Incorporating demand uncertainty and forecast error in supply chain planning models

This paper develops a framework for examining the effect of demand uncertainty and forecast error on unit costs and customer service levels in the supply chain, including Material Requirements Planning (MRP) type manufacturing systems. The aim is to overcome the methodological limitations and confusion that has arisen in much earlier research. To illustrate the issues, the problem of estimating the value of improving forecasting accuracy for a manufacturer was simulated. The topic is of practical importance because manufacturers spend large sums of money in purchasing and staffing forecasting support systems to achieve more accurate forecasts. In order to estimate the value a two-level MRP system with lot sizing where the product is manufactured for stock was simulated. Final product demand was generated by two commonly occurring stochastic processes and with different variances. Different levels of forecasting error were then introduced to arrive at corresponding values for improving forecasting accuracy. The quantitative estimates of improved accuracy were found to depend on both the demand generating process and the forecasting method. Within this more complete framework, the substantive results confirm earlier research that the best lot sizing rules for the deterministic situation are the worst whenever there is uncertainty in demand. However, size matters, both in the demand uncertainty and forecasting errors. The quantitative differences depend on service level and also the form of demand uncertainty. Unit costs for a given service level increase exponentially as the uncertainty in the demand data increases. The paper also estimates the effects of mis-specification of different sizes of forecast error in addition to demand uncertainty. In those manufacturing problems with high demand uncertainty and high forecast error, improved forecast accuracy should lead to substantial percentage improvements in unit costs. Methodologically, the results demonstrate the need to simulate demand uncertainty and the forecasting process separately.     

Optimal lot sizing with unreliable production system

The classical lot sizing model deals with economic lot sizing for production in a deterministic framework. In real life, various forms of uncertainty affect the production. These include machine breakdown, quality variations, and so on. This paper develops a model with unreliable production systems and under alternative repair option strategies.     

Economic lot sizing problem with inventory bounds

This paper studies a economic lot sizing (ELS) problem with both upper and lower inventory bounds. Bounded ELS models address inventory control problems with time-varying inventory capacity and safety stock constraints. An O(n²) algorithm is found by using net cumulative demand (NCD) to measure the amount of replenishment requested to fulfill the cumulative demand till the end of the planning horizon. An O(n) algorithm is found for the special case, the bounded ELS problem with non-increasing marginal production cost.     

Stock Control of Manufacturing Parts — A Case Study

The approach adopted for stock control of manufacturing parts in a small company is described. In particular, material requirements planning is compared with the standard stock control method previously in use, and safety buffering is considered. By altering the company's stock-holding and ordering policies a significant saving is achieved.     

Buffer sizing in multi-product multi-reactor batch processes: Impact of allocation and campaign sizing policies

This paper studies the impact of management policies, such as product allocation and campaign sizing, on the required size of the finished goods inventories in a multi-product multi-reactor batch process. Demand, setup and batch processing times for these products are assumed to be stochastic, and the inventory buffer for every product type needs to be such that target customer service levels are met. To perform this analysis, we develop a queueing model that allows us to explicitly estimate service levels as a function of the buffer size, and the allocation/campaign sizing policies. This model can be used to evaluate the service level given an existing buffer configuration, as well as to determine the buffer sizes required across products to meet a pre-specified service level. It also allows us to formulate a number of insights into how product allocation decisions and campaign planning policies affect buffer sizing decisions in symmetric production systems.     

A queuing approach for inventory planning with batch ordering in multi-echelon supply chains

This paper presents stylized models for conducting performance analysis of the manufacturing supply chain network (SCN) in a stochastic setting for batch ordering. We use queueing models to capture the behavior of SCN. The analysis is clubbed with an inventory optimization model, which can be used for designing inventory policies . In the first case, we model one manufacturer with one warehouse, which supplies to various retailers. We determine the optimal inventory level at the warehouse that minimizes total expected cost of carrying inventory, back order cost associated with serving orders in the backlog queue, and ordering cost. In the second model we impose service level constraint in terms of fill rate (probability an order is filled from stock at warehouse), assuming that customers do not balk from the system. We present several numerical examples to illustrate the model and to illustrate its various features. In the third case, we extend the model to a three-echelon inventory model which explicitly considers the logistics process.     

