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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Effect of maintenance policies on the just-in-time production system

Using simulation, experimental design, and regression analysis, mathematical models are developed here to describe the effect that maintenance policy, machine unreliability, processing time variability, ratio of preventive maintenance time to processing time, ratio of minimal repair time to preventive maintenance time, and production line size have on various measures of performance, namely total production line output and production line variability of the just-in-time production system. The analysis of the data shows that under different situations, different maintenance policies do not have the same effect on the production line performance. The following conclusions were obtained; when the number of production machines is low (five machines or less), and/or when the ratio of minimal repair time to preventive maintenance time is high, maintenance policy III leads to a higher performance than maintenance policy II. Otherwise maintenance policy II, which is more sensitive to the change of the ratio of minimal repair time to preventive maintenance time, leads to a higher performance. The results of the study can be utilized in choosing a maintenance policy as a function of the production process parameters. Once a policy is chosen, the practitioner can select the most important factors to control under that policy in order to minimize the machine idle time, maximize the production process reliability, improve productivity, and therefore increase the production line performance.     

Optimal preventive maintenance policies in a serial production system

There have been many publications dealing with preventive maintenance policies for stochastically deteriorating systems. However, most of them study systems having one device subject to failure. Much of the limited research dealing with multi-device production systems has been conducted through simulation experiments. In this paper, the preventive maintenance problem for serial production systems is formulated as a mathematical model. This formulation permits management to analyse the impact of a preventive maintenance policy on a serial production system without resorting to simulation. Numerical examples are used to provide managerial implications for maintaining a serial production system. The results show that the operating characteristics of the stations are interrelated; therefore, it is important to examine the joint effects of a maintenance policy on the various stations of the production system simultaneously rather than study each station separately.     

A heuristic for production scheduling and inventory control in the presence of sequence-dependent setup times

The consideration of sequence-dependent setup times is one of the most difficult aspects of production scheduling problems. This paper reports on the development of a heuristic procedure to address a realistic production and inventory control problem in the presence of sequence-dependent setup times. The problem considers known monthly demands, variable production rates, holding costs, minimum and maximum inventory levels per product, and regular and overtime capacity limits. The problem is formulated as a Mixed-Integer Program (MIP), where subtour elimination constraints are needed to enforce the generation of job sequences in each month. By relaxing the subtour elimination constraints, the MIP formulation can be used to find a lower bound on the optimal solution. CPLEX 3.0 is used to calculate lower bounds for relatively small instances of this production problem, which are then used to assess the merit of a proposed heuristic. The heuristic is based on a simple short-term memory tabu search method that coordinates linear programming and traveling salesperson solvers in the search for optimal or near-optimal production plans.     

MRP lot sizing with variable production/purchasing costs: formulation and solution

The research on lot sizing is extensive; however, no author in the literature reviewed to date provides an optimal solution algorithm to a prevalent problem which is found in manufacturing. A multi-level, general product-structure, variable-cost model is presented which follows the procedure of a closed-loop material requirements planning (MRP) system, and incorporates many conditions that production and material managers find in practice. A branch and bound (B&B7) algorithm is developed. The efficiency of B&B is derived from effective lower bounds and solution procedures which are determined on the basis of the space-time structure of the MRP lot-sizing problem and its non-convex total-cost function. This path-dependent lower bound is computationally efficient and guarantees an optimal solution. The B&B algorithm is tested on problems and compared to heuristics in the literature.     

Dynamic order acceptance and scheduling problem with sequence-dependent setup time

This paper studies the order acceptance and scheduling problem under a single machine environment when the orders come stochastically during the planning horizon and a sequence-dependent setup time is required between the processing of different types of orders. The objective is to maximise the expected revenue subject to the due date constraints. The problem is formulated as a stochastic dynamic programming model. A rule based on the opportunity cost of the remaining system capacity for the current system state is proposed to make the order acceptance decisions. The remaining system capacity is estimated by a heuristic which generates a good schedule for the accepted orders. Its opportunity cost is estimated by both mathematical programme and greedy heuristic. Computational experiments show that the profit generated by the integrated dynamic programming decision model is much higher than the widely used first-come-first-accept policy in industries and the benefit increases with the length of planning horizon, the arrival rate and the length of lead time. Acceptance decision based on mathematical programming outperforms greedy heuristic by about 7% and its computational time is short. It also shows that the quality of the solutions generated by the opportunity cost based order acceptance rule is satisfactory.     

On the effect of downtime costs and budget constraint on preventive and replacement policies

This work proposes a general approach to study and improve the effectiveness of the system with respect to its expected life-cycle cost rate. The model we propose considers a production system which is protected against demand fluctuations and failure occurrences with elements like stock piles, line and equipment redundancy, and the use of alternative production methods. These design policies allow to keep or minimize the effect on the nominal throughput, while corrective measures are taken. The system is also subject to an aging process which depends on the frequency and quality of preventive actions. Making decisions is difficult because of discontinuities in intervention and downtime costs and the limited budget. We present a non-linear mixed integer formulation that minimizes the expected overall cost rate with respect to repair, overhaul and replacement times and the overhaul improvement factor proposed in the literature. The model is deterministic and considers minimal repairs and imperfect overhauls. We illustrate its application with a case based on a known benchmark example.