Rolling horizon,multi-product production planning with chance constraints and forecast evolution for wafer fabs

In this paper, we study production planning models for semiconductor wafer fabrication facilities (wafer fabs) that consider both safety stocks at the finished goods inventory level and workload-dependent lead times. The evolution of demand forecasts over time follows the multiplicative Martingale Model of Forecast Evolution (MMFE) for multiple products and is incorporated into the planning models via shortfall-based chance constraints, permitting the simultaneous determination of production quantities and safety stocks. We study two variants of this formulation, one that considers forecast updates and one that does not. A planning model with workload-dependent lead times that does not consider safety stocks is used for comparison. The performance of the planning models is assessed in a rolling horizon environment using a simulation model of a scaled-down wafer fab. We find that the chance-constrained model with forecast updates outperforms the one without forecast updates with respect to expected service level and profit. Both chance-constrained models outperform the model without safety stocks. These results indicate that considering forecast evolution in production planning models can lead to improved performance by exploiting the advance demand information provided by the forecast updates.     

Optimal Cycle Times in a Two-Stage Serial System With Set-Up and Inventory Costs

Two 2-stage serial production systems under constant average demand rate and infinite horizon are considered. The first and the simpler system assumes zero final product inventory; while the second assumes it nonzero but with a continuous demand. The stages have finite production rates greater than or equal to the demand rate and operate with periodic start-ups and shutdowns. No stock-outs are allowed in the inventories. Analytical results for determining a cyclic schedule with the minimum sum of set-up and inventory costs are presented. The optimal lot sizing policy for the first system involves integer splitting/merging of lots; however noninteger split/merge policy may be optimal in some instances of the second.     

Production Lot-Sizing Under Learning Effects: An Efficient Solution Technique

In this paper, we consider a production-inventory model which assumes that learning occurs as a function of the number of units produced. We analyze two cases: the first case allows for no forgetting between production runs and the second case (a generalization of the first case) allows for some given degree of forgetting between production runs. In the first case, we show that learning only has an impact on initial lot-sizes for large order quantities and that steady state lot-sizes will approach the traditional EOQ amount. In addition, we show that succeeding lot-sizes are always nonincreasing. Applying these results to the second case when forgetting occurs, we develop efficient heuristic algorithms with complexity O(N logN) to determine order quantities. Results from our algorithms are compared to optimal solutions; these comparisons indicate that our algorithms usually provide solutions within one percent of the optimal cost.     

Integration of vendor selection into production and remanufacturing planning subject to emission constraints

This paper presents a new model formulation that incorporates vendor selection into production and remanufacturing planning subject to emission constraints. The objective is to determine a feasible production and remanufacturing plan at minimal cost. In each period, the given external demand must be satisfied for both new and remanufactured products. Remanufactured products can be substituted by new products, but not vice versa. When a product is (re)manufactured, the appropriate machine must be set up, which entails set-up costs and/or set-up time. The procurement of raw material that is offered by several vendors at different prices is integrated into this planning problem. To solve this integrated production and remanufacturing planning problem, we apply two solution approaches based on mathematical programming: first, a combination of column generation and a period-oriented fix-and-relax heuristic and second, an adapted fix-and-optimise heuristic. The results of our numerical investigation demonstrate the high solution quality of both solution approaches.     

A variable neighbourhood search for integrated production and preventive maintenance planning in multi-state systems

This paper presents a variable neighbourhood search (VNS) to the integrated production and maintenance planning problem in multi-state systems. VNS is one of the most recent meta-heuristics used for problem solving in which a systematic change of neighbourhood within a local search is carried out. In the studied problem, production and maintenance decisions are co-ordinated, so that the total expected cost is minimised. We are given a set of products that must be produced in lots on a multi-state production system during a specified finite planning horizon. Planned preventive maintenance and unplanned corrective maintenance can be performed on each component of the multi-state system. The maintenance policy suggests cyclical preventive replacements of components, and a minimal repair on failed components. The objective is to determine an integrated lot-sizing and preventive maintenance strategy of the system that will minimise the sum of preventive and corrective maintenance costs, setup costs, holding costs, backorder costs and production costs, while satisfying the demand for all products over the entire horizon. We model the production system as a multi-state system with binary-state components. The formulated problem can be solved by comparing the results of several multi-product capacitated lot-sizing problems. The proposed VNS deals with the preventive maintenance selection task. Results on test instances show that the VNS method provides a competitive solution quality at economically computational expense in comparison with genetic algorithms.     

