Alternative configurations for cutting machines in a tube cutting mill

In a steel tube mill where an endless stream of steel tube is supplied from a manufacturing facility, trim waste is never made regardless of cutting patterns used and the standard cutting stock problem seems meaningless. Therefore, the continuous stock cutting problem with setup is introduced to minimize the sum of cutting time and pattern changing time to meet the given demand. We propose a new configuration of cutting machines to achieve higher production efficiency, namely the open-ended configuration as opposed to the traditional closed-ended configuration, thereby two variants of the problem are defined. We propose linear formulations for both problems using binary expansion of the number of pieces of different types in a pattern. Furthermore, we define the time for pattern change as a linear function of the number of knives used in the pattern to be more realistic. Computational studies suggest that the open-ended cutting machine may improve the production time by up to 44% and that our linear formulations are more efficient than the existing ones.     

Optimale Produktionsplanung bei Frischprodukten mit dem Programm FORTUNA — Eine Fallstudie

The production rate of perishable goods depends heavily on the actual stock level and the daily demand. Production planning is therefore short-term. The production of curd (cottage cheese), with which the case study deals, is a typical example. When the daily production process is started, the demand is still unknown. When planning is non-computerized, this causes considerable fluctuations in the stock level and increases the danger of perishing. It also necessitates an over capacity for production to maintain a high level of service. The computer software package FORTUNA is a result of this problem being studied. It is based on a Markovian decision process of the type of a AHM-Inventory Production model. The computer program makes forecasts of the daily demand, computes optimal decision rules for short-term tuning of the daily production rate and produces weekly or monthly labour schedules. The second part of this paper contains the application of FORTUNA in a dairy. It reports about the analysis of the demand pattern, the identification of the parameters of the cost structure, the performance criteria of non-monetary goals, the comparison with manual planning and the long term effects.     

An integer programming approach to short-term production scheduling in a tobacco plant

In this paper, a mathematical model is developed that facilitates daily production scheduling in a tobacco processing plant. The implied objectives are to meet specific horizon production targets (obtained from a master production schedule), to maintain safety stock requirements and to ensure that the demand for labour lies within given limits. The express objective is to minimise the number of machines used in the production process. Additionally, the model incorporates work-in-progress, aspects of the demand for product transportation within the plant and machine capacity (utilisation) reduction effects associated with production sequencing. These aspects are relevant when dealing with time intervals as small as a day but can be averaged out when dealing with monthly time intervals. The developments in this paper represents stage II of the modelling of the tobacco plant, where stage I (already completed) was centred on obtaining a monthly master production schedule for a year ahead and assisting in macro planning activities. This paper also sees the development of a simple user-friendly heuristic which facilitates production sequencing on a daily basis given the master production schedule obtained from Stage I.     

Hierarchical Stochastic Production Planning with Delay Interaction

This paper explores the problem of hierarchical stochastic production planning (HSPP) for flexible automated workshops (FAWs), each consisting of a number of flexible manufacturing systems (FMSs). The objective is to devise a production plan which tells each FMS how many parts to produce and when to produce them so as to simultaneously minimize the amount of work in progress, maximize the machine utilization, and satisfy demands for finished products over a finite horizon of N time periods. Here, the problem formulation includes not only uncertainty in demand, capacities, and material supply (which is standard in the literature), but also uncertainties in processing times, rework, and waste products. It considers also multiple products and multiple time periods. This is in contrast to most work which looks at either a single periods or at an infinite horizon. The delay interaction aspect arises from taking into account the transportation of parts between FMSs. Apparently, any job which requires processing on more than one FMS cannot be transported directly from one FMS to the next. Instead, a semifinished product completed in one period must be put into shop storage until some future time period at which it can be transported to the next FMS for further processing. Herein, a stochastic interaction/prediction algorithm is developed by using standard calculus of variations techniques. By means of the software package developed, many HSPP examples have been studied, showing that the algorithm is very effective.     

Inventory decisions for a finite horizon problem with product substitution options and time varying demand

The inventory control of substitutable products has been recognized as a problem worthy of study in the operations management literature. Product substitution provides flexibility in supply chain management and enhances response time in production control. This paper proposes a finite horizon inventory control problem for two substitutable products, which are ordered jointly in each replenishment epoch. Demand for the products are assumed to be time–varying. In case of a stock–out for one of the products, its demand is satisfied by using the stock of the other product. The optimal ordering schedule, for both products, that minimizes the total cost over a finite planning horizon is derived. Numerical examples along with sensitivity analyses are also presented.     

