Optimal Production Control Policy Research Articles

Integrated Capacity Planning and Production Control of an Assembly Manufacturing System

For an assembly manufacturing system, its capacity planning problem and production control problem are usually considered separately. However, production capacity cannot exert its maximum productivity without employing optimal production control; and optimal production control may not satisfy the demand without sufficient production capacity. Therefore, it is important to jointly optimize capacity planning and production control. First, the mathematical formulation of integrated production control and capacity planning problem for an assembly manufacturing system with multiple upstream production lines and one downstream assembly line is proposed in this paper. Second, we develop a method to obtain the marginal probability distribution of the inventory level in the assembly system, which can be employed to calculate the average production cost under an approximate optimal production control policy. Since optimal control policy is subject to production capacity (i.e., machine number), we employ the integer programming method to optimize the machine number (i.e., production capacity), which consequently influences the control policy. Numerical experiments are conducted to verify the correctness of the method of calculating steady-state probability distribution, and the effectiveness of the algorithm of integrated optimization of production control and production capacity.

A Robust Production Control Policy for Hedging Against Inventory Inaccuracy in a Multiple-Stage Production System With Time Delay

Inventory inaccuracy has significant negative impact on the performance of production control. In this paper, we investigate the robust production control problem for a multiple-stage production system with inventory inaccuracy and time delay between stages. The objective of this problem is to minimize the average production cost. The problem is solved in two steps. First, an approximate optimal production control policy is developed for a multiple-stage production system with time delay but without inventory inaccuracy. Second, we reveal that the discontinuity of the controls makes the policy sensitive to the error of inventory data, and then propose a robust production control policy to eliminate this sensitivity, in which the control variables change smoothly when state variables cross boundaries between different domains in the state space. We also prove that the robustness of the proposed robust policy is better than that of the approximate optimal policy. Finally, numerical experiments are conducted to examine the performance of the proposed robust policy for hedging against inventory inaccuracy.

Lockout/tagout and optimal production control policies in failure-prone non-homogenous transfer lines with passive redundancy

This paper considers a production problem for a transfer line subject to random failures and repairs, and differs from other studies on transfer lines. It considers a manufacturing system consisting of three machines (two machines with passive redundancy, and one in series with the previous ones) producing one part type. The control problem is subject to non-negative constraints on work-in-process (WIP). The decision variables are the production rates of two main machines and a standby machine, and influence the WIP levels, the inventory levels and the system's capacity, which is assumed to be described by a finite-state Markov chain. The objective of this paper is to minimise WIP and finished goods inventory costs; it also aims to respect the essential space–time during intervention on machine down, in order to minimise the possibility of the circumvention of protection devices or of the retraction of lockout/tagout procedures through a passive redundancy system. This paper therefore verifies the effect of passive redundancy on optimal stock levels. Given that an analytical or even a numerical solution of the problem is very difficult to find, and that we want to have a more realistic model for industries, we present a combined approach, which is presented based on a combination of analytical formalism, simulation modelling, design of experiments, and response surface methodology to optimise a transfer line with passive redundancy, producing one part type. The usefulness of the proposed approach is illustrated through a numerical example and a sensitivity analysis.

Sales team's initiatives and stock sensitive demand — A production control policy

The present article deals with an optimal production control policy for stock and sales team's initiatives sensitive demand. The capacity of the production quantity and stock of produced items are state variable and the effort of sales-team/agent is a control variable in this model. Finally, a net profit function by trading off procurement cost, cost for effort of sales-team, cost for capacity of production and sales price is maximized by Pontryagin's Maximal Principle. The local and global stability analysis of the dynamical systems is well performed. The proposed model is justified by proper numerical illustration.

Joint optimal lot sizing and production control policy in an unreliable and imperfect manufacturing system

This paper deals with the problem of the joint determination of the optimal lot sizing and optimal production control policy for an unreliable and imperfect manufacturing system, where the quality control of lots produced is performed using an acceptance sampling plan. The proportion of defective items, the time between failures and the time to repair are generally distributed. The incurred total cost includes manufacturing cost, transportation cost, inspection costs, rejection cost of defective items, replacement cost for returned defective items from customers, and holding and backlog costs. The associated cost minimization problem is formulated with a stochastic dynamic programming model where the lot sizing and production rate are considered as decision variables. Given the difficulties in solving such a highly stochastic model analytically or numerically, we adopted a modified hedging point policy (HPP) to control the production rate, as well as an economic lot sizing policy for batch processing control; we also relied on a simulation-based experimental approach to determine a close approximation of the optimal control parameters. It is shown that production should be accelerated at the maximum production rate, not only when building the safety stock, as in the classical HPP, but also after rejecting a lot, in order to recuperate the loss in inventory and to maintain the on-hand safety stock. Numerical experiments and thorough sensitivity analyses are provided to illustrate the effectiveness of the proposed control policy and the robustness of the resolution approach. Some interesting behaviours regarding the impact of different parameters on the optimal decision variables are observed and discussed.

