An integrated robust replenishment/production/distribution policy under inventory inaccuracy

In this paper, a centralised production/distribution system is studied, in which the manufacturer controls the processes of raw material ordering, production and final goods distribution. The inventory records of raw materials, work-in-process, final goods in the manufacturer and the retailers are inaccurate. The objective of this research is to develop an integrated policy that can hedge against the negative impact of inventory inaccuracy at all stages of a supply chain. To achieve this aim, a backward recursive integrated robust policy is constructed. First, the time, quantity and vehicle route of the next distribution are forecasted by a distribution sub-policy; then the forecasted distribution time and quantity are used as the objective of the production process control, which is implemented by a production control sub-policy. Raw materials are ordered by a replenishment sub-policy according to the forecasted raw materials consumption in the production process. Numerical experiments are conducted to verify the feasibility and robustness of the proposed policy, which shows that besides of deploying radio frequency identification (RFID) devices in inventory management systems for raw materials, WIPs, final goods of the manufacturer and the retailers, integrated robust policies also can be employed to hedge against the impact of inventory inaccuracy.     

Two-level hedging point control of a manufacturing system with multiple product-types and uncertain demands

This research is motivated by the co-operative production process of networked manufacturing systems (NMS). Manufacturing resource sharing and flexible production scheduling are two features of NMS. For an individual manufacturing system in an NMS, ‘flexible production scheduling’ means that it can produce multiple product-types and the switching of products is quick enough to respond to the demand fluctuation. ‘Manufacturing resource sharing’ means the utilisation of extra production capacity from other manufacturing systems in the NMS. Of course, that will bring extra cost. This paper focuses on the optimal production control problem of such a situation: one manufacturing system, multiple product-types, and uncertain demands. Here, it is assumed that there are two demand-levels for each product-type: the lower one and the higher one. The total normal production capacity is larger than the total lower demands and smaller than the total higher demands. If the total demands cannot be satisfied and the work-in-process (WIP) of all product-types decrease to a certain level, e.g. zero WIP, the extra production capacity may be utilised. For such a system, a new two-level hedging point policy is proposed, in which two hedging points (a higher one and a lower one) are given for each product-type. Different from the prioritised hedging point (PHP) policy which is usually applied to one-machine and multiple part-type systems, our control policy considers all part-types at the same prioritised level and keeps the work-in-process states of all product-types on a straight line in the state space. Thus, the total costs for WIP inventory and the occupation of extra capacity can be obtained in a closed form, which is a function with respect to the hedging points. Then the method for optimising the hedging points is proposed and the special structure of the optimal hedging point is obtained. Numerical experiments verify the optimality and the special structure of the hedging point obtained by our method.     

Two-critical-number control policy for a stochastic production inventory system with partial backlogging

This paper deals with a production–inventory control model with partial backlogging, in which a reflected Brownian motion governs the inventory level variation. We consider a single storage facility with infinite capacity and assume that shortages are allowed and the total amount of stock-out is a mixture of backordering and lost sales. In addition, the production facility is controlled by a two-parameter (m, M) policy, which switches the production rate when the inventory level reaches the threshold values. The aim is to determine the optimal control parameters m and M by minimising the long-run total expected cost of the system. Some results are illustrated using numerical examples. A sensitivity analysis of the optimal solution with respect to major parameters is also carried out.     

Joint pricing and inventory strategies in a supply chain subject to inventory inaccuracy

This paper focuses on pricing strategies, inventory policies for a supply chain when Radio Frequency Identification (RFID) technology is adopted to cope with inventory inaccuracy. The supply chain consists of one supplier and one retailer, in which the RFID tag price is shared between the supplier and the retailer. We present and compare the performance differences between a wholesale price contract and a consignment contract when the retailer is the Stackelberg leader and the supplier is the follower. Based on the optimal pricing and inventory decisions, an interesting observation of contract selection is that there are two critical values of inventory available rate such that when the inventory availability is less than the lower value, both the supplier and the retailer prefer a consignment contract; when the inventory availability is greater than the upper value, a wholesale price contract is their best choice; when the inventory availability is between the two values, the supplier prefers a wholesale price contract and the retailer prefers a consignment contract. Additionally, there exist threshold values of RFID tag price and sharing rate to determine the contract preference for the retailer. Furthermore, the profits of both the supplier and the retailer are independent of the RFID tag price sharing rate in a wholesale price contract, and the supplier has the incentive to invest in RFID tag cost in a consignment contract.     

