Optimal preventive maintenance in a production inventory system

We consider a production inventory system that produces a single product type, and inventory is maintained according to an (S, s) policy. Exogenous demand for the product arrives according to a random process. Unsatisfied demands are not back ordered. Such a make-to-stock production inventory policy is found very commonly in discrete part manufacturing industry, e.g., automotive spare parts manufacturing. It is assumed that the demand arrival process is Poisson. Also, the unit production time, the time between failures, and the repair and maintenance times are assumed to have general probability distributions. We conjecture that, for any such system, the down time due to failures can be reduced through preventive maintenance resulting in possible increase in the system performance. We develop a mathematical model of the system, and derive expressions for several performance measures. One such measure (cost benefit) is used as the basis for optimal determination of the maintenance parameters. The model application is explained via detailed study of 21 variants of a numerical example problem. The optimal maintenance policies (obtained using a numerical search technique) vary widely depending on the problem parameters. Plots of the cost benefit versus the system characteristic parameters (such as, demand arrival rate, failure rate, production rate, etc.) reveal the parameter sensitivities. The results show that the actual values of the failure and maintenance costs, and their ratio are significant in determining the sensitivities of the system parameters.     

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.     

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 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.     

时变变质率产品的订购-定价策略

研究时变变质率产品的订购与定价联合决策问题。以系统平均利润最大化为目标函数且将已变质产品的变质处理成本考虑在内,构建了相应的订购与定价联合决策模型,其中需求同时依赖于价格和库存水平、系统允许缺货且缺货量部分延迟订购。接着,对于已知的定价策略,证明并给出了最优补货策略唯一存在的充分条件;另一方面,对于已知补货策略的情况也证明了最优定价策略的存在性。此外,证明了在联合订购与定价决策下得到的最优销售价格总是大于单独进行定价决策时得到的最优价格。进而,在模型证明和分析的基础上给出一个寻求最优解的算法。最后,通过数值模拟的方法对模型中主要参数的灵敏度进行了分析,并给出相应的管理建议。结果表明：如果零售商忽略库存水平对需求的影响或变质处理成本,制定的销售价格将偏低;对于价格弹性较高的产品,零售商应采取低价销售策略;当顾客的等待耐心较差或产品的替代性较强时,最优策略应该是提高产品的销售定价并缩短缺货期。     

Shortage decision policies for a fluid production model with MAP arrivals

We consider on a continuous production/inventory process where a single machine produces a certain product into a finite buffer. The demands arrive according to a Markov Additive Process governed by a continuous-time Markov chain, and their sizes are independent and have phase-type distributions depending on the type of arrival. Two shortage policies are considered: the backorder policy, in which any demand that cannot be satisfied immediately is backlogged, and the order policy, in which any demand that cannot be satisfied immediately is supplied (alternatively, the latter policy can be considered as lost sales). We assume that the total cost includes a production loss cost, a penalty cost, a fixed cost for an order and a variable cost for the ordered amount. By applying the regenerative theory, we use tools from the exit-time theorem for fluid processes to obtain the discounted cost functionals under both policies. In addition, the models are extended to include a non-zero safety stock. Numerical examples, sensitivity analysis and comparative study are included.     

A distribution free newsvendor model with consignment policy and retailer’s royalty reduction

Reducing the system cost and achieving significant profit are the key factors for every successful business sector. A consignment contract under distribution-free approach may be a fruitful combination to achieve a profitable business. This model deals with a single-period newsvendor problem with a consignment policy. The consignment policy is an agreement between any two parties, named as the consignor and the consignee. Under Stackelberg approach, firms act as leader and follower. Both parties carry some parts of the holding cost instead of one. A new policy for paying the fixed fee to the consignee is introduced. This paper considers no specific probability distribution for customer’s demand except a known mean and standard deviation. An efficient approach is proposed to reduce the retailer’s cost and building a sustainable consignment contract. The solution of this model is obtained using distribution free approach. A comparison between the traditional supply chain policy and the consignment policy is established. The price-sensitivity on demand is analysed. Some numerical examples and graphical representations are given for both traditional and consignment policy. Result proves that consignment policy is dominating over the traditional policy and a significant reduction of retailer’s royalty is found.     

