Robust policies for a multi-stage production/inventory problem with switching costs and uncertain demand

In this paper, we seek robust policies for a multi-stage production/inventory problem to minimise total costs, including switching, production, inventory or shortage costs. While minimising switching costs often leads to non-convexity in the model, 0–1 variables are introduced to linearise the objective function. Considering the impossibility of obtaining the exact distribution of uncertain demand, we study the production/inventory problem under worst cases to resist uncertainty. In contrast to traditional inventory problems, unexpected yields in production are considered. Robust support vector regression is developed to approximate the yields of each unit. A mixed-integer linear programming is proposed, employing the duality theory to address the min–max model. A practical case study from cold rolling is considered. Experiments on the actual steel production data are reported to illustrate the validity of the proposed approach.     

Scheduling policies in multi-product manufacturing systems with sequence-dependent setup times and finite buffers

Multi-product production systems with sequence-dependent setup times are typical in the manufacturing of semiconductor chips and other electronic products. In such systems, the scheduling policies coordinating the production of multiple product types play an important role. In this paper, we study a multi-product manufacturing system with finite buffers, sequence-dependent setup times and various scheduling policies. Using continuous-time Markov chain models, we evaluate the performance of such systems under seven scheduling policies, i.e. cyclic, shortest queue, shortest processing time, shortest overall time (including setup time and processing time), longest queue, longest processing time, and longest overall time. The impacts of these policies on system throughput are compared, and the conditions characterising the superiority of each policy are investigated. The results of this work can provide production engineers and supervisors practical guidance to operate multi-product manufacturing systems with sequence-dependent setups.     

Increasing production rate in U-type assembly lines with sequence-dependent set-up times

U-shaped assembly lines are commonly used in just-in-time production systems as they have some advantages over straight lines. Although maximizing production rates on these lines by assigning tasks to stations is common practice in industrial environments, studies on the stated assembly line balancing problem are limited. This article deals with maximizing the production rate on U-shaped assembly lines under sequence-dependent set-up times. Sequence-dependent set-up times mean that after a task is performed, a set-up time, the duration of which depends on adjacent tasks, is required to start the next task operation. These set-ups are considered by dividing them into two groups, named forward and backward set-ups, to make the problem more practical. Two heuristics based on simulated annealing and genetic algorithms are improved beside the mathematical model. Experimental results show that solving the stated problem using the mathematical model is nearly impossible, while heuristics may obtain solutions that have acceptable deviations from the lower bounds.     

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.     

A production scheduling problem with uncertain sequence-dependent set-up times and random yield

A scheduling problem in a real production line with uncertain sequence-dependent set-up times and a random yield is considered. The production line can produce multiple product types as production lots, each of which is composed of a number of products of the same product type. To changeover product types, a sequence-dependent set-up operation should be performed, and only the lower and upper bounds are known for the sequence-dependent set-up times. Moreover, the processing time to produce the required number of product for each production lot is uncertain due to the random yield. For the objective of minimising the average tardy probability of given production lots, a systematic approximation scheme to estimate tardy probabilities of lots in any given production sequence is developed by taking not only the uncertainties but also the computational efficiency into account. As practical solution approaches, a simulated annealing and a discrete particle swarm optimisation algorithms using the approximation scheme are developed, and their performance are evaluated by computational experiments. Since there has been no research on the scheduling problems with uncertain sequence-dependent set-up times and random yield, the authors expect this research will make an excellent contribution to develop practical scheduling methodologies in uncertain scheduling environments.     