Optimal production control policy in unreliable batch processing manufacturing systems with transportation delay

This paper considers the problem of production planning of unreliable batch processing manufacturing systems. The finished goods are produced in lots, and are then transported to a storage area in order to continuously meet a constant demand rate. The main objective of this work is to jointly determine the optimal lot sizing and optimal production control policy that minimise the total expected cost of inventory/backlog and transportation, over an infinite time horizon. The decision variables are the lot sizing and the production rate. The problem is formulated with a stochastic dynamic programming model and the impulse control theory is applied to establish the Hamilton–Jacobi–Bellman (HJB) equations. Based on a numerical resolution of the HJB equations, it is shown that the optimal control policy is governed by a base stock policy for production rate control and economic lot size for batch processing. A thorough analysis and practical issues are addressed with a simulation-based approach. Thus, a combined discrete–continuous simulation model is developed to determine the optimal parameters of the proposed policy when the failure and repair times follow general distributions. The results are illustrated with numerical examples and confirmed through sensitivity analysis.

Robust production control policy for a single machine and single part-type manufacturing system with inaccurate observation of production surplus

The optimal production control policy (i.e., the hedging point policy) for a single machine and single part-type manufacturing system for the case where the production surplus is accurately known has been reported in the literature. However, the production surplus is often observed inaccurately in practice. Ignoring this inaccuracy in using the optimal policy leads to not only non-robust situations but also high production costs. To consider the effect of the inaccurate observation, robustness of the production control policy is required. The robustness can be evaluated in terms of the difference between the production surplus trajectory under the policy with an inaccurate observation and the trajectory under the policy with an accurate production surplus (i.e., the hedging point policy). A difference of zero is the ideal case; however, this is generally impossible to achieve since the extent of the observation error is generally unknown. This article proposes a new robust production control policy that can give a small difference between the two trajectories. Compared with the hedging point policy, the proposed policy is more insensitive to production surplus inaccuracy in the neighborhood of the hedging point but responds more slowly to a failure of the machine. Simulation studies show that the proposed policy has a better robustness than the hedging point policy for cases where, just as in actual industrial practice, the machine failure time is much shorter than the up time of the machine. In these cases, with an increase in the observation error, the robustness of the proposed policy becomes increasingly better than that for the hedging point policy.

Production rate control of an unreliable manufacturing cell with adjustable capacity

This article addresses the production control problem of an adjustable capacity unreliable manufacturing cell responding to a single product type demand. The manufacturing cell is composed of an unreliable machine, called the ‘central machine’. Due to availability fluctuations, the central machine may fall short of meeting the long-term demand rate. In order to quickly adjust the production capacity and thus meet the demand, a reserve machine is called upon in support if the finished product inventory level drops below a specific threshold. Such a machine involves higher production costs compared with the central one. This article aims to determine the optimal production control policy for the involved machines in order to minimise production, inventory and backlog costs over an infinite horizon. This article proposes a continuous dynamic programming formulation of the problem and adopted a numerical scheme to solve the optimality conditions equations. The optimal production policy is shown to be described by a state dependent hedging point policy (SDHPP). To determine the optimal control policy parameters, an experimental approach based on design of experiments, simulation modelling, and response surface methodology is proposed. Several sensitivity analyses have been carried out and have shown the robust behaviour of the developed policy facing expected variations of the system parameters. The results also show that the proposed SDHPP policy outperforms classical stand-by and parallel machines based control policies. The usefulness of the proposed approach is outlined for more complex situations where the system must deal with non-exponential failure and repair time distributions.

Dynamic production control in a serial line with process queue time constraint

This research examines the production control problem in two-station tandem queueing systems under time constraints. In these two-station tandem queueing systems, jobs must first be processed at the upstream station and then the downstream station. For each job, the sum of the waiting and processing time in the downstream queue is limited by an upper bound. This time constraint is called the process queue time constraint. When the process queue time constraint is violated, a significant scrap cost will be accrued. In this research, we develop a Markov decision model to study the production control problem under process queue time constraints. The objective is to minimise the sum of the expected long-run average inventory holding costs and scrap costs. According to the Markov decision model, an interesting exhaustive structure of the optimal production control policy is found. Based on this exhaustive structure, an efficient algorithm is developed to solve the production control problem numerically. The performance of the proposed algorithm is verified by a simulation study. Compared with other heuristics in the literature, the proposed algorithm can significantly reduce production costs while improving system throughput and utilisation.