Optimal integrated maintenance/production policy for randomly failing systems with variable failure rate

This article deals with the combined production and maintenance plans for a manufacturing system satisfying a random demand. We first establish an optimal production plan which minimises the average total inventory and production cost. Second, using this optimal production plan, and taking into account the deterioration of the machine according to its production rate, we derive an optimal maintenance schedule which minimises the maintenance cost. A numerical example illustrates the proposed approach, this analytical approach, based on a stochastic optimisation model and using the operational age concept, reveals the significant influence of the production rate on the deterioration of the manufacturing system and consequently on the integrated production/maintenance policy.     

Joint optimisation of maintenance and production policies considering random demand and variable production rate

This paper deals with a randomly failing manufacturing system M1 which has to satisfy a random demand during a finite horizon given a required service level. To help meet this demand, subcontracting is used through another production system M2. M1 operates with a variable production rate and its failure rate depends on both time and the production rate. In these conditions, as a first step, we establish a preliminary production plan corresponding to a given service level. In a second stage, we integrate the effect of the machine degradation introducing a unitary degradation cost. The optimal production plan is then obtained by minimising the sum of the production, the inventory and the degradation costs. In the final stage, we propose another optimal plan combined with a preventive maintenance policy aiming at reducing the machine degradation while minimising the total cost including the production, inventory and maintenance costs.     

Economic lot sizing for an imperfect production system subject to random breakdowns

This article considers an economic manufacturing quantity model for an imperfect production process that is subject to random machine breakdowns. The product is manufactured intermittently in batches to meet a constant demand. During a production run, the system is assumed to deteriorate over time. As a result, a fixed proportion of items produced are defective. The system is also subject to random breakdowns. A no-resumption inventory control policy is adopted. Under this policy, the production run is aborted when a breakdown occurs. Production will be resumed only when all on-hand inventories are depleted. Corrective maintenance is carried out immediately after a breakdown. The time-to-shift and the time-to-breakdown are two random variables following different exponential distributions. The objective is to find an optimal production lot size that minimizes the expected (long-run) total cost per unit time. Several models are investigated and a numerical approach is developed to obtain an optimal production lot size.     

Quality issue in forecasting problem of production and maintenance policy for production unit

In this study, we consider an unreliable deteriorating production system that produces conforming and non-conforming products to satisfy a random demand under a given service level and during a finite horizon. The production system is subjected to a failure-prone machine. The quality of the produced products is affected by the machine deterioration since the rate of defectives increases as the deterioration increases. Preventive maintenance actions can be piloted on the production system to reduce the influence of deterioration and the defective rate. A joint control policy is based on a stochastic production and maintenance planning problem with goals to determine, firstly, the economic plan of production and secondly, the optimal maintenance strategy. The proposed jointly optimisation minimises the total cost of production, inventory, maintenance and defectives. A failure rate and quality relationship are defined to show the influence of the production rates variation on the failures rate as well as on the defective rate. A numerical example and an industrial case study are adopted to illustrate the proposed approach and a sensitivity analysis to validate the jointly optimisation.     

The supplier–buyer integrated production-inventory model with random yield

This paper revisits the traditional supplier–buyer integrated production-inventory model which deals with the problem of a manufacturer (supplier) supplying a product to a retailer (buyer) serving the consumer market with constant stationary demand. The product is manufactured in batches at a finite rate. The supplier's production batch is depleted by the buyer's replenishment orders at periodic intervals. The buyer's inventory is then consumed by the market demand at a fixed rate. The problem is the simultaneous computation of the manufacturer's production lot-size and the buyer's replenishment order quantity, i.e. the integrated production-inventory policy parameters. The key characteristic considered in this paper is that the manufacturing process is imperfect, and, hence, there are defective items in each production lot. As a result, each replenishment order shipped to the buyer includes defective products and the non-defective percentage in each such shipment is random. Considering the case where the supplier replenishes the buyer via equal-sized shipments, we develop an analytical expression of the total expected cost for the supplier–buyer system under consideration, with and without a considerable inspection time. We first examine the case where the inspection time is negligible, and then we present a generalisation to consider the inspection time explicitly. Our goal is to model the impact of random yield on the system performance. Our findings are useful for computing the integrated production-inventory policy parameters while considering the supply uncertainty due to an imperfect manufacturing process. Through numerical examples, we quantify the impact of supply with random yield on the system performance and illustrate its relationship with the demand and production rate.     

Flexible work-in-process production system in supply chain management under quality improvement

For a complex product production, any flexible manufacturing system with a work-in-process inventory is recommended for a supply chain management (SCM) system. Building a flexible manufacturing system increases the total cost of the supply chain; for this reason, a discrete investment is important. For flexible production systems, production rate within a finite specific interval of production rate as work-in-process inventory is calculated. The aim of the supply chain is to reduce the total cost when demand during the lead time is a random variable with a normal distribution. A crashing cost is utilised to reduce the duration of lead time within the supply chain system. A model is proposed to obtain the optimal flexible production rate with the reduced total cost of the supply chain. A classical optimisation technique is employed to obtain the closed-form and quasi-closed-form solutions of the decision variables. An improved algorithm is designed to obtain the global minimum cost of SCM under the framework of a flexible production system. An illustrative numerical example and sensitivity analysis are given to test the model. A numerical study proves that this model obtains the minimum cost with the optimal decision variables.     