A decomposition method for multi-product kanban systems with setup times and lost sales

We consider kanban controlled production systems with three or more different products processed on a single manufacturing facility. Customers for a product arrive according to a Poisson process. If a customer's demand cannot be met from stock, the customer leaves and satisfies his demand elsewhere (lost sales). Between the production of different products setup changes must be performed that take a significant time. Setup times and processing times are product-specific and follow exponential distributions. A production run continues until the target inventory level given by the number of kanbans for the product has been reached (exhaustive processing). Then the manufacturing facility is set up for the next product according to a fixed setup cycle. The exact model is mathematically intractable even for smaller systems. Therefore, we propose a decomposition-based approximation method for estimating steady-state performance measures     

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.     

The effect of supply and demand uncertainties on the optimal production and sales plans for new products

When introducing a new product, firms face a hierarchy of decisions at the strategic and operational levels including capacity sizing, time to market or starting sales, initial inventory required by the product’s release time and production management in response to changes in the demand (hereafter referred to as production-sales policies). The goal of this paper was to show the importance of considering both supply and demand uncertainties in the determination of the production-sales policy which has been overlooked in the existing literature. More specifically, we test two main hypotheses: (1) ignoring supply and demand uncertainties may lead to potentially incorrect decisions; and, (2) the decision could be different if risk is used as the primary performance measure instead of the commonly used expected (mean) profit. We perform extensive experimentation with a Monte Carlo simulation model of the stochastic supply-restricted new product diffusion and use different statistical procedures, namely, the Welch’s t-test and a nonparametric double-bootstrap method to compare the average and percentiles of the profit for different policies, respectively. The results indicate that the correctness of the two hypotheses depends on the diffusion speed, consumers’ backlogging behaviour, production capacity, price and variable production and inventory costs. The findings also have important implications for managers regarding market entry time, parameter estimation, production strategy and the implementation of the proposed model.     

An application of cost-effective fuzzy inventory controller to counteract demand fluctuation caused by bullwhip effect

This paper develops a fuzzy inventory model to counteract the demand fluctuation in supply demand networks, which combines fuzzy logic controller with (s,?S) policy based on economic order quantity (EOQ) model. Following a literature review and a discussion of counteractions to the bullwhip effect and the obstruction of general counteraction in supply demand networks, a multi-echelon fuzzy inventory model in supply demand networks is proposed. A simulation model with one- and two-echelon supply demand network is built and tested for (s, S) policy based on the classical EOQ model and the proposed fuzzy inventory model. Based on the simulation, results of the relevance performance are presented and discussed, which show that the proposed multi-echelon fuzzy inventory model provides not only a cost-effective management of inventory (e.g. lower inventory levels and cost) in market uncertainty, but also another effective alternative for counteracting demand fluctuation. In particular, the proposed multi-echelon fuzzy inventory model shows benefit in counteracting demand fluctuation in multi-echelon supply demand networks. Finally, some conclusions and suggestions for further research works are presented.     

Infinite horizon production planning with periodic demand: solvable cases and a general numerical approach

In this paper, we consider a single part-type pull manufacturing system, which controls its production rates in response to periodic demand. When tracking the demand results in a product surplus, an inventory storage cost is incurred. Likewise, if an overall shortage occurs then a backlog cost is paid. In addition, production costs accrue when the system is not idle. Given an infinite planning horizon, the objective is to determine the cyclic production rates in order to minimize the total cost. With the aid of the maximum principle, extremal behavior of the system is studied and the continuous-time production planning problem is reduced to a discrete problem with a limited number of switching points at which time the production rates change. Using this result, an efficient numerical algorithm is proposed, which will yield an approximation to the optimal solution within any desired level of accuracy. In addition, we determine the analytical solution to the problem for three special cases: (i) the system capacity is not limited and the inventory storage cost factor is equal to the backlog cost factor; (ii) the production cost is negligible; and (iii) the surplus and shortages costs are negligible.     

Lot-sizing for a single-product recovery system with backordering

In this article, a single-product recovery system is studied. Used products are collected from customers and kept at the recoverable inventory warehouse for future recovery. The constant demand rate can be satisfied either by newly produced products or by recovered ones (serviceable inventory), which are regarded as perfectly as the new ones. Excess demand is completely backordered. Following an exact analytical approach, the optimal production and recovery policy is obtained. A numerical cost comparison of this model with the corresponding one without backordering is also performed. The results are general, as they were valid for finite and infinite production and recovery rates.     