Multi-objective production scheduling with controllable processing times and sequence-dependent setups for deteriorating items

The production scheduling problem is to find simultaneously the lot sizes and their sequence over a finite set of planning periods. This paper studies a single-stage production scheduling problem subject to controllable process times and sequence-dependent setups for deteriorating items. The paper formulates the problem by minimising two objectives of total costs and total variations in production volumes simultaneously. The problem is modelled and analysed as a mixed integer nonlinear program. Since it is proved that the problem is NP-hard, a problem-specific heuristic is proposed to generate a set of Pareto-optimal solutions. The heuristic is investigated analytically and experimentally. Computational experiences of running the heuristic and non-dominated sorting genetic algorithm-I over a set of randomly generated test problems are reported. The heuristic possesses at least 56.5% (in the worst case) and at most 94.7% (in the best case) of total global Pareto-optimal solutions in ordinary-size instances.     

Optimization of multistage production systems with variable production times and costs

Introducing a concept of ‘ production speed ’ as a decision variable, a production model with variable (speed-dependent) production time and cost for producing a product item was constructed. Optimization analysis was mode on a single-item, multistage production system in an attempt to determine the optimal production speeds for all stages and the optimal cycle time. For a case of multiple-item production, an optimal job sequence and the optimal production speeds for all jobs were analysed, such that the total flow time was minimized as a primary objective and, in addition, the total production cost was minimized as a secondary objective.     

Maintenance policies for a production system with constrained production rate and buffer capacity

This paper considers the maintenance policies for a production system constrained by its production rate and buffer capacity to cope with unexpected failures and to deal with the variability of demand and production lead times. Using a system dynamics model, we characterize, simulate and compare results obtained by applying several maintenance policies--corrective, age-based maintenance, age and buffer-based maintenance, and modified age and buffer-based maintenance--to the system. This comparison is performed assuming that optimal values of the model parameters involved in the design of each maintenance policy have already been found by using the modified Powell method. We compare and discuss the benefits of different optimization criteria in the maintenance decision making process for a production system with constrained production rate and buffer capacity.     

Evaluating order acceptance policies for divergent production systems with co-production

The impacts of using different order acceptance policies in manufacturing sectors are usually well known and documented in the literature. However, for industries facing divergent processes with co-production (i.e. several products produced at the same time from a common raw material), the evaluation, comparison and selection of policies are not trivial tasks. This paper proposes a framework to enable this evaluation. Using a simulation model that integrates a custom-built ERP, we compare and evaluate different order acceptance policies in various market conditions. Experiments are carried out using a case from the forest products industry. Results illustrate how and when different market conditions related to divergent/co-production industries may call for available-to-promise (ATP), capable-to-promise (CTP), and other known strategies. Especially, we show that advanced order acceptance policies like CTP may generate a better income for certain types of market and, conversely to typical manufacturing industries, ATP performs better than other strategies for a specific demand patterns.     

Development of lifetime warranty policies and models for estimating costs

In today's fiercely competitive products market, product warranty has started playing an important role. The warranty period offered by the manufacturer/dealer has been progressively increasing since the beginning of the 20th Century. Currently, a large number of products are being sold with long-term warranty policies in the form of extended warranty, warranty for used products, service contracts and lifetime warranty policies. Lifetime warranties are relatively a new concept. The modelling of failures during the warranty period and the costs for such policies are complex since the lifespan in these policies are not defined well and it is often difficult to tell about life measures for the longer period of coverage due to usage pattern/maintenance activities undertaken and uncertainties of costs over the period. This paper focuses on defining lifetime, developing lifetime warranty policies and models for predicting failures and estimating costs for lifetime warranty policies.     

Shortage decision policies for a fluid production model with MAP arrivals

We consider on a continuous production/inventory process where a single machine produces a certain product into a finite buffer. The demands arrive according to a Markov Additive Process governed by a continuous-time Markov chain, and their sizes are independent and have phase-type distributions depending on the type of arrival. Two shortage policies are considered: the backorder policy, in which any demand that cannot be satisfied immediately is backlogged, and the order policy, in which any demand that cannot be satisfied immediately is supplied (alternatively, the latter policy can be considered as lost sales). We assume that the total cost includes a production loss cost, a penalty cost, a fixed cost for an order and a variable cost for the ordered amount. By applying the regenerative theory, we use tools from the exit-time theorem for fluid processes to obtain the discounted cost functionals under both policies. In addition, the models are extended to include a non-zero safety stock. Numerical examples, sensitivity analysis and comparative study are included.     

