Base-stock control for single-product tandem make-to-stock systems

In this paper, we consider a multiple-stage tandem production/inventory system producing a single product. Processing time at each stage is assumed to have a general stationary processing time distribution. The cost of holding work-in-process (WIP) inventory is different at each stage. Therefore, decisions on when to release work to the system as well as when to transfer WIP from one stage to another need to be made. We formulate this problem of release/production control as a Markov decision process. However, the optimal policy is rather complex, making its implementation impracticable in practice. We therefore investigate the performance of simple base stock policies. Our approach aggregates several stages into one and uses a simple approximation to compute approximately optimal base stock levels. We present the results of a simulation study that tests the performance of our approximation in estimating the best base stock levels, and the performance of base stock policies as compared with the optimal policy.     

Base stock versus WIP cap in single-stage make-to-stock production–inventory systems

A single-stage production-inventory system produces parts in a make-to-stock mode, and unsatisfied demand is backordered. The system operates under a so-called base stock with WIP cap replenishment policy, which works as follows. Whenever the Work-In-Process (WIP) plus finished goods inventory falls below a specified level, called base stock, a replenishment order for the production of a new part is issued. If the WIP inventory is below a different specified level, called WIP cap, the order goes through and a new part is released for production; otherwise, the order is put on hold until the WIP inventory drops below the WIP cap. First, it is shown that the optimal base stock that minimizes the long-run, average, inventory holding cost for a given minimum customer service level, is a non-increasing function of the WIP cap that reaches a minimum value, called minimum optimal base stock, at a finite WIP cap value, called critical WIP cap. Then, it is shown that the optimal WIP cap is less than or equal to the critical WIP cap and therefore the optima! base stock is greater than or equal to the minimum optimal base stock. More interestingly, however, it is conjectured that the optimal WIP cap is in fact exactly equal to the critical WIP cap and therefore the optimal base stock is exactly equal to the minimum optimal base stock. The minimum optimal base stock is none other than the optimal base slock of the same system operating under a classical base stock policy (with no WIP cap). Finally, the optimal parameters of a system operating under a base stock with WIP cap policy are related to the optimal parameter of the same system operating under a make-to-stock CONWIP policy.     

Optimal composition of number and size of machines in a multi-stage make-to-order system with due dates

We develop an optimisation model to minimise costs for work-in-process (WIP), finished goods inventory (FGI), backorders, and capacity for a multi-stage production system applying a work-ahead window work release policy. Customers arrive to a make-to-order production system and have stochastic due dates. The parameters to optimise are the capacity invested at each stage, consisting of the number of machines and the processing rate (defined by a set of possible processing rates), as well as the work-ahead window. An optimality condition is provided showing when it is optimal to invest into a single machine at each stage if processing rates are continuous decision variables. The optimality of increasing capacity towards the customer end of the production line is proven under certain conditions. For a special case consisting of two stages with M/M/s queues with exponentially distributed customer required lead time, explicit expressions for WIP, FGI and backorders are developed. A set of numerical examples illustrates the influence of predefined processing rates on the optimal number and selection of machines. A simple solution heuristic for the problem with a predefined set of processing rates is proposed and its performance is shown in a numerical example. Additionally, the influence of uncertain input rates into the production system is discussed.     

Optimal production operations sequencing

The goal of this research is to address the following issues: Under what circumstances should a company perform operations resequencing? Which design leads to the most desirable inventory cost and customer service trade-off? For make-to-stock production–inventory systems with no WIP safety stocks, we establish the optimal production operations sequencing and determine easy-to-use criteria for resequencing when technologically possible. We show that in many cases, resequencing decisions can be made using a graphical decision tool, namely cost–time profiling. For more complex systems with work-in-progress safety stock inventories, we analyze how system attributes drive overall performance. Some specific resequencing opportunities are examined in terms of their effects on cost and on the levels of optimum safety stocks.     

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.     

Analyzing the effect of inventory policies on the nonstationary performance with transfer functions

In this paper we apply transfer function methods to analyze the performance of supply chains in response to nonstationary demand and, in particular, we investigate how various inventory policies and demand forecasting parameters affect supply chain responsiveness. In a single-echelon inventory system we investigate the performance of a common base stock policy. Specifically, we describe the order and inventory trajectories using discrete transfer functions, and we derive closed-form analytical expressions for the transient behavior in response to a step change in demand. We introduce performance measures commonly used to analyze nonstationary performance and derive closed-form expressions for these measures. Next, we study the performance of a two-echelon supply chain under installation stock and echelon stock policies. We explicate the performance tradeoff in response to stationary versus nonstationary demand, and show that the transient response of orders and inventory levels can be either underdamped or overdamped depending on the exponential smoothing parameter. We show that the echelon stock policy is more responsive than the installation stock policy when both policies have similar stationary performances.     