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.     

Optimal age replacement scheduling for a random work system with random lead time

System maintenance and spare parts are two closely related logistics activities since maintenance generates the demand for spare parts. Most studies on integrated models of preventive replacement and inventory of spare parts have focused on age replacement scheduling, while random replacement policy, which is sensible and necessary in practice, is rarely discussed and applied. The purpose of this paper is to present a generalised age replacement policy for a system which works at random time and considers random lead time for replacement delivery. To model an imperfect maintenance action, we consider that the system undergoes minimal repairs at minor failures and corrective replacements at catastrophic failures. Before catastrophic failures, the system is replaced preventively at age T or at the completion of a working time, whichever occurs first. The main objective is to determine an optimal schedule of age replacement that minimises the mean cost rate function of the system in a finite time horizon. The existence and uniqueness of optimal replacement policy are derived analytically and computed numerically. It can be seen that the proposed model is a generalisation of the previous works in maintenance theory.     

Joint inventory-and-pricing strategy for a stochastic continuous-review system

We analyze an infinite-horizon continuous-review stochastic inventory system in which the selling price and inventory replenishment are determined simultaneously. The demand process is Poisson with a price-dependent arrival rate. The ordering cost includes a fixed setup cost and a variable cost proportional to the order quantity. We obtain closed-form solutions for the optimal inventory control strategy and optimal pricing strategy, which provide managerial insights as well as quantitative and qualitative relationships between decision rules and system parameters. We show that the optimal price is a unimodal function of the inventory level. We also develop efficient algorithms to compute the optimal strategies and present numerical examples.     

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.     

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.     

A stochastic model for joint inventory and outbound shipment decisions

In this paper, we consider a vendor realizing a sequence of random order arrivals in random sizes. The vendor has the autonomy to hold/consolidate small orders until an economical dispatch quantity accumulates. Consequently, the actual inventory requirements at the vendor are in part determined by the parameters of the shipment release policy in use. In this context, we investigate the impact of shipment consolidation on the expected long-run average cost by simultaneously computing the optimal order quantity for inventory replenishment at the vendor and the optimal dispatch quantity for outbound shipments. Since we consider the case where demand follows a general stochastic bulk arrival process, obtaining exact analytical expressions for some key operating characteristics of the cost function is intractable. Hence, we provide easy-to-compute approximations which enable efficient numerical solutions for the problem. We also investigate: (i) the cases where consolidated shipments are preferred over immediate deliveries; (ii) the sensitivity of optimal integrated policy variables to demand/cost parameters; (iii) the potential savings that can be obtained by shipment consolidation; and (iv) the tradeoffs between the waiting time induced by shipment consolidation and costs saved. Our results provide insights into the impact of outbound transportation operations on inventory replenishment decisions and outbound distribution system design. Moreover, numerical testing suggests that significant cost savings (up to 57%) are possible with shipment consolidation.     

Joint production control and product quality decision making in a failure prone multiple-product manufacturing system

This paper considers joint production control and product quality specifications decision making in unreliable multiple-product manufacturing system. This is with the knowledge that an optimum compromise should guide the decision making process. In fact, tight process specifications will generally lead to products with good quality and higher market values, but at the same time associated with a higher rate of non-conforming parts rejection leading to higher non quality costs and lower plant productivity. Moreover, in unreliable manufacturing context the decision maker should adopt an adequate production policy to hedge against future capacity shortages caused by machine failures in order to meet customer demand. This paper intends to extend previous findings to tackle this problem and study the overall decision making process aiming to guide the production and quality specification decisions in multiple-product context. The overall optimal decision policy is defined here as one that maximises the long term average per unit time profit of a combined measure of quality and quantity dependent sales revenue, minus inventory and backlog costs, in the presence of random plant failures and random repair durations.     

Optimal inventory policies for uniform replenishment systems with time-dependent demand

This study develops an analysis of lot size inventory systems where the replenishment rate is uniform and demand follows a power demand pattern. Shortages are not allowed. Holding cost, replenishing cost and purchasing cost are considered in inventory system control. The objective of the study is to find the economic production quantity that minimises total inventory cost per unit of time. We conclude that optimal inventory policies depend on the demand pattern index chosen to represent customer demand. Theoretical results are illustrated with a business case study. A sensitivity analysis is proposed to describe the optimal policy behaviour.     

Robust production control policy for a multiple machines and multiple product-types manufacturing system with inventory inaccuracy

Inventory inaccuracy often exists in manufacturing systems, which has great negative impact on the performance of production control, e.g. very high work-in-process holding cost or backlog penalty. To hedge against inventory inaccuracy, the robust production control problems will be investigated for a multiple machines and multiple product-types manufacturing system with uncertain production capacity. The objective of our problem is to minimise the average production cost. To solve this problem, a robust production control policy is developed, which is insensitive to the inventory record errors, and whose robustness is better than the traditional hedging point policy for optimal production control. Finally, numerical experiments are conducted to examine the performance of the proposed robust production control policy against inventory inaccuracy. Based on the experimental results, the conditions of applying the proposed policy are also obtained.     