Scheduling manufacturing systems with work-in-process inventory control: Reentrant systems

In this paper, we propose a procedure for production flow control in reentrant manufacturing systems. The system under study consists ofN machines and producesM product types simultaneously. Each part goes through the system following a predefined process and may visit a machine many times. All machines are subject to random failures and need random repair times. The scheduling objectives are to keep the production close to demand and to keep the WIP inventory level and cycle times at low values. The model is motivated by semiconductor fabrication production. A three-level hierarchical controller is constructed to regulate the production. At the top level of this hierarchy, we perform capacity planning by selecting the desirable buffer sizes and the target production level for each operation. A production flow rate controller is at the middle level which recalculates the production rates whenever a machine fails or is starved or blocked. The loading times for individual parts are determined at the bottom level of the hierarchy. Comparison with alternative control is made through simulation and it shows that the control policy performs well.     

Analysis of the steady state probability distribution of a manufacturing system under the prioritised hedging point control policy

In order to evaluate the average production cost of a multi-product-type, multi-stage and multi-parallel-machine manufacturing system (denoted as mP/mS/mM), one of the effective ways is to obtain its steady-state probability distribution. Because the two-product-type and multi-parallel-machine system that demand backlog is not allowed can be considered as a basic building block of the mP/mS/mM system, we begin by investigating the method of obtaining its steady-state probability distribution under the prioritised hedging point control policy. Although the shape of the distribution domains of the work-in-process (WIP) levels influences the steady-state probability balance equations, we develop a unified form of the marginal probability balance equations for all the possible shapes of distribution domains, which can be used to calculate the marginal probability distribution for each product type for the two-product-type and multi-parallel-machine system. Furthermore, we extend this analysis method to both the multiple-product-type, multi-parallel-machine, and single-stage system and the more complex mP/mS/mM system, and propose a method to obtain their approximate marginal probability distributions of the WIP levels. Finally, numerical experiments are conducted to verify the accuracy of the proposed method of analysing the steady-state probability distribution of an mP/mS/mM system.     

Joint replenishment and manufacturing activities control in a two stage unreliable supply chain

This paper deals with dynamic stochastic situations faced by supply chains. In this context, various interactions, disparate decisions and random phenomena must be considered. These issues are considered in this paper through a two stage supply chain control problem. The supplier and the transformation stage are both subject to random events such as periods of unavailability due to internal difficulties or market constraints. Our objective is to find information sharing control policies for the supply and production activities that minimises the expected discounted cost of ordering, inventories/backlog and transformation over an infinite horizon. This is an optimal control problem with state constraints and hybrid dynamics of the production and replenishment activities. It is shown that, from a mathematical point of view, the considered problem is difficult to tackle and it calls upon optimal and impulsive control theory notions. A dynamic stochastic model is thus proposed. The existence of an optimal control policy and Hamilton-Jacobi-Bellman optimality condition in terms of the value function of the problem are derived and discussed. A numerical schema is then proposed to solve the obtained optimality conditions equations. A complete control policy is finally developed. The confirmation of such a policy structure is illustrated through sensitivity analysis. Some particular cases are also presented and discussed.     

Optimal production plan for a multi-products manufacturing system with production rate dependent failure rate

This study deals with the problem of dependence between production and failure rates in the context of a multi-product manufacturing system. It provides an answer about how to produce (i.e. the production rates) and what to produce (i.e. which product) over a finite horizon of H periods of equal length. We consider a single randomly failing and repairable manufacturing system producing two products P_a and P_b . The product P_a is produced to supply the strategic demand d(k) of the principal customer via a buffer stock S over k periods (k?=?1,?2,?…?,?H). The second product P_b is produced to meet a secondary but very profitable demand. It is produced during a given interval at the end of each period k. We develop a genetic algorithm to determine simultaneously the optimal production rate of the first product during each period k and the optimal duration of the production interval of the second product, maximising the total expected profit.     