The effect of labour costs,holding costs,and uncertainty in demand on pull inventory control policies

Multi-plant coordination has been complicated by the recent trend towards globalization. In this paper, a model that simultaneously establishes values for various aggregate parameters such as target inventories and also identifies characteristics of the best pull control strategy is applied to a specific global manufacturing network. A simulation study is done to explore the effect of labour costs and holding costs on target inventories, actual inventories and pull control strategy. A second simulation experiment is used to examine the effect of variability in demand on these same decision variables. Implications for management are discussed and suggestions for further work are presented.     

Scheduling job shop problems with sequence-dependent setup times

In this work we consider job shop problems where the setup times are sequence dependent under minimisation of the maximum completion time or makespan. We present a genetic algorithm to solve the problem. The genetic algorithm is hybridised with a diversification mechanism, namely the restart phase, and a simple form of local search to enrich the algorithm. Various operators and parameters of the genetic algorithm are reviewed to calibrate the algorithm by means of the Taguchi method. For the evaluation of the proposed hybrid algorithm, it is compared against existing algorithms through a benchmark. All the results demonstrate that our hybrid genetic algorithm is very effective for the problem.     

Balancing two-sided assembly lines with sequence-dependent setup times

Two-sided assembly lines are often designed to produce large-sized products, such as automobiles, trucks and buses. In this type of production line, both left-side and right-side of the line are used in parallel. In all studies on two-sided assembly lines, sequence-dependent setup times have not yet been considered. However, in real life applications, setups may exist between tasks. Performing a task directly before another task may influence the latter task inside the same station, because a setup for performing the latter task may be required. Furthermore, if a task is assigned to a station as the last one, then it may cause a setup for performing the first task assigned to that station since the tasks are performed cyclically. In this paper, the problem of balancing two-sided assembly lines with setups (TALBPS) is considered. A mixed integer program (MIP) is proposed to model and solve the problem. The proposed MIP minimises the number of mated-stations (i.e., the line length) as the primary objective and it minimises the number of stations (i.e., the number of operators) as a secondary objective for a given cycle time. A heuristic approach (2-COMSOAL/S) for especially solving large-size problems based on COMSOAL (computer method of sequencing operations for assembly lines) method is also presented. An illustrative example problem is solved using 2-COMSOAL/S. To assess the effectiveness of MIP and 2-COMSOAL/S, a set of test problems are solved. The computational results show that 2-COMSOAL/S is very effective for the problem.     

Statistical analysis of electric power production costs

Electricity cannot be conviently stored. Thus there should be sufficient production at all times to meet the demand for electric power. If a low-cost generating unit fails this will lead to its substitution by a higher cost unit. The cost of producing electric power is a random variable because it depends upon two uncertain quantities, demand and the availability of the generating units. Analytical computation of the mean and the variance of the production costs can become quite cumbersome and time consuming for large systems, and therefore Monte Carlo simulation becomes an attractive alternative. A simulation study based on time series analysis of actual load data is described in which the primary objective was to determine the respective contributions of the demand and the generator availabilities to the variability of the estimates of the production cost. A secondary objective was to find out the extent to which an accurate temperature forecast reduces this variability. The results show that demand is a significant source of variation, and an accurate temperature forecast mitigates the effect of load uncertainty in the forecast of production costs.     