Activity-Based Costing: A Manufacturing Management Decision-Making Aid

ABSTRACT

Serious distortion can occur in manufacturing product costing systems that use a single volume-related base (like direct labor hours) to assign overhead costs to products. Activity-based costing (ABC) assumes that activities consume resources, and products consume activities; hence, ABC makes activities its focus. Costs are traced from activities to products based on demand for the focus activity (or activities). Conventional cost systems are imprecise due to the lack of detail in the allocation of overhead. In contrast, ABC provides more accurate product cost because it captures many dynamic variables while assigning overhead costs through defined activities.     

Modelling and analysis for sequentially optimising production,maintenance and delivery activities taking into account product returns

This paper develops and analyses a stochastic optimisation problem with a service level constraint for generating a sequentially optimal plan of production, maintenance and delivery activities in a deteriorating manufacturing system. Stochastic demand along with product returns are both assumed the latter of which allows for restocking products returned by the customer which are still new and thus in saleable condition. A constrained production/maintenance/delivery problem with service level, stochastic demand, delivery time, failure rate and product returned is formulated based on quadratic model. This quadratic formulation is adapted to provide an inventory, delivery, production and maintenance policies. The objective of this paper is to study the delivery time influence on the planning of the production, maintenance and delivery activities. Finally, we present simulation results to illustrate the exploitation of the proposed approach.     

The performance of rolling production schedules in a process industry

In this paper we study lot-sizing and changeover decisions in production schedules that are implemented on a rolling-horizon basis. The study is carried out by comparing production schedules for the packaging operations of a pharmaceutical company that produces various products on several capacitated production lines. The schedules are obtained by solving a mixed-integer programming formulation by using a heuristic procedure. We examine the effects of the number of periods in the planning horizon, the starting inventory and the demand fluctuation on the schedules. We show empirically that the saving in annual production cost diminishes rapidly as more demand periods are added to the planning horizon. Computational results are reported.     

Cycle time-oriented mid-term production planning for semiconductor wafer fabrication

Wafers are produced in an environment with uncertain demand and failure-prone machines. Production planners have to react to changes of both machine availability and target output, and revise plans appropriately. The scientific community mostly proposes WIP-oriented mid-term production planning to solve this problem. In such approaches, production is planned by defining targets for throughput rates and buffer levels of selected operations. In industrial practice, however, cycle time-oriented planning is often preferred over WIP-oriented planning. We therefore propose a new linear programming formulation, which facilitates cycle time-oriented mid-term production planning in wafer fabrication. This approach plans production by defining release quantities and target cycle times up to selected operations. It allows a seamless integration with the subordinate scheduling level. Here, least slack first scheduling translates target cycle times into lot priorities. We evaluate our new methodology in a comprehensive simulation study. The results suggest that cycle time-oriented mid-term production planning can both increase service level and reduce cycle time compared to WIP-oriented planning. Further, it requires less modelling effort and generates plans, which are easier to comprehend by human planners.     

The effect of correlated demand on the cyclical scheduling system

This paper investigates the effect of correlated demand on the cyclical scheduling system. The paper first analytically demonstrates that a blend-to-order production environment will generally realize correlated demand for blending components, even if the demands for finished blends are mutually independent. The degree of component demand correlation is shown to depend on the nature of the recipes used to blend finished products. A simulation model is then used to investigate the effects of this correlation, for the case of blending components produced on a single process under a cyclical scheduling policy. The results demonstrate that component demand correlation increases the variance of the production cycle length, and induces correlation between the cycle length and demand per period within the cycle. Both effects contribute to an increase in the variability of total demand during the production cycle, thus increasing the requirement of safety stock for the blending components. In the environment under concern, an analysis of the cyclical scheduling system--which assumes independent random demand--will underestimate the true safety stock requirement.     