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.     

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.     

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.     

Optimal decision of an economic production quantity model for imperfect manufacturing under hybrid maintenance policy with shortages and partial backlogging

Considering the characteristics of the stochastic shift of the machine state and the uncertainty of the product quality of production, in this paper, we develop an optimisation decision of economic production quantity model for an imperfect manufacturing system under hybrid maintenance policy with shortages and partial backlogging. We assume that the production process is imperfect stemming from the machine reliability and the probability of out-of-control, a hybrid maintenance policy combined of emergency maintenance and preventive maintenance is executed during each production run. Three decision models based on the scenarios of machine breakdown and repair time are developed. The optimal production quantity and maintenance inspection number during each production run are solved with minimising the expected average cost of the system. Numerical examples are used to demonstrate the effectiveness and feasibility of the model. Sensitivity analysis is conducted to analyse the impacts of key parameters on the optimal decision. Some implications related to the effective and economical execution of maintenance policy for practitioners are derived.     

An Environmental Hedging Point Policy to control production rate and emissions in unreliable manufacturing systems

This paper proposes a new Hedging Point Policy (HPP) which integrates environmental concerns into the optimal control of unreliable manufacturing systems. The considered system is composed of a production facility subjects to random failures and producing a product family intended for a given market with stable demand. The manufacturing facility’s operations cause harmful emissions to the environment, and may incur sanctions in the form of an environmental tax imposed by the relevant authorities. Given the significant compromise that must take place between inventory, backlog and taxes costs, the main objective of this paper is to propose a feedback adaptive control policy which provides a better control of the production rate and the emissions generated. Under the HPP category, a new structure called the Environmental Hedging Point Policy (EHPP) is proposed. To illustrate the effectiveness of the proposal, an experimental approach based on simulation modelling, variance analysis and response surface methodology (RSM) is applied. The results show a significant gain in terms of incurred costs compared to those incurred when the system is governed by a classical HPP. An improved version of EHPP is also proposed for systems with high emission rates. Several sensitivity analyses are conducted to illustrate the robustness and effectiveness of the proposed policies.     

On the stability and bullwhip effect of a production and inventory control system

This paper focuses on the discrete-time automatic pipeline, inventory and order-based production control system (APIOBPCS), a well-established production and inventory control model. The feedback mechanism within the replenishment rule enables the model to mitigate the bullwhip effect, but introduces a stability problem. In this research, a comprehensive stability analysis is conducted for arbitrary lead times using difference equation theory. On the basis of stability, a state space approach is advocated to analyse the impact of replenishment parameters, demand processes, and lead times on the robustness of the bullwhip effect. The stability results demonstrate that the production control system can easily be destabilised without incorporating the work-in-progress (WIP) feedback loop. Furthermore, it reveals that the stability problem for long lead times can be simplified with the stability condition independent of the lead time. The results obtained in this study provide useful guidelines for the selection of replenishment parameters to guarantee stability and mitigate the bullwhip effect.     

An optimised target-level inventory replenishment policy for vendor-managed inventory systems

In vendor-managed inventory (VMI) systems the supplier is responsible for replenishing customers and for deciding when and how much to deliver. One of two inventory policies is typically employed by the supplier. The first one, called the maximum level (ML) policy, gives full freedom to the supplier to deliver any quantity as long as it respects customer inventory capacities. The alternative, which is more constrained, is called the order-up-to (OU) policy. It states that the supplier has to bring the customer inventory up to its maximum capacity level upon delivery. We propose a new tactical policy in the context of VMI systems, called optimised target-level (OTL), under which when the supplier visits a customer, the quantity delivered is such that the final inventory will always be at the same customer-dependent OTL. We perform a computational evaluation of this new policy against both traditional strategies on benchmark instances. We show that it yields lower costs and inventory levels than the OU policy, and is only marginally more expensive than the ML policy, while being easier to implement.     