Coordinated order and production policies in supply chains

This paper is focused on the coordination of order and production policy between buyers and suppliers in supply chains. When a buyer of an item decides independently, he will place orders based on his economic order quantity (EOQ). However, the buyers EOQ may not lead to an optimal policy for the supplier. Should the buyer have the more powerful position to enforce his EOQ on the supplier, then no incentive exists for him to deviate from his EOQ. To provide an incentive to order in quantities suitable to the supplier, the supplier could offer a price discount or side payment. One critical assumption made throughout the literature dealing with incentive schemes to influence buyers ordering policy is that the supplier has complete information regarding buyers cost structure. This paper provides a bargaining model with asymmetric information about the buyers cost structure. A self-selection model for the determination of an optimal set of contracts which are specifically designed for different cost structures of the buyer, assumed by the supplier, will be presented.     

Intelligent dynamic control policies for serial production lines

Heuristic production control policies such as CONWIP, kanban, and other hybrid policies have been in use for years as better alternatives to MRP-based push control policies. It is a fact that these policies, although efficient, are far from optimal. Our goal is to develop a methodology that, for a given system, finds a dynamic control policy via intelligent agents. Such a policy while achieving the productivity (i.e., demand service rate) goal of the system will optimize a cost/reward function based on the WIP inventory. To achieve this goal we applied a simulation-based optimization technique called Reinforcement Learning (RL) on a four-station serial line. The control policy attained by the application of a RL algorithm was compared with the other existing policies on the basis of total average WIP and average cost of WIP. We also develop a heuristic control policy in light of our experience gained from a close examination of the policies obtained by the RL algorithm. This heuristic policy named Behavior-Based Control (BBC), although placed second to the RL policy, proved to be a more efficient and leaner control policy than most of the existing policies in the literature. The performance of the BBC policy was found to be comparable to the Extended Kanban Control System (EKCS), which as per our experimentation, turned out to be the best of the existing policies. The numerical results used for comparison purposes were obtained from a four-station serial line with two different (constant and Poisson) demand arrival processes.     

Simulating operator learning during production ramp-up in parallel vs. serial flow production

The aim of this research is to demonstrate how human learning models can be integrated into discrete event simulation to examine ramp-up time differences between serial and parallel flow production strategies. The experimental model examined three levels of learning rate and minimum cycle times. Results show that while the parallel flow system had longer ramp-up times than serial flow systems, they also had higher maximum throughput capacity. As a result, the parallel flow system frequently outperformed lines within the first weeks of operation. There is a critical lack of empirical evidence or methods that would allow designers to accurately determine what the critical learning paramters might be in their specific operations, and further research is needed to create predictive tools in this important area.     

Optimal leadtimes planning in serial production systems with earliness and tardiness costs

We consider a production system consisting of N processing stages. The actual leadtimes at the stages are stochastic. The objective is to determine the planned leadtimes at each stage so as to minimize the expected total inventory costs, tardiness penalties, and a backlog penalty for not meeting demand due date at the last stage. Recursive relationships are used for automatic generation and efficient computation of the objective function. The efficiency of the proposed algorithms allows us to obtain new insights regarding operating policies, leadtime delivery reliability, and production line design. The problem is formulated as a convex non-linear programming problem. The latter is then solved using classical convex optimization algorithms. For the special case of exponentially distributed leadtimes, the objective function is derived in a closed form.     

Single machine scheduling problem with stochastic sequence-dependent setup times

In this study, we consider stochastic single machine scheduling problem. We assume that setup times are both sequence dependent and uncertain while processing times and due dates are deterministic. In the literature, most of the studies consider the uncertainty on processing times or due dates. However, in the real-world applications (i.e. plastic moulding industry, appliance assembly, etc.), it is common to see varying setup times due to labour or setup tools availability. In order to cover this fact in machine scheduling, we set our objective as to minimise the total expected tardiness under uncertain sequence-dependent setup times. For the solution of this NP-hard problem, several heuristics and some dynamic programming algorithms have been developed. However, none of these approaches provide an exact solution for the problem. In this study, a two-stage stochastic-programming method is utilised for the optimal solution of the problem. In addition, a Genetic Algorithm approach is proposed to solve the large-size problems approximately. Finally, the results of the stochastic approach are compared with the deterministic one to demonstrate the value of the stochastic solution.