Simultaneous order-lot pegging and wafer release planning for semiconductor wafer fabrication facilities

In semiconductor wafer fabrication facilities, order-lot pegging is the process of assigning wafer lots to orders and meeting the due dates of orders is considered one of the most important operational issues. In many cases of order-lot pegging, some orders cannot be fulfilled with the current wafers in the lots being processed, necessitating the release of additional new wafer lots into the wafer fabrication facility. In this paper, we propose a simultaneous decision model for order-lot pegging and wafer release planning in semiconductor wafer fabrication facilities, and develop a Lagrangian heuristic for solving the model. The results of computational experiments conducted using randomly generated problem instances that mimic actual field data from a Korea semiconductor wafer fabrication facility indicate that the performance of the Lagrangian heuristic is superior to that of a practical greedy algorithm for practical-sized problem instances. The results also point to how sensitivity analysis can be used to answer important managerial questions for effective management of the semiconductor wafer fabrication process.     

New Tabu search heuristics for the dynamic facility layout problem

A manufacturing facility is a dynamic system that constantly evolves due to changes such as changes in product demands, product designs, or replacement of production equipment. As a result, the dynamic facility layout problem (DFLP) considers these changes and is defined as the problem of assigning departments to locations during a multi-period planning horizon such that the sum of the material handling and re-arrangement costs is minimised. In this paper, three tabu search (TS) heuristics are presented for this problem. The first heuristic is a simple TS heuristic. The second heuristic adds diversification and intensification strategies to the first, and the third heuristic is a probabilistic TS heuristic. To test the performances of the heuristics, two sets of test problems from the literature are used in the analysis. The results show that the second heuristic out-performs the other proposed heuristics and the heuristics available in the literature.     

Cycle time estimation for wafer fab with engineering lots

Due to the interaction between the process complexity and equipment diversity in a wafer fab, it is rather difficult to estimate the material flow time of wafer lots. Facing competition, it is common for a wafer fab to produce a certain quantity of engineering lots. However, introducing engineering lots into the factory will increase the complexity of the material flow control and the difficulty in cycle time estimation. The purpose of this paper is to develop cycle time estimation algorithms for a wafer fab by analyzing the material flow characteristics. Simulation results have shown that the algorithm is capable of generating satisfactory cycle time estimations with or without existing engineering lots.     

Single-machine group scheduling problem considering learning,forgetting effects and preventive maintenance

An integrated single-machine group scheduling model is proposed, which incorporates both learning and forgetting effects and preventive maintenance (PM) planning. The objective is to minimise the expected makespan by optimising job sequence and PM decisions. This model contains sequence-dependent set-up time, actual processing time, planned PM time and expected minimal repair time simultaneously. Based on the properties of group production, three learning functions under different circumstances are proposed to deduce the variable processing time of each part, considering the learning effect when consecutively producing identical or similar parts, together with the forgetting effect when transferring jobs interrupts the production process and makes retrogress in learning. Both run-based maintenance and minimal repair policies are specified to handle the uncertainty of machine breakdowns. The search algorithm for the model is developed, and the numerical example is studied. The computational results and sensitivity analysis show that this improved group scheduling model can well balance the machine resource requirements from different practical manufacturing-related activities.     

Lot sizing in a production system with rework and product deterioration

Producing new and recovering defective products often takes place on a common facility, with these activities carried out in lots. Consequently, there is a necessity to coordinate the production and rework activities with respect to the timing of operations and also regarding appropriate lot sizes for both processes while completely satisfying a given demand. Thereby, it has to be taken into account whether the state of defective items may change in the course of time while they wait to be reworked. Such a deterioration of reworkable goods can result in increasing rework time and rework cost per unit. In this paper an EPQ model which addresses all of these aspects is presented. Considering set-up and inventory holding costs as well as set-up times, optimization algorithms are developed covering different planning situations. Closed-form results for optimal lot sizes can be obtained and exploited for new analytical insights into coordinated lot sizing in the case of returns and product deterioration.     