Reverse Logistics: a stochastic EOQ-based inventory control model for mixed manufacturing/remanufacturing systems with return policies

This paper focuses on mixed manufacturing/remanufacturing systems, where manufacturing or purchase of new items integrates product reuse or remanufacturing, with the purpose to achieve a complete and timely demand satisfaction. We formulate a stochastic Economic Order Quantity (EOQ)-based inventory control model for a mixed manufacturing/remanufacturing system. The model is intended to identify the need of placing a manufacturing/purchasing order, to avoid the occurrence of stock-out situations. We then formulate a total cost minimisation problem, to derive the optimal return policy, this latter being a financial incentive paid to customers to increase the flow of returned items. The model developed is investigated through simulations, in order to assess the effect of stochasticity (of demand, return fraction and return delay) on the optimal return policy of the system; then, it is validated through a case study, to derive indications concerning its practical application in real cases. Our study ultimately provides a framework for practitioners to establish EOQ policies in reverse logistics contexts and to evaluate the opportunity of establishing a return policy in those contexts.     

Robust production planning and control for multi-stage systems with flexible final assembly lines

Production planning of final assembly systems is a challenging task, as the often fluctuating order volumes require flexible solutions. Besides, the calculated plans need to be robust against the process-level disturbances and stochastic nature of some parameters like manual processing times or machine availability. In the paper, a simulation-based optimisation method is proposed that utilises lower level shop floor data to calculate robust production plans for final assembly lines of a flexible, multi-stage production system. In order to minimise the idle times when executing the plans, the capacity control that specifies the proper operator–task assignments is also determined. The analysed multi-stage system is operated with a pull strategy, which means that the production at the final assembly lines generates demands for the preceding stages providing the assembled components. In order to guarantee the feasibility of the plans calculated for the final assembly lines, a decomposition approach is proposed to optimise the production plan of preceding stages. By this way, the robust production can be ensured resulting in reduced losses and overall production costs even though the system is exposed to changes and disturbances.     

Optimal policy in a hybrid manufacturing/remanufacturing system with financial hedging

This paper proposes a hybrid manufacturing/remanufacturing model with the financial hedging in the case where the randomness in demand is correlated with the financial markets. The provided models are mainly for those risk-averse remanufacturers who faced with random demand and yield. The aim of this paper is to maximise remanufacturer utility by purchasing financial instruments and producing new and remanufactured products. A hybrid manufacturing/remanufacturing system production planning model is first built under mean-variance framework, and then the financial hedging is integrated into the hybrid production system. There are three main findings. First, the variance of profit with financial hedging is always less than the variance of the model without financial hedging. Second, the remanufacturer with high (low) risk aversion is more likely to produce new (remanufactured) products. Third, the model without (with) financial hedging tends to produce new (remanufactured) products unless remanufacturing cost is low (high) enough. All those findings proved that financial hedging can reduce the operational uncertainty effectively and increase the proportion of remanufacturing, which will make remanufacturing firms more economical and environmentally friendly. Therefore, remanufacturing firms can consider using financial hedging to reduce operational uncertainty.     

Production and subcontracting control for an unreliable manufacturing system with setups

This paper deals with the problem of joint production, setup and subcontracting control of unreliable manufacturing systems producing two product types. The production requires setups each time it switches from one product type to another. Subcontracting is an integral part of the decision-making process due to limited production capacity in existing facility. The objective is to propose an effective control policy for the considered system which simultaneously manages production, setup and subcontracting activities. The complexity of the problem lies in the interaction between internal manufacturing decisions and subcontracting that outsource a part of the production, in a dynamic and stochastic environment. An experimental optimisation approach is adopted to determine the optimal control parameters which minimise the average total cost. Extensive sensitivity analyses are performed to illustrate the robustness and the usefulness of the adopted approach. An in-depth study comparing five control policies across a wide range of system parameters is also conducted. Extended cases closer to reality are also investigated considering elements such as the preventive maintenance and the production of non-conforming products. The best control policy in terms of economic performance is then obtained. Valuable insights providing a better understanding of interactions involving production, setup, and subcontracting are discussed.     

On deficiencies of common ordering policies for multi-level inventory control

We consider two common types of ordering policies for multi-level inventory control: installation stock (R,Q)-policies and echelon stock (R,Q)-policies. The batch quantities are assumed to be given, but each policy is optimized with respect to its reorder point R. We demonstrate that there is no bound for the worst case performance ratio of these policies when applied to distribution inventory systems with a central warehouse and a number of retailers.