Target Inventory Level Research Articles

Rolling horizon heuristics for production planning and set-up scheduling with backlogs and error-prone demand forecasts

Three families of models and fast heuristic methods are developed for identifying a production plan and immediate set-up schedule for a manufacturing line with changeover times. The initial model is exact, but is optimally solvable only for very short planning horizons. A second modelling and solution method optimizes production one period at a time, first in a backward pass to identify target inventory levels, and then in a forward pass to build up these target inventories. Finally, a third method plans set-ups and lots on a period-by-period basis, estimating the capacity usage of future set-ups. All three methods are first tested under static conditions and then on a rolling horizon basis with differing degrees of demand forecast accuracy, tightness of capacity and length of horizon. Computational experiments confirm that even under great forecasting uncertainty the planning horizon should extend beyond the time at which the horizon is rolled forward and the forecasts updated. Tests also show that the degree of capacity tightness and horizon length affects which approximate models and methods are most successful. The degree of forecast error appears to have limited impact on the planning horizon to be used and relative performance of the models.

Strategic inventory deployment in the steel industry

Integrated Steel Manufacturers (ISMs) perform all of the steps necessary to convert iron ore into finished products. As a result they are characterized by high capital expenditures and long cycle times. The custom nature of finished products and significant demand uncertainty explains why ISMs typically produce to order. However, recent increased competition from low cost mini-mills is causing some ISMs to compete by serving the needs of higher-paying customers who want exotic products, and faster and reliable deliveries. Consequently, ISMs are exploring the option of satisfying a portion of their demand by converting strategically placed semi-finished inventory into finished products, which helps to reduce both the time between order receipt and order dispatch, and its variability. In this study we propose a two-stage stochastic integer programming model that can be used to choose the semi-finished products that should be made to stock, and their target inventory levels. Properties of this model are exploited to develop a fast heuristic applicable to large-scale instances of the problem encountered in industry. Numerical experiments are used to validate the heuristic, and examples based on data from a particular ISM are used to illustrate important managerial insights.

Analysis of Multi-Product Kanban Systems with State-Dependent Setups and Lost Sales

We propose a decomposition-based approximation method that generates fairly accurate estimates for steady-state performance measures of a kanban-controlled production system. The manufacturing facility of this system can process items of several different products. Setup and processing times are assumed to be exponentially distributed. Customers arrive according to mutually independent Poisson processes. A customer whose demand cannot be met from stock leaves the system and satisfies his demand elsewhere (lost sales). The manufacturing facility processes items of a product until a target inventory level given by the number of kanbans has been reached. Then the manufacturing facility is set up for the next product according to a fixed setup sequence if the next product's inventory level is below target. Otherwise, this product is skipped (cyclic-exhaustive processing with state-dependent setups). The manufacturing facility idles when the inventory levels of all products are at their target levels.

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

On the interpretation of cointegration in the linear–quadratic inventory model

The traditional formulation of the linear–quadratic inventory model with unit roots predicts cointegration between inventories and sales. That formulation implies that marginal production costs and the marginal benefits of inventories are both tending to ∞, and the cointegrating coefficient reflects the optimal trade-off between these competing factors. This paper suggests a reformulation of the problem in which marginal production costs and marginal inventory benefits are both stationary and in which the cointegrating coefficient is the same as the value that characterizes the target inventory level in the cost function.

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.

A panel data study on Spanish firms' inventory investment

This paper raises several questions about inventory investment of a sample of 172 big nonfinancial Spanish companies. Inventory investment has been usually explained by two alternative theories: the production smoothing model and the (S,s) model. First, we provide a descriptive analysis based on industry-level data to show some shortcomings of the first model. Then, we test a flexible accelerator model using firm-level data. The results seem to show that inventory investment, previous-period inventories and sales are closely and significantly related. This evidence, although not conclusive, rejects both the pure production smoothing model and the (S,s) model. At the same time, our results confirm the view of a target inventory level and the plausibility of the so-called stock-adjustment model, so that the optimal inventory holding buffers sales volatility.

A model predictive framework for planning and scheduling problems: a case study of consumer goods supply chain

Model Predictive Control is a well established technique for the control of processes and plants. We present a similar concept for planning and scheduling problems. There have mainly been two approaches to solve the planning and scheduling problems. The first approach is to model the planning and scheduling as one monolithic problem and solve it for the entire horizon. Needless to say, this approach requires an extensive computational effort and becomes impossible to solve in the case of large-scale scheduling problems. The other approach is to hierarchically-decompose the problem into a planning level problem and a scheduling level problem. This approach leads to tractable problems. Neither of these approaches provide the framework for incorporating uncertainties in the processing time of batches, or random equipment breakdowns, or demand uncertainties in the future. Furthermore, these approaches only provide ‘one snapshot’ of the planning problem and not a ‘walk through the timeline’. Model predictive planning and scheduling provides a framework for studying dynamics. Model predictive planning and scheduling requires a forecasting model and an optimization model. Both these models work in tandem in a simulation environment that incorporates uncertainty. The similarity with the model predictive approach which is widely used in process-control is that in each period, the forecasting model calculates the target inventory (controlled variable) in the future periods. These inventory levels ensure desired customer service level while minimizing average inventory. The scheduling model then tries to achieve these target inventory levels in the future periods by scheduling tasks (manipulated variables).