Campaign planning for multi-stage batch processes in the chemical industry

Inspired by a case study from industry, the production of special chemical products is considered. In this industrial environment, multi-purpose equipment is operated in batch mode to carry out the diverse processing tasks. Often, extensive set-up and cleaning of the equipment are required when production switches between different types of products. Hence, processes are scheduled in campaign mode, i.e. a number of batches of the same type are processed in sequence. The production of chem ical products usually involves various stages with significant cumulative lead times. Typically, these production stages are assigned to different plants. A hierarchical modelling approach is presented which co-ordinates the various plant operations within the entire supply network. In the first stage, the length of the campaigns, their timing, the corresponding material flows, and equipment requirements have to be determined. At this stage, an aggregation scheme based on feasibility constraints is employed in order to reflect the limited availability of the various types of production equipment. The second stage consists of an assignment model, which allocates the available equipment units between the production campaigns determined in the first stage of the solution procedure. In the third stage, resource conflicts are resolved, which may occur if clean-out operations and minimal campaign lengths have to be considered. The proposed hierarchical approach allows a more compact model formulation compared to ot her approaches known from the literature. As a result, a very efficient and flexible solution approach is obtained. In particular, commercially available standard solvers can be used to solve a wide range of campaign planning problems arising in the chemical industry.     

The Effects of Learning on Optimal Lot Size Determination—Single Product Case

In this article the effects of learning on production lot sizing models are analyzed for the single product case. A general equation is developed for the average production time per unit, for producing the the annual demand in batches with some percentage of learning not retained between lots. Two models are developed, the first restricted to equal lot sizes and the second restricted to equal production intervals. A sample problem is solved to demonstrate the applications of learning to lot size determination.     

MILP-based campaign scheduling in a specialty chemicals plant: a case study

Supply chain management in chemical process industry focuses on production planning and scheduling to reduce production cost and inventories and simultaneously increase the utilization of production capacities and the service level. These objectives and the specific characteristics of chemical production processes result in complex planning problems. To handle this complexity, advanced planning systems (APS) are implemented and often enhanced by tailor-made optimization algorithms. In this article, we focus on a real-world problem of production planning arising from a specialty chemicals plant. Formulations for finished products comprise several production and refinement processes which result in all types of material flows. Most processes cannot be operated on only one multi-purpose facility, but on a choice of different facilities. Due to sequence dependencies, several batches of identical processes are grouped together to form production campaigns. We describe a method for multicriteria optimization of short- and mid-term production campaign scheduling which is based on a time-continuous MILP formulation. In a preparatory step, deterministic algorithms calculate the structures of the formulations and solve the bills of material for each primary demand. The facility selection for each production campaign is done in a first MILP step. Optimized campaign scheduling is performed in a second step, which again is based on MILP. We show how this method can be successfully adapted to compute optimized schedules even for problem examples of real-world size, and we furthermore outline implementation issues including integration with an APS.     

Risk-averse two-stage stochastic programs in furniture plants

We present two-stage stochastic mixed 0–1 optimization models to hedge against uncertainty in production planning of typical small-scale Brazilian furniture plants under stochastic demands and setup times. The proposed models consider cutting and drilling operations as the most limiting production activities, and synchronize them to avoid intermediate work-in-process. To design solutions less sensitive to changes in scenarios, we propose four models that perceive the risk reductions over the scenarios differently. The first model is based on the minimax regret criteria and optimizes a worst-case scenario perspective without needing the probability of the scenarios. The second formulation uses the conditional value-at-risk as the risk measure to avoid solutions influenced by a bad scenario with a low probability. The third strategy is a mean-risk model based on the upper partial mean that aggregates a risk term in the objective function. The last approach is a restricted recourse approach, in which the risk preferences are directly considered in the constraints. Numerical results indicate that it is possible to achieve significant risk reductions using the risk-averse strategies, without overly sacrificing average costs.     

Normative Models for Some Warehouse Sizing Problems

The problem examined is the determination of the optimum size for a warehouse used to store products over a finite planning horizon. Both fixed and changeable warehouse size problems are treated under conditions of deterministic and probabilistic storage demand. The latter is formulated as a linear programming problem and transformed via duality theory into an equivalent network flow problem for efficient solution. Costs considered are those due to warehouse construction, storage of products within the facility, and storage demand not satisfied by storage in the warehouse.