Joint effect of stock threshold level and production policy on an unreliable production environment

In this article we develop an economic manufacturing quantity (EMQ) model subject to stochastic machine breakdown, repair and stock threshold level (STL). Instead of constant production rate, in this model production rate is considered as a decision variable. Since, the stress of the machine depends on the production rate, failure rate of the machine will be a function of the production rate. Again, in this article consideration of safety stock in all existing literature is replaced by the concept of stock threshold level (STL). Further, extra capacity of the machine is considered to buffer against the possible uncertainties of the production process where machine capacity is predetermined. The basic model is developed under general failure and general repair time distributions. Since, the assumption of variable production rate makes the objective function quite complex, so main emphasis is given on computational methodology to solve the present problem. We suggest two computational algorithms for the determination of production rate and stock threshold level which minimize the expected cost rate in the steady state. Finally, through numerical examples we illustrate the key insights of our model from managerial point of view.     

A Two-product,Single-machine,Storage-constrained Production Problem

This paper considers a two-product, single-machine production scheduling problem where there is an added constraint on the amount of finished stock that can be held. The need for a ratio of the cycle times of the two products is a feature both of two-product production scheduling problems contained on one machine and two-product inventory problems with constraints on storage capacity. This means an easy solution algorithm is possible for the problem addressed in the paper which has both types of constraints.     

Determining a common production cycle time for an economic lot scheduling problem with deteriorating items

This paper considers the economic lot scheduling problem (ELSP) for a production-inventory system where items produced are subject to continuous deterioration. The problem is to schedule multiple products to be manufactured on a single machine repetitively over an infinite planning horizon. Each product is assumed to have a significant rate of deterioration. Only one product can be manufactured at a time. The demand rate for each product is constant, but an exponential distribution is used to represent the distribution of the time to deterioration. A common cycle time policy is assumed in the production process. A near optimal production cycle time is derived under conditions of continuous review, deterministic demand, and no shortage.     

An iterative sequential heuristic procedure to a real-life 1.5-dimensional cutting stock problem

This paper addresses a real-life 1.5D cutting stock problem, which arises in a make-to-order plastic company. The problem is to choose a subset from the set of stock rectangles to be used for cutting into a number of smaller rectangular pieces so as to minimize total production cost and meet orders. The total production cost includes not only material wastage, as in traditional cutting stock problems, but also production time. A variety of factors are taken into account, like cutter knife changes, machine restrictions, due dates and other work in progress limitations. These restrictions make the combinatorial structure of the problem more complex. As a result, existing algorithms and mathematical models are no longer appropriate. Thus we developed a new 1.5D cutting stock model with multiple objectives and multi-constraints and solve this problem in an incomplete enumerative way. The computational results show that the solution procedure is easy to implement and works very well.     

Optimal production plans and shipment schedules in a supply-chain system with multiple suppliers and multiple buyers

This research addresses an optimal policy for production and procurement in a supply-chain system with multiple non-competing suppliers, a manufacturer and multiple non-identical buyers. The manufacturer procures raw materials from suppliers, converts them to finished products and ships the products to each buyer at a fixed-interval of time over a finite planning horizon. The demand of finished product is given by buyers and the shipment size to each buyer is fixed. The problem is to determine the production start time, the initial and ending inventory, the cycle beginning and ending time, the number of orders of raw materials in each cycle, and the number of cycles for a finite planning horizon so as to minimize the system cost. A surrogate network representation of the problem developed to obtain an efficient, optimal solution to determine the production cycle and cycle costs with predetermined shipment schedules in the planning horizon. This research prescribes optimal policies for a multi-stage production and procurements for all shipments scheduled over the planning horizon. Numerical examples are also provided to illustrate the system.     

Hierarchical Production Control in Dynamic Stochastic Jobshops with Long-Run Average Cost

We consider a production planning problem for a dynamic jobshop producing a number of products and subject to breakdown and repair of machines. The machine capacities are assumed to be finite-state Markov chains. As the rates of change of the machine states approach infinity, an asymptotic analysis of this stochastic manufacturing systems is given. The analysis results in a limiting problem in which the stochastic machine availability is replaced by its equilibrium mean availability. The long-run average cost for the original problem is shown to converge to the long-run average cost of the limiting problem. The convergence rate of the long-run average cost for the original problem to that of the limiting problem together with an error estimate for the constructed asymptotic optimal control is established.     

Joint determination of optimal safety stocks and production policy for an imperfect production system

In this article, we develop an imperfect economic manufacturing quantity (EMQ) model for an unreliable production system subject to process deterioration, machine breakdown and repair and buffer stock. The basic model is developed under general process shift, machine breakdown and repair time distributions. We suggest a computational algorithm for determination of the optimal safety stock and production run time which minimize the expected cost per unit time in the steady state. For a numerical example, we illustrate the outcome of the proposed model and perform a sensitivity analysis with respect to the model-parameters which have direct influence on the optimal decisions.     