Managing inventory and service levels in a safety stock‐based inventory routing system with stochastic retailer demands

The inherent uncertainty in supply chain systems compels managers to be more perceptive to the stochastic nature of the systems' major parameters, such as suppliers' reliability, retailers' demands, and facility production capacities. To deal with the uncertainty inherent to the parameters of the stochastic supply chain optimization problems and to determine optimal or close to optimal policies, many approximate deterministic equivalent models are proposed. In this paper, we consider the stochastic periodic inventory routing problem modeled as chance‐constrained optimization problem. We then propose a safety stock‐based deterministic optimization model to determine near‐optimal solutions to this chance‐constrained optimization problem. We investigate the issue of adequately setting safety stocks at the supplier's warehouse and at the retailers so that the promised service levels to the retailers are guaranteed, while distribution costs as well as inventory throughout the system are optimized. The proposed deterministic models strive to optimize the safety stock levels in line with the planned service levels at the retailers. Different safety stock models are investigated and analyzed, and the results are illustrated on two comprehensively worked out cases. We conclude this analysis with some insights on how safety stocks are to be determined, allocated, and coordinated in stochastic periodic inventory routing problem. Copyright © 2017 John Wiley & Sons, Ltd.     

Integer programming approach to reactive scheduling in make-to-order manufacturing

New algorithms based on mixed integer programming formulations are proposed for reactive scheduling in a dynamic, make-to-order manufacturing environment. The problem objective is to update a long-term production schedule subject to service level and inventory constraints, whenever the customer orders are modified or new orders arrive. Different rescheduling policies are proposed, from a total reschedule of all remaining and unmodified customer orders to a non-reschedule of all such orders. In addition, a medium restrictive policy is considered for rescheduling only a subset of remaining customer orders awaiting material supplies. Numerical examples modeled after a real-world scheduling/rescheduling of customer orders in the electronics industry are presented and some results of computational experiments are reported.     

A dispatching rule-based approach to production scheduling in a printed circuit board manufacturing system

This paper focuses on a production-scheduling problem in a printed circuit board (PCB) manufacturing system that produces multiple product types with different due dates and different manufacturing processes. In the PCB manufacturing system, there is a number of serial workstations, and there are multiple parallel machines at each workstation. Also, setup operations are required at certain workstations or machines, and some product types have re-entrant flows. We develop new dispatching rules for scheduling at each workstation, considering the special features of PCB manufacturing. With the dispatching rules, we determine not only the start time of each lot at a machine but also the batch size of each product at each machine. Simulation experiments are carried out to test the performance of the production-scheduling method and dispatching rules devised in this study. Results show that the production-scheduling method suggested in this study performs better than methods with well-known dispatching rules and heuristic algorithms for lot sizing in terms of the total tardiness of orders.     

Buffering from material recovery uncertainty in a recoverable manufacturing environment

Remanufacturing is becoming an increasingly important alternative to firms as they develop environmentally sound strategies aimed at minimizing waste and resources. Remanufacturing helps minimize costs through such methods as extending product life cycles via refurbishments and technical upgrades which require only a fraction of the resources and energy associated with a new product. The remanufacturing environment is characterized by a far greater degree of uncertainty than new manufacturing, due to such factors as material recovery uncertainty and probabilistic routings. In this study the use of safety stocks, with a material requirement planning system, to deal with the high inherent uncertainty in the system is examined. It is shown that some safety stocks must be kept in the system but have limited applicability. Additional safety stocks do not provide the manager in this environment with any added benefit beyond that obtained by keeping a minimum recommended level. The results obtained are somewhat counter-intuitive, since adding additional levels of safety stock does not add additional coverage when lead times are greater than one planning period. This lead time effect is explained fully and recommendations as to safety stock level to invest in are made.     