Lead-time analysis and a control policy for production lines

We address a control problem for a production line that produces one product to stock and faces random demand. During stockouts, the system quotes a fixed response time for each arriving order, and the customers place their orders only if the response time promised meets their deadlines. Customer orders are filled on a first come, first served basis. A penalty cost is incurred whenever a customer is served later than promised. A two-parameter admission/inventory control policy is implemented that maintains a bounded backlog and a constant inventory position (total inventory minus backlog) in the system. For production lines with exponential processing times and Poisson demand, the mean profit rate of the system is computed analytically using closed queueing network formulae. For systems with general processing or interarrival time distributions, the profit rate is estimated via simulation. Simple properties are established that ensure that the profit maximising control parameters can be determined in finite time using exhaustive search. Numerical results show that the proposed policy performs better than the make-to-order/zero-inventory and the lost-sales/make-to-stock policies.     

FPA method for optimal production planning under availability/degradation machine and subcontracting constraint

This work treats an industrial problematic of a manufacturing system M₁ subject to random failure and that satisfies a random demand under required service level. To ensure the satisfaction of the demand, it calls up on a second manufacturing system M₂ that is a subcontractor and has a stochastic service level. This paper aims to determine an optimal production plan taking into account the degradation of the manufacturing system following its production rate and its availability. The unavailability of the machine M₁ is due to the non-negligible preventive and corrective maintenance actions duration. To consider a realistic case of the subcontractor, we consider that is not able to respond to the variation of the demand, and then it assumed that the manufacturer can order a minimum fixed quantity. We then derive an optimal production plan taking into account the degradation of the machine and simultaneously minimising: inventory, degradation and production cost. An algorithm based on finite perturbation analysis is proposed to determine the optimal production plan and the sensitivity study of the availability is presented.     

Joint hybrid repair and remanufacturing systems and supply control

The control of a stochastic manufacturing system that executes capital asset repairs and remanufacturing in an integrated system is examined. The remanufacturing resources respond to planned returns of worn-out equipment at the end of their expected life and unplanned returns triggered by major equipment failures. Remanufacturing operations for planned demand can be executed at different rates and costs corresponding to different replacement and repair modes. The replacement components inventory is provided by an upstream supply with random lead times. The objective is to determine a control policy for both the supply and remanufacturing activities that minimises the average repair/replacement, acquisition and inventory/shortage total cost over an infinite horizon. We propose a suboptimal joint remanufacturing and supply control policy, composed of a multi-hedging point policy (MHPP) for the remanufacturing stage and an (s, Q) policy for the replacement parts supply. The MHPP is based on two inventory thresholds that trigger the use of predefined remanufacturing modes. Control policy parameters are obtained combining analytical modelling, simulation experiments and response surface methodology. The effects of the distribution, mean and variability of the lead time are tested and a sensitivity analysis of cost parameters is conducted to validate the proposed control policy. We also show that our policy leads to a significant cost reduction as compared to a combination of a hedging point policy (HPP) and an (s, Q) policy.     

Economic batch quantity in a multi-stage production system

A mathematical model has been developed in this paper for determining the total annual variable cost for a product which requires processing on a number of production stages. The demand for the product is assumed uniform over time and it is manufactured in equal lot sizes. In order to minimize the manufacturing cycle time of o production lot, the movement of the items between production stages is in sub-batches of equal sizes, As a result of manufacturing a production lot in sub-batches, the following additional costs are incurred: (1) additional cost of stock holding for process inventory; (2) cost of transporting sub-batches; (3) cost of multiple set-ups. A simple method is then adopted for minimizing the total annual variable cost of the multistage production system. An example has been solved to illustrate the method.     

Influence of maintenance policies on multi-stage manufacturing systems in dynamic conditions

Manufacturing systems are subject to a degradation process that leads to machine failure if no action is taken. Machine failures reduce the performance of the manufacturing system with loss of profits. The research proposed here concerns the evaluation of the manufacturing system performance in dynamic conditions when different maintenance policies are implemented in a multi-machine manufacturing system controlled by multi-agent-architecture. There are two extreme maintenance policies that can be applied: no preventive maintenance, where action is taken on the failure state, and intensive preventive maintenance, which can eliminate unforeseen failures, but at a high cost. Dynamic policy maintenance is proposed to reduce the number of maintenance operations of the preventive policy. A discrete simulation environment has been developed in order to investigate the performance measures and the indexes of the costs of maintenance policies. The simulations have been conducted for several levels of mix, product demand and working time uncertainty. The simulation results show that the proposed approach leads to better performance for the manufacturing system and reduces the number of maintenance operations (cost index of the maintenance policy), except in the case of the mean time between failure, which is characterised by a very low standard deviation.