Decentralized multi-product multi-stage systems with backorders

A multi-stage production/inventory system with decentralized two-card kanban control policies producing multiple product types is considered. The system involves one-at-a-time processing at each stage, finite target levels in the buffers and batch transfers between production stages. The demand process for each product is assumed to be Poisson and excess demand is backordered. Products have a priority structure and the processor at each stage is shared according to a switching rule. Our objective is to obtain steady-state performance measures such as the average inventory and service levels for each product type. We propose an approximation algorithm based on: (i) characterization of the delay by a product type before receiving the processor's attention at each stage; and (ii) creation of subsystems for all the storage activity and phase-type modeling of the remaining system's behavior. Numerical examples are presented to show the accuracy of the method and its potential use in system design.     

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.     

Production planning with stochastic seasonal demandand capacitated production

We consider a production/inventory problem with stochastic seasonal demand. A scarce resource limits production in each time period, and setup time is negligible. Linear and stationary costs are assessed for production, holding inventory, and stock-outs. The calculation of optimal solutions is difficult so heuristics are used. The heuristics used in business practice are shown to cost an average of 30% above optimal policy costs. A superior heuristic is constructed utilizing an analytic approximation for optimal policies that costs an average of 2% over optimal policy costs.     

Control of a manufacturing system with random product yield and downward substitutability

We consider a manufacturing system where the quality of the end product is uncertain and is graded into one of several quality levels after production. We assume stochastic demand for each quality level, stochastic production times, and random quality yields. We also assume downward substitutability (i.e., customers who require a given product will be satisfied by a higher quality product at the same price). The firm produces to stock and has the option to refuse satisfying customers even when it has items in stock. We formulate this problem as a Markov Decision Process in the context of a simple M/M/1 make-to-stock queue with multiple customer classes to gain insight into the following questions: (i) how does the firm decide when to produce more units (i.e., what is the optimal production policy?) and (ii) how does the firm decide when to accept/reject orders and when to satisfy customers demanding lower quality products using higher quality products? In the case of two product classes, we completely characterize the structure of the optimal production and acceptance/substitution policies. However, the structure of the optimal policy is complicated and we therefore develop a simple heuristic policy for any number of classes which performs very well. We finally extend our heuristic to the system where production occurs in batches of size of larger than one, the system where there is a setup cost for initiating production, and the case where processing time distribution is Erlang.     

Single-item production–delivery scheduling problem with stage-dependent inventory costs and due-date considerations

This paper studies an integrated scheduling problem for a single-item, make-to-order supply chain system consisting of one supplier, one capacitated transporter and one customer. Specifically, we assume the existence in the production stage of an intermediate inventory that works as a buffer to balance the production rate and the transportation speed. Jobs are first processed on a single machine in the production stage, and then delivered to the pre-specified customer by a capacitated vehicle in the delivery stage. Each job has a due date specified by the customer, and must be delivered to the customer before its due date. Moreover, it is assumed that a job that is finished before its departure date or arrives at the customer before its due date will incur a stage-dependent corresponding inventory cost (WIP inventory, finished-good inventory or customer inventory cost). The objective is to find a coordinated production and delivery schedule such that the sum of setup, delivery and inventory costs is minimised. We formulate the problem as a nonlinear model in a general way and provide some properties. We then derive a precise instance from the general model and develop a heuristic algorithm for solving this precise instance. In order to evaluate the performance of the heuristic algorithm, we propose a simple branch-and-bound (B&B) approach for small-size problems, and a lower bound based on the Lagrangian relaxation method for large-size problems. Computational experiments show that the heuristic algorithm performs well on randomly generated problems.     

酒品包装生产中动态缓冲管理机制

考虑存在资源约束的流线式酒品包装生产车间,为了减少企业生产成本,提出了一种以控制在制品(WIP)库存为主要参考指标的动态缓冲管理方法。本方法通过实时监控缓冲区的WIP库存,根据在监控窗口中缓冲区出现WIP库存由高于安全下限变化到低于安全下限的频率以及随后是否出现WIP库存耗尽的情况,对库存安全上下限进行动态调节进而实现对缓冲的动态管理。为了验证方法的有效性,安排了3组不同的仿真实验。实验结果表明：与传统的缓冲管理策略相比,基于动态缓冲管理策略的控制方法在WIP库存控制方面存在22%以上的优势,采用该方法可以有效的控制生产系统中的在制品库存。     

Performance Opportunity for Workforce Agility in Collaborative and Noncollaborative Work Systems

To gain insight into the potential logistical benefits of worker cross-training and agile workforce policies, we study simple models of flexible workers in serial production systems. The primary control issue is how to assign workers to jobs/stations over time. Under assumptions of complete worker flexibility and collaborative work, we prove that a simple expedite policy minimizes along each sample path the cycle time (delay) for each job. Therefore, the expedite policy also minimizes work in process and maximizes throughput along every sample path. We also compute the performance improvement opportunity achievable using flexible workers as opposed to the optimal static allocation of workers. This enables us to examine th e factors that make workforce agility a potentially attractive strategy. We also consider the intuitive analog of the expedite policy for the noncollaborative work environment, which we call the pick-and-run policy; however, we demonstrate by counterexample that it is not always optimal. Finally, we extend some of our insights from the demand-constrained environment to a capacity-constrained environment operating under a CONstant WIP (CONWIP) protocol     