Mixed integer programming for scheduling flexible flow lines with limited intermediate buffers

This paper presents new mixed integer programming formulations for scheduling of a flexible flow line with blocking. The flexible flow line consists of several processing stages in series, separated by finite intermediate buffers, where each stage has one or more identical parallel machines. The line produces several different product types and each product must be processed by, at most, one machine in each stage. A product which has completed processing on a machine may remain there and block the machine until a downstream machine becomes available for processing. The objective is to determine a production schedule for all products so as to complete the products in a minimum time. The basic mixed integer programming formulations have been enhanced to model blocking scheduling with alternative processing routes where for each product a set of routes is available for processing. A reentrant flow line where a product visits a set of stages more than once is also considered. Numerical examples are presented to illustrate applications of the various models proposed.     

The Application of Preprocessing and Cutting Plane Techniques for a Class of Production Planning Problems

This paper investigates properties of integer programming models for a class of production planning problems. The models are developed within a decision support system to advise a sales team of the products on which to focus their efforts in gaining new orders in the short term. The products generally require processing on several manufacturing cells and involve precedence relationships. The cells are already (partially) committed with products for stock and to satisfy existing orders and therefore only the residual capacities of each cell in each time period of the planning horizon are considered. The determination of production recommendations to the sales team that make use of residual capacities is a nontrivial optimization problem. Solving such models is computationally demanding and techniques for speeding up solution times are highly desirable. An integer programming model is developed and various preprocessing techniques are investigated and evaluated. In addition, a number of cutting plane approaches have been applied. The performance of these approaches which are both general and application specific is examined.     

Solving a bi-criterion cutting stock problem with open-ended demand: a case study

We consider a real-life cutting stock problem with two types of orders. All orders have to be cut from a given number of raws (also known as stock unit, master reel or jumbo). For each order the width of the final (also known as reels or units) and the number of finals is given. An order is called an exact order when the given number of finals must be produced exactly. An order is called an open order when at least the given number of finals must be produced. There is a given maximum on the number of finals that can be produced from a single raw which is determined by the number of knives on the machine. A pattern specifies the number of finals of a given width that will be produced from one raw. A solution consists of specifying a pattern for each raw such that in total the number of finals of exact orders is produced exactly and at least the number of finals of open orders is produced. There are two criteria defined for a solution. One criterion is the cutting loss: the total width of the raws minus the total width of the produced finals. The second criterion is the number of different patterns used in the solution. We describe a branch-and-bound algorithm that produces all Pareto-optimal solutions.     

A Two-Level Production Control Model with Target Amount Rescheduling

This paper deals with the problem of two-level production control with disturbances. A production system is considered with several machines on the lower level and a section on the upper one. Each machine produces a given target amount by a given due date (common to all machines). Each machine has several possible speeds, which are subject to disturbances. On the machine level, at the routine control point, decision-making centres on introducing the proper speed and determining the next control point. It is assumed that all the target amounts are transferable; i.e. a part of each target amount can be processed by any other machine. In a case when it is realized, for a certain machine, that the target cannot be completed on time, the section reschedules the remaining target amounts among the machines. New target amounts are determined for the machines so that the overall target can be accomplished on time. A stochastic optimization formulation is presented, followed by a heuristic solution and simulation results.     

Dynamic models of production with multiple operations and general processing times

Traditional integer programming model formulations for job-shops and flow-shops do not easily account for characteristics common to high-technology manufacturing such as high-volume semiconductor manufacturing. These characteristics are: (1) products (wafers) are processed by the same machine type more than once during the operation sequence, (2) many lots of similar type are run, and (3) there can be multiple machines of the same type. In this paper, we present two new integer programming formulations which easily account for these characteristics. The approach is based on restricting the allowed domain of events for the start of lot processing. The first model restricts production starts to the beginning of a planning time period. The second model uses a special time grid at each operation with width equal to the processing time, and allows starts to be scheduled at the grid points. In an example problem replicating a high-volume wafer fabrication process, it is shown that it is computationally practical to obtain solutions for the restricted start models where it is not computationally possible for the traditional integer programming model formulations.     

On Markovian approximations for virtual-build-to-order systems

The Virtual Build-to-Order (VBTO) approach strives to allow a producer to fulfil customers with the specific product variants they seek more efficiently than a conventional order fulfilment system. It does so by opening the planning pipeline. Here the feasibility of modelling the VBTO system as a Markov process is investigated. Two system configurations are considered—a random pipeline feed policy that assumes only knowledge of the overall demand pattern and an informed policy that ensures a mix of different variants in the system. First-order Markov models, which assume stationarity requirements are satisfied, are developed for small VBTO systems. The model for the informed feed policy has excellent agreement with simulation results and confirms the superiority of this policy over the random policy. The model for the random policy is more accurate at high variety than at low variety levels. Accuracy is improved with a second-order Markov model. Although impractical for modelling large scale VBTO systems for either configuration, the Markov approach is valuable in providing insights, theoretical foundations and validation for simulation models. It aids the interpretation of observations from simulations of large scale systems and explains the mechanism by which an unrepresentative stock mix develops over time for the random policy.     

A dynamic production planning and scheduling algorithm for two products processed on one line

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.