模糊环境下提前期对安全库存的影响

设置安全库存可以有效管理供应链的不确定性,提高服务水平,降低缺货风险.本文基于可信性理论,研究了当需求为模糊变量,提前期分别为固定值和模糊变量时.节点企业安全库存量的确定问题.通过实际算例,分析了模糊环境下提前期对安全库存量的影响.     

The impact of controllable production rates on the performance of inventory systems: A systematic review of the literature

The lot sizing problem has attracted the attention of researchers for more than a century, and it still belongs to the most relevant decision problems in many manufacturing companies. During the evolution of research on lot sizing, the seminal economic order quantity (EOQ) model proposed by Harris [1913. How many parts to make at once. Factory, the Magazine of Management, 10 (2), 135-136.] has remained the most popular model, despite its limitations. To support lot sizing decisions in practice, researchers have frequently extended Harris’ basic EOQ model to better reflect the characteristics of real production processes. One of these extensions is the consideration of controllable (variable) production rates, which gives production planners more flexibility in managing the build-up and depletion of inventory and in controlling costs.The aim of this paper is to provide a comprehensive and systematic overview of EPQ-type lot sizing models that consider controllable production rates. First, the paper proposes a conceptual framework that captures the characteristics of controllable production rates including the planning horizon (short vs. long term), the number of potential interventions per production run (one vs. multiple), the effect of controllable production rates on the performance of the inventory system (e.g., unit production costs, energy consumption, product quality), and the type of lot sizing model considered (e.g., two-stage models, multi-stage models, multi-item models). Secondly, the paper presents the results of a systematic literature review and evaluates the state-of-research of lot sizing models with controllable production rates. Based on the analysis of the literature, key trends are summarized and promising research opportunities are discussed.     

An integrated production and inventory model to dampen upstream demand variability in the supply chain

We consider a two-echelon supply chain: a single retailer holds a finished goods inventory to meet an i.i.d. customer demand, and a single manufacturer produces the retailer’s replenishment orders on a make-to-order basis. In this setting the retailer’s order decision has a direct impact on the manufacturer’s production. It is a well known phenomenon that inventory control policies at the retailer level often propagate customer demand variability towards the manufacturer, sometimes even in an amplified form (known as the bullwhip effect). The manufacturer, however, prefers to smooth production, and thus he prefers a smooth order pattern from the retailer. At first sight a decrease in order variability comes at the cost of an increased variance of the retailer’s inventory levels, inflating the retailer’s safety stock requirements. However, integrating the impact of the retailer’s order decision on the manufacturer’s production leads to new insights. A smooth order pattern generates shorter and less variable (production/replenishment) lead times, introducing a compensating effect on the retailer’s safety stock. We show that by including the impact of the order decision on lead times, the order pattern can be smoothed to a considerable extent without increasing stock levels. This leads to a situation where both parties are better off.     

Augmenting the lot sizing order quantity when demand is probabilistic

In this paper we consider a single item, discrete time, lot sizing situation where demand is random and its parameters (e.g., mean and standard deviation) can change with time. For the appealing criterion of minimizing expected total relevant costs per unit time until the moment of the next replenishment we develop two heuristic ways of selecting an appropriate augmentation quantity beyond the expected total demand through to the planned (deterministic) time of the next replenishment. The results of a set of numerical experiments show that augmentation is important, particularly when orders occur frequently (i.e., the fixed cost of a replenishment is low relative to the costs of carrying one period of demand in stock) and the coefficient of variability of demand is relatively low, but also under other specified circumstances. The heuristic procedures are also shown to perform very favourably against a hindsight, baseline (s, S) policy, especially for larger levels of non-stationarity.     

The Effect of Estimation Risk in Establishing Safety Stock Levels in an Inventory Model

This article illustrates the impact of estimation risk on decisions involving a one-period inventory problem such as the Christmas-tree stocking problem. It is shown that when estimation risk is ignored, stock levels may be incorrectly compiled and service levels may be inadequate. This article describes a regression-based method which adjusts the size of the stock by incorporating an additional safety stock requirement which reflects the uncertainty associated with lack of precise knowledge of the true parameters.     