Production control in a complex production system using approximate dynamic programming

Development of an efficient production and inventory control policy for a production system with multiple working stations, intermediate components and end products is difficult. In particular, uncertain demand and large changeover times at the work stations cause significant problems. In this paper, we consider an assembly line for dishwashers which require multiple types of wire racks that must be fabricated and coated at different work centres before supplying the assembly lines. An approximate dynamic programming (ADP) method is proposed to address the complexities associated with such a system. In addition, an Artificial Neural Network model is designed to approximate state values of the system, thus helping the system to make decisions at particular states. A near optimal production and inventory control policy is developed through an ADP algorithm. The proposed method can be extended to any similar system.     

Models for integrated production-inventory systems: steady state and cost analysis

We consider a two-echelon production-inventory system with a central supplier connected to production systems (servers) at several locations, each with a local inventory. Demand of customers arrives at each production system according to a Poisson process and is lost if the local inventory is depleted. To satisfy a customer’s demand, a server at the production system takes exactly one unit of raw material from the associated local inventory. The central supplier manufactures raw material to replenish the local inventories, which are controlled by a continuous review base stock policy. We derive stationary distributions of joint queue length and inventory processes in explicit product form. After performing a cost analysis, we find out that the global search for the vector of optimal base stock levels can be reduced to a set of independent optimisation problems. The explicit form of the stationary distribution enables us to get additional structural insights, e.g. about monotonicity properties and stability conditions. Obtaining the product form relies on some simplifying assumptions. The results are therefore compared with simulations of a more realistic system, which supports to use it as approximation.     

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.     

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.     

An integrated inventory model involving manufacturing setup cost reduction in compound Poisson process

The collaboration of vendor and buyer is one of the key factors for successful supply chain management. The most common strategy for a cooperative system is to propose an integrated replenishment plan. Almost all inventory models assume that setup cost is deterministic and is not subject to control. However, in many practical situations, setup cost can be reduced at an added investment. The paper assumes that setup cost can be reduced at an added investment and shortage is permitted during the lead time. This article relaxes the assumption that the demand of lead time is deterministic and is assumed to be a compound Poisson process. A model is derived to determine an optimal integrated inventory policy with controllable setup cost. The expected annual integrated total cost function is derived and a solution procedure is established to find out the optimal solution. Finally, a numerical example is provided to illustrate the solution procedure.     

Joint production and shipment lot sizing for a delivery price-based production facility

A joint economic production quantity (EPQ) and delivery quantity model for a production system is investigated in this paper. More specifically, an EPQ policy is implemented in the production system, while a smaller shipping quantity is periodically dispatched to the customer. The production system is also responsible for the shipment cost, i.e. a delivery price-based procurement from the customer. The considered cost includes setup cost to launch the batch production, inventory carrying cost, and transportation cost, where the transportation cost is a function of the delivery quantity. A per unit time cost model is developed and analysed to determine the optimal production and delivery quantities. Under some mild conditions, it can be shown that the joint cost function is convex with respect to the production quantity; and the number of delivery is an integer in each replenishment cycle. Computational study has demonstrated the significant impact of the joint decision model on the operating cost. In particular, the reduction in total cost can be more than 15% when inventory carrying costs, and/or transportation costs, are high.     

Unique optimal solution to a multiperiod,single product,single stage production smoothing problem

A single product, single Btage, multiperiod production smoothing problem is considered in this paper. Demands are monotonically increasing in successive periods, and in each period, they occur at a uniform rate. The important feature is that a production run can be started or ended at any time, and not necessarily at the start of any period. Considering production costs, costs due to change of production rate and inventory costs, unique optimal policies are derived. The special feature of the solution is that no iterative search procedure is needed to arrive at the optimal policy. On the other hand, a set of three conditions are derived. Once any one of these conditions is satisfied, the optimal policy is easily determined. Cost formulae are given for optimal policies derived. Three examples are solved to illustrate the optimal policies derived. Finally scope for application of the model is suggested.