An optimal batch size for a production system operating under periodic delivery policy

A manufacturing system that procures raw materials from suppliers in a lot and processes them into a finished product is considered in this research. An ordering policy is proposed for raw materials to meet the requirements of a production facility which, in turn, must deliver finished products demanded by outside buyers at fixed points in time. First, a general cost model is formulated considering both raw materials and finished products. Then, using this model, a simple procedure is developed to determine an optimal ordering policy for procurement of raw materials, and the manufacturing batch size, to minimize the total cost of meeting customer demands in time. The dependent relationships between production batch size and rawmaterial purchasing quantity, and various delivery patterns considered in recent literature are critically reviewed. The quality of the solution is evaluated. Numerical examples are provided.     

Inventory control model for a supply chain system with multiple types of items and minimum order size requirements

This paper considers a replenishment problem for a single buyer who orders multiple types of items from two or more heterogeneous suppliers in order to sell to end customers. The buyer periodically orders each type of item from the suppliers according to a select inventory control policy. Processing the order, each supplier enforces the policy that an order from the buyer must meet a predetermined minimum order quantity (MOQ). Therefore, the buyer must decide how much to order from each supplier considering the current inventory level, demand forecast, and MOQ requirement. The buyer's problem is formulated as an integer programming model and an efficient implementation strategy is suggested to apply the model to real problems. Numerical experiments are performed to test the validity of the proposed model as well as the efficiency of the implementation strategy. The experimental results show that this model combined with the implementation method yields a considerable cost reduction compared to the most efficient policy currently available.     

A sequencing problem for a mixed-model assembly line in a JIT production system

In an assembly line of a just-in-time (JIT) production system, workers have the power and the responsibility to stop the line when they fail to complete their operations within their work zones. This paper deals with a sequencing problem for the mixed-model assembly conveyor line in the JIT production system. In some environment, the most important criterion is the line stoppage rather than the variation of production rates. The problem is to find an optimal sequence of units that minimizes the total line stoppage time. Lower and upper bounds of the total line stoppage time are derived and the branch-and-bound method is applied to the problem. A numerical example is given.     

Note on: An optimal batch size for a production system operating under periodic delivery policy

In this note we present a comparative study of solutions given by Sarker and Khan [Comput Ind Engng 37 (1999) 711].     

An approximate solution to a jit-based ordering system

In this paper we consider a multi-stage multi-product production, inventory and transportation system including lot production processes and develop a goal programming model for a pull type ordering system based on the concept of a Just-In-Time(JIT) production system. We also present a pragmatic approach which reduces the required computational time for the formulated mixed integer goal programming problem using a mathematical programming modeling language. The proposed solution procedure is realized utilizing the post-optimal analysis which can be performed by the modeling language.     

The performance of workload rules for order acceptance in batch chemical manufacturing

We investigate the performance of workload rules used to support customer order acceptance decisions in the hierarchical production control structure of a batch chemical plant. Customer order acceptance decisions need to be made at a point in time when no detailed information is available about the actual shop floor status during execution of the order. These decisions need therefore be based on aggregate models of the shop floor, which predict the feasibility of completing the customer order in time. In practice, workload rules are commonly used to estimate the availability of sufficient capacity to complete a set of orders in a given planning period. Actual observations in a batch chemical manufacturing plant show that the set of orders accepted needs to be reconsidered later, because the schedule turns out to be infeasible. Analysis of the planning processes used at the plant shows that workload rules can yields reliable results, however at the expense of a rather low capacity utilization. In practice this is often unacceptable. Since, solving a detailed scheduling problem is not feasible at this stage, this creates a dilemma that only can be solved if we can find more detailed aggregate models than workload rules can provide.     

Reinforcement learning for combined production-maintenance and quality control of a manufacturing system with deterioration failures

This paper describes and examines thoroughly a stochastic production/inventory system that produces a single type of products. During the production process, the system is affected by several deterioration failures. It is restored to its initial and previous deterioration state by repair and maintenance activities. Both maintenance and repair duration are assumed as exponential random variables. Moreover, the quality of the manufactured products is assumed to be affected by the current deterioration level of the system. The aim of this paper is to find the optimal trade-off between conflicting performance metrics for the optimization of the total expected profit of the system. To tackle such optimization problems, researchers frequently employ Dynamic Programming. This method, though, is not appropriate for the addressed problem due to complexity reasons. To this end, a Reinforcement Learning-based approach is proposed in order to obtain the optimal joint production, maintenance and product quality control policies. To the authors’ knowledge, the proposed approach is novel and there are few examples of such implementation in the academic literature.     

Economic production quantity with rework process at a single-stage manufacturing system with planned backorders

In traditional inventory models such as the economic order quantity (EOQ) and the economic production quantity (EPQ) the sole objective is to minimize the total inventory-related costs, typically holding cost and ordering cost. These models do not consider the presence of defective products in the lot or rework of them. Recently, Jamal, Sarker, and Mondal (Jamal, A. A. M., Sarker, B. R., & Mondal, S., (2004). Optimal manufacturing batch size with rework process at single-stage production system. Computers and Industrial Engineering, 47(1), 77–89) proposed a model, which dealt with the optimum batch quantity in a single-stage system in which rework is done by addressing two different operational policies to minimize the total system cost, but their models do not consider planned backorders. In this direction, this paper develops an EPQ type inventory model with planned backorders for determining the economic production quantity for a single product, which is manufactured in a single-stage manufacturing system that generates imperfect quality products, and all these defective products are reworked in the same cycle. We also establish the range of real values of the proportion of defective products for which there is an optimal solution, and the close form for the total cost of inventory system. The use of the inventory model is illustrated with numerical examples. The classical EOQ, EPQ inventory models with or without planned backorders and Jamal, Sarker and Mondal’s model (Jamal, A. A. M., Sarker, B. R., & Mondal, S., (2004). Optimal manufacturing batch size with rework process at single-stage production system. Computers and Industrial Engineering, 47(1), 77–89) are shown to be special cases of the EPQ inventory model presented in this paper.     

An economic manufacturing quantity model for a two-stage assembly system with imperfect processes and variable production rate

This article considers a two-stage assembly system with imperfect processes. The former is an automatic stage in which the required components are manufactured. The latter is a manual stage which deals with taking the components to assemble the end product. In addition, the component processes are independent of each other, and the assembly rate is variable. Shortage is allowed, and the unsatisfied demand is completely backlogged. Then, we formulate the proposed problem as a cost minimization model where the assembly rate and the production run time of each component process are decision variables. An algorithm for the computations of the optimal solutions under the constraint of assembly rate is also provided. Finally, a numerical example and sensitivity analysis are carried out to illustrate the model.     

Scheduling of a limited communication channel for optimal control

In this paper a method for optimal off-line scheduling of a limited resource used for control purposes is presented. For various reasons, real-time communication channels are prone to have limited bandwidth. To overcome this obstacle, the rate of actions must be chosen accordingly at design time, both with respect to the limitation of the resource and to control performance. A resulting off-line schedule implements the rate of actions as a repetitive sequence of communication instants. Periodic control theory is used to define a cost functional for LQ-control, that measures the performance of a sampled-data system in relation to a desired continuous time performance. In contrast to uniform sampling, the communication sequence is here allowed to be time-varying. This approach results in a complex combinatorial optimization problem, whose solution gives the optimal off-line schedule, i.e., the sequence in which the actions should take place. The optimization problem is solved by a neighborhood search method where a heuristic method is used to generate initial guesses close to the optimum. The optimal schedule is typically such that the sampling is non-uniform, but the resulting LQ-control law is time-varying and takes this non-uniform sampling into account.