Evolutionary Pareto optimizers for continuous review stochastic inventory systems

Multi-objective inventory control has been studied for a long time. The trade-off analysis of cycle stock investment and workload, so called the exchange curve concept, possibly dates back to several decades ago. A classical way to such trade-off analysis is to utilize the Lagrangian relaxation technique or interactive method to search for the optimum in a sequence of single objective optimization problems. However, the field of optimization has been changed over the last few decades since the concept of evolutionary computation was introduced. In this paper, a continuous review stochastic inventory system with three objectives about cost and shortage is resolved by evolutionary computation in order to plan for the control policies under backordering and lost sales. Two evolutionary optimizers, multi-objective electromagnetism-like optimization (MOEMO) and multi-objective particle swarm optimization (MOPSO), are employed to well and fast approximate the non-dominated policies in term of lot size and safety stock. Trade-offs are observed in a non-dominated set that no one excels the others in all objectives. Computational results show that the evolutionary Pareto optimizers could generate trade-off solutions potentially ignored by the well-known simultaneous method. Comparisons between the results of backordering and lost sales indicate that decision makers will make more deliberate choices about lot sizing and safety stocking when unsatisfied demand is completely lost.     

From competitive to collaborative supply networks: A simulation study

In a scenario where a vendor books its manufacturing capacity options to multiple retailers it is not unlikely that the vendor runs out of capacity and then it cannot serve more orders until future periods of time. This paper suggests that, once the vendor becomes a bottleneck for the network, it is possible to apply negotiation policies between the different retailers to allow re-allocation of options and then overcome this loose/loose situation. Two simple policies to carry out bookings through negotiation practices, allowing partial bookings and not allowing them, are presented in this study. The effectiveness of this approach is tested with a series of simulation experiments whose main results demonstrate that application of negotiation practices within the network when the vendor has not more available capacity to be booked leads to improve the service level, the overall profit and to diminish the sales opportunity cost.     

Lot sizing with inventory gains

The lot sizing problem with inventory gains generalizes the classical lot sizing problem to one in which stock is not conserved. Instances of this problem can be polynomially transformed into instances of the classical problem. The implications for problems involving different production capacity limitations, backlogging and multilevel production are discussed.     

Price markdown scheme in a multi-echelon supply chain in a high-tech industry

This paper studies the price markdown scheme in a supply chain that consists of a supplier, a contract manufacturer (CM), and a buyer (retailer). The buyer subcontracts the production of the final product to the CM. The CM buys the components from the supplier and charges the buyer a service fee for the final product produced. The price markdown is made possible by the supplier with the development of new manufacturing technologies that reduce the production cost for the sourced component. Consequently, the buyer adjusts the retail price in order to possibly stimulate stronger demand that may benefit both the supplier and the buyer. Under this scenario, we identify the optimal discount pricing strategies, capacity reservation, and the stocking policies for the supplier and the buyer. We also investigate the optimal inventory decision for the CM to cope with the price discount by considering both demand and delivery uncertainties. Our results suggest that higher production cost accelerates the effects of higher price sensitivity on lowering the optimal capacity and stocking policies in the supply chain. The effect of mean demand error on the optimal prices is relatively marginal compared with that from price sensitivity. We also found that increasing the standard deviation of the random demand does not necessarily increase the stocking level as one would predict. The results show that delivery uncertainty plays an important role in the inventory carried beyond the price break. We discuss potential extensions for future research.     

MRP performance effects due to forecast bias and demand uncertainty

The effects of forecast bias and demand uncertainty in a batch production environment are investigated using an integrated MRP planning and execution test bed. The use of inflated planned lead time and safety stock to compensate for forecast error is evaluated. Analysis is performed in terms of meeting both the MPS due dates and customer delivery requirements. Forecast bias and demand uncertainty are shown to affect MPS and delivery performance quite differently. Results also show that increasing either planned lead times or safety stock is effective in improving delivery performance. If demand uncertainty dominates completion time variability, the use of safety stock will achieve delivery objectives with less finished goods inventory.