Optimal batch ordering policies for assembly systems with guaranteed service

For a supply chain modelled as a multi-echelon inventory system, effective management of its inventory at each stock is critical to reduce inventory costs while assuring a given service level to customers. In our previous work, we used the guaranteed-service approach (GSA) to design optimal echelon batch ordering policies for continuous-review serial systems with Poisson customer demand and fixed order costs. The approach assumes that the final customer demand is bounded and each stock has a guaranteed service time in the sense that the demand of its downstream stock can always be satisfied in the service time. This paper extends this work by considering more general assembly systems. We first derive an analytical expression for the total cost of the system in the long run. The problem of finding optimal echelon batch ordering policies for the system can then be decomposed into two independent sub-problems: order size decision sub-problem and reorder point decision sub-problem. We develop efficient dynamic programming algorithms for the two sub-problems. Numerical experiments on randomly generated instances show the effectiveness of the proposed approach.     

考虑双目标的JIT生产系统看板数量设定

针对现有JIT系统看板数量决策问题研究多以单目标为主的不足,提出了一种基于实验设计的双目标JIT生产系统看板数量设定方法。该方法同时考虑了高订单满足率和低系统平均在制品水平的双目标优化,以B公司CR油嘴JIT生产系统为例,建立了该JIT生产线的Witness仿真模型以实现数据的收集,以各看板循环回路的看板数量和看板容量进行水平设定,并进行正交实验设计及数据的直观分析处理,然后采用全因子实验的方法,基于帕累托最优的思想获得生产系统看板数量帕累托最优解,形成近似最优看板数量组合的帕累托最优前沿。生产管理人员可根据不同的生产计划和绩效目标从组合中选择合适的看板数量。最后的研究结果验证了该方法的可行性和有效性。     

Effect of modeling fixed cost in a serial inventory system with periodic review

We study a two-echelon serial inventory system with stochastic demand. We assume that fixed ordering costs are charged only when an order initiates a non-zero shipment. The system is centrally controlled and ordering decisions are based on echelon base stock policies. The review period of the upper echelon is an integer multiple of the review period of the lower echelon. We derive an exact analytical expression for the objective function. From this expression, we determine optimal base stock levels and review periods. Through a numerical study we show that there may be several combinations of optimal review periods and that under high fixed ordering costs both stockpoints have the same order frequency. In addition, we identify parameter settings under which the system behaves like a PUSH-system, where the upstream stockpoint never holds any stock. Generally, in literature fixed ordering costs are charged at every review moment, even if no shipment results due to zero upstream stock. We test the impact of this simplifying assumption and illustrate when it is justified.     

Integrating advance order information in make-to-stock production systems

Increased cooperation between supply chain partners and information technology are enabling the availability of advance order information for contract suppliers. Control mechanisms that take into account this availability are necessary in order to achieve the potential improvements in performance. We investigate the structure of optimal control policies for a discrete-time make-to-stock queue with advance order information, Since the optimal policy does not have a simple structure, we then propose a heuristic policy which is an extension of the base stock system that incorporates advance order information through a release lead time parameter. In order to quantify the benefits due to advance order information, we investigate the performance of the proposed mechanism and benchmark it against against the optimal control policy.     

An inventory model with emergency orders under explicit energy cost considerations

The inventory model in this paper is targeted to production systems with constant production rates but underlying possibilities for undesirable circumstances to threaten the production schedule. The inventory policy proposed explicitly considers energy cost when determining optimal size for order quantity, safety stock and inventory cycle length such that the total expected cost per unit time is minimised. The results are compared to a traditional inventory policy that does not consider the direct impact of energy cost. An analysis of the model reveals three production environment characteristics in which inventory policies are most significantly affected by changes in energy cost: heavy product weight, high regular product demand or high emergency product demand. If any one of the three key factors increases, then changes of the inventory decisions or related logistics costs become more significant. The cost effectiveness of implementing the proposed inventory policy also becomes more significant as any one of the three key factors increase with respect to energy cost.     

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.     

Petri Net model of repetitive push manufacturing with Polca to minimise value-added WIP

A common simplifying assumption used in the literature is to minimise average Work In Process (WIP), while achieving maximum production rate, which does not consider the fact that the value of WIP increases down the stream of a production process as labour, time, energy and resources are added to it. This paper aims at minimising queues of parts waiting downstream of production process and in turn minimising value-added WIP by constraining more and more inventory of unfinished products at the earlier stages of production. For this reason, generic black token closed loop Petri Net (PN) model of Flexible Flow Shop (FFS) with Paired-cell Overlapping Loops with Card Authorisation (POLCA) is developed. Tokens in the control loops represent Polca cards to control the flow of material from order release till finished products. Marking of PN is done through Mix Integer Linear Programming after the computation of semi-positive P invariants. Simulation is being done to obtain queues of parts, waiting at each station during demand variation. Results were compared with PN model of FFS without Polca. Results showed the constriction of unnecessary WIP towards the initial stage of production instead of at bottlenecks, with proposed model, and in turn minimisation of value-added WIP.