem that motivated this work.     

A mixed-integer linear programming model for integrated production and preventive maintenance scheduling in the capital goods industry

The scheduling literature is extensive, but much of this work is theoretical and does not capture the complexity of real world systems. Capital goods companies produce products with deep and complex product structures, each of which requires the coordination of jobbing, batch, flow and assembly processes. Many components require numerous operations on multiple machines. Integrated scheduling problems simultaneously consider two or more simultaneous decisions. Previous production scheduling research in the capital goods industry has neglected maintenance scheduling and used metaheuristics with stochastic search that cannot guarantee an optimal solution. This paper presents a novel mixed integer linear programming model for simultaneously solving the integrated production and preventive maintenance scheduling problem in the capital goods industry, which was tested using data from a collaborating company. The objective was to minimise total costs including: tardiness and earliness penalty costs; component and assembly holding costs; preventive maintenance costs; and set-up, production, transfer and production idle time costs. Thus, the objective function and problem formulation were more extensive than previous research. The tool was successfully tested using data obtained from a collaborating company. It was found that the company’s total cost could be reduced by up to 63.5%.     

A linear programming approach to capacity estimation of automated production lines with finite buffers

This paper considers a highly automated manufacturing line which consists of a sequence of workstations. Relatively small buffers are assigned between workstations in order to guarantee a small manufacturing interval and quick feedback in the event of process failure to make acceptable product. These small buffers could lead to a noticeable loss of line capacity due to the phenomenon of blocking and starvation. We show by means of simple examples how the buffer sizes and the mix and loading sequence of different types of jobs could significantly affect the production rate of the line. A linear programming based method is then developed to estimate the line capacity for a given configuration of machines and buffers sizes and for a given job mix and sequence. This method also gives the expected machine utilizations, the time machines are blocked/starved and, more importantly, the reason for this lost production capacity. By judiciously interpreting this information, one or more of the following steps can be taken to improve the production rate: (a) change the loading sequence, (b) increase the buffer space selectively, (c) make the products in smaller or larger batches, and (d) add new machines.     

An implementation of a decomposition-coordination approach to refinery production scheduling

This paper presents an implementation of a decomposition-coordination approach to petroleum refinery production scheduling. In this approach the scheduling problem is not formulated as a single mathematical programming model to be solved through a computerized system, but it is dealt with as a mathematical programming process, in which a number of small problems are practically solved, and their solutions are combined into an overall schedule Our approach does not pursue an exact optimum, but quite satisfactory schedules have been generated from a practical viewpoint and productivity in the scheduling process has been remarkably raised

An interactive computerized scheduling system has been tailored using a commercial MPS and its Extended Control Language (ECL). The man-hours required for making a final schedule has been reduced to one-third as compared with the previous way     

A Bayesian stochastic programming approach to an employee scheduling problem

Bayesian forecasting models provide distributional estimates for random parameters, and relative to classical schemes, have the advantage that they can rapidly capture changes in nonstationary systems using limited historical data. Unlike deterministic optimization, stochastic programs explicitly incorporate distributions for random parameters in the model formulation, and thus have the advantage that the resulting solutions more fully hedge against future contingencies. In this paper, we exploit the strengths of Bayesian prediction and stochastic programming in a rolling-horizon approach that can be applied to solve real-world problems. We illustrate the methodology on an employee production scheduling problem with uncertain up-times of manufacturing equipment and uncertain production rates. Computational results indicate the value of our approach.     

Topology optimization of tensegrity structures under compliance constraint: a mixed integer linear programming approach

A tensegrity structure is a prestressed pin-jointed structure consisting of discontinuous struts and continuous cables. For exploring new configurations of tensegrity structures, this paper addresses a topology optimization problem of tensegrity structures under the compliance constraint and the stress constraints. It is assumed that a cable loosens and loses the elongation stiffness when its tensile prestress vanishes due to the applied external load. It is shown that the topology optimization problem can be formulated as a mixed integer linear programming (MILP) problem. The proposed method does not require any connectivity information of cables and struts to be known in advance. Numerical experiments illustrate that various configurations of tensegrity structures can be found as the optimal solutions.     

Duality in fuzzy linear programming: a survey

The concepts of both duality and fuzzy uncertainty in linear programming have been theoretically analyzed and comprehensively and practically applied in an abundance of cases. Consequently, their joint application is highly appealing for both scholars and practitioners. However, the literature contributions on duality in fuzzy linear programming (FLP) are neither complete nor consistent. For example, there are no consistent concepts of weak duality and strong duality. The contributions of this survey are (1) to provide the first comprehensive overview of literature results on duality in FLP, (2) to analyze these results in terms of research gaps in FLP duality theory, and (3) to show avenues for further research. We systematically analyze duality in fuzzy linear programming along potential fuzzifications of linear programs (fuzzy classes) and along fuzzy order operators. Our results show that research on FLP duality is fragmented along both dimensions; more specifically, duality approaches and related results vary in terms of homogeneity, completeness, consistency with crisp duality, and complexity. Fuzzy linear programming is still far away from a unifying theory as we know it from crisp linear programming. We suggest further research directions, including the suggestion of comprehensive duality theories for specific fuzzy classes while dispensing with restrictive mathematical assumptions, the development of consistent duality theories for specific fuzzy order operators, and the proposition of a unifying fuzzy duality theory.     

Fleet sizing of automated guided vehicles: a linear programming approach based on closed queuing networks

We use multi-class closed queuing networks to model operations of automated guided vehicles in a manufacturing or distribution environment. We approximate the dynamics of the system using the first moment balance equations of the embedded stochastic chain representing the network under the steady-state conditions. These moments account for loaded and empty-travel times, as well as times when vehicles are being loaded/unloaded or waiting to be dispatched. We model the steady-state behaviour of the closed queuing network by a linear program whose optimal value is the estimate of the required fleet-size. The result of the analytical model is compared with those of the simulation studies for a set of numerical examples. The comparison shows that the analytical model provides a good estimate for the required number of vehicles.     

MOAPPS 1.0: Aggregate production planning using the multiple-objective tabu search

In recent years, there has been a trend in the research community to solve large-scale complex planning and design problems using the modern heuristics optimization techniques (i.e. tabu search, genetic algorithms, etc.). This is mainly due to unsuitability of the classical solution techniques in many circumstances. Depending upon the assumptions made and the modelling approach used, aggregate production planning (APP) problems can be quite complex and large scale. Therefore, there is a need to investigate the suitability of modern heuristics for their solution. In this paper, the multiple-objective APP problem is formulated as a pre-emptive goal-programming model and solved by a specially developed multiple-objective tabu search algorithm. The mathematical formulation is built upon Masud and Hwang's model (original model) due to its extensibility characteristics. The present model extents their model by including subcontracting and setup decisions. The multiple-objective tabu search algorithm is applied to both the original and extended model. Results obtained from the solution of the original model are then compared. It is observed that the multiple-objective tabu search algorithm can be used as an alternative solution mechanism for solving APP problems. During this study, an object-oriented program is also developed using C++. This software is named as MOAPPS 1.0 (Multiple Objective Aggregate Production Planning Software).     

Master production scheduling,customer service and manufacturing flexibility in an assemble-to-order environment

A key element of manufacturing planning and control involves the inter-functional coordination of various manufacturing requirements. This paper reports the results of a simulation experiment that compares alternative master production scheduling (MPS) procedures in an assemble-to-order environment. The MPS procedures are superbills and covering sets. For a given investment in safety stocks the managerial problem is how to construct the MPS in order to minimize the firm's delivery time pressures. The results of the simulation experiment strongly support the use of the superbill techniques over the covering set technique. Moreover, of the experimental factors that influence delivery time performance, the choice of master production scheduling technique has the largest effect. Demand variability has the next greatest effect on delivery time performance. The safely stock level has the third greatest effect and product commonality was fourth. Finally, the managerial implications of the results are discussed in detail.     

Theory of constraints and linear programming: a comparison

Since initial work done by Goldratt in the mid-1980s and as the concepts related to the theory of constraints (TOC) have become more developed, many have concluded that the TOC approach offers nothing in addition to what can be accomplished through linear programming (LP). Through the use of an example, this paper compares TOC to LP and clarifies the differences surrounding the TOC philosophy and the LP technique