An empirical model of inventory investment by durable commodity intermediaries

This paper introduces a new detailed dataset of high-frequency observations on inventory investment by a U.S. steel wholesaler. Our analysis of these data leads to six main conclusions: orders and sales are made infrequently; orders are more volatile than sales; order sizes vary considerably; there is substantial high-frequency variation in the firm's sales prices; inventory/sales ratios are unstable; and there are occasional stockouts. We model the firm generically as a durable commodity intermediary that engages in commodity price speculation. We demonstrate that the firm's inventory investment behavior at the product level is well-approximated by an optimal trading strategy from the solution to a nonlinear dynamic programming problem with two continuous state variables and one continuous control variable that is subject to frequently binding inequality constraints. We show that the optimal trading strategy is a generalized (S, s) rule. That is, whenever the firm's inventory level q falls below the order threshold s(p), the firm places an order of size S(p) − q in order to attain a target inventory level S(p) satisfying S(p) ≥ s(p), where p is the current spot price at which the firm can purchase unlimited amounts of the commodity after incurring a fixed order cost K. We show that the (S, s) bands are decreasing functions of p, capturing the basic intuition of commodity price speculation, namely, that it is optimal for the firm to hold higher inventories when the spot price is low than when it is high in order to profit from “buying low and selling high.” We simulate a calibrated version of this model and show that the simulated data exhibit the key features of inventory investment we observe in the data.

Production Quotas as Bounds on Interplant JIT Contracts

We consider the situation of a supplier plant whose customer plants desire just-in-time (JIT) deliveries. Randomness in both the production and demand processes make satisfying every demand that might occur in true JIT fashion impossible. Therefore, supplier plants typically negotiate bounds on JIT contracts with their customers. In this paper, we focus on the use of “quotas” or “target inventory levels” as a mechanism for establishing such bounds. That is, the supplier firm is responsible for meeting periodic demands up to the quota, but not beyond. In this paper, we consider the problem of setting an appropriate quota from the perspective of the supplier plant and interpret our results in the context of the negotiation process between the supplier and its customers. Under the assumption that “safety capacity” (i.e., overtime or a vendoring option) is available, we develop two models that address this problem. The first model assumes that quota shortfalls cannot be carried over to the next regular time production period and are made up with overtime/vendoring, which incurs fixed plus variable costs. The second model assumes that shortages can be backlogged to the next regular time production period at a cost. We use numerical examples to demonstrate how the models we developed were used by a clutch supplier to a large auto manufacturer to negotiate its JIT contracts.

A three-stage simulation based approach to inventory management with discrete demand

This paper proposes a three-stage simulation-based approach to determine target inventory level for a plastic moulding company. The classical formula of a periodic review inventory system requires continuous demand with a normal distribution. This is often not the case in real world companies. For this reason, a three-stage approach based on a SLAM II simulation model is proposed. Our model allows for a statistically based determination of target inventory level for both normal and non-normal distributed demand. This model includes inventory management, production planning and control, finished goods shipment, and functional area of manufacturing. Analysis of simulation results indicates an inventory reduction plan and the feasibility of a layout design to relocate equipment for the plant.

The Stochastic Economic Lot Scheduling Problem: Cyclical Base-Stock Policies with Idle Times

In this paper we discuss stochastic Economic Lot Scheduling Problems (ELSP), i.e., settings where several items need to be produced in a common facility with limited capacity, under significant uncertainty regarding demands, production times, setup times, or combinations thereof. We propose a class of production/inventory strategies for stochastic ELSPs and describe how a strategy which minimizes holding, backlogging, and setup costs within this class can be effectively determined and evaluated. The proposed class of strategies is simple but rich and effective: when the facility is assigned to a given item, production continues until either a specific target inventory level is reached or a specific production batch has been completed; the different items are produced in a given sequence or rotation cycle, possibly with idle times inserted between the completion of an item's production batch and the setup for the next item. An optimal strategy within the class can be determined, and all relevant performance measures can be evaluated in just a few CPU seconds, using a 486-based PC. We also derive a number of easily computable lower bounds for the optimal cost value and establish a comparison with deterministic ELSPs.

A service-level-oriented heuristic approach to production planning in a robotized spinning-mill

SUMMARY This paper presents a heuristic approach to production planning and inventory control. The heuristic was developed for scheduling the production of N-products on many machines when both production and demand rates are stochastic. The key for scheduling production is a target inventory level to be maintained at the beginning of each period; hysteresis factors within the heuristic make the production plan more or less sensitive to transient conditions in both demand and production. Experimental results of its application in a production environment are provided.

The impact of adenine and inventory utilization decisions on blood inventory management.

The use of citrate-phosphate-dextrose-adenine as an anticoagulant for whole blood increases the storage period permitted for whole blood and red cells from 21 to 35 days. A simulation model was used to analyze the possible consequences for outdates and shortages of the addition of adenine. The model accepts as input (1) the maximum age (21 or 35 days), (2) parameters describing the demand and supply distributions, and (3) parameters describing inventory control (crossmatch recycle period, transfusion fraction, deviation from optimal target inventory levels). These parameters were varied over wide ranges, and a full factorial design was carried out. The observed shortage and outdate rates were then related (via multiple regression) to the parameter values. The resulting shortage and outdate functions indicated the effect of parameter changes, including extending the lifetime from 21 to 35 days, and the joint effect of changing more than one parameter. Conclusions indicate that, while the contribution of an increased lifetime to reducing shortages and outdates can be substantial, this contribution can be easily dissipated by relaxing the tightness of other inventory management controls.

A blood ordering strategy for hospital blood banks derived from a computer simulation.

The ultimate goal of a hospital blood bank inventory control programs is to reduce wastage of blood products and unnecessary use of laboratory services without jeopardizing patient safety. The development of a practical blood ordering policy at the hospital level is an integral part of any such program. In order to explore various blood ordering options in detail, a computer simulation of a hospital blood inventory was used to assess the impact on blood band performance measures of reductions in group O and non-group-O levels from baseline levels, assuming both a 21-day and 35-day shelf life. On the basis of data derived from this study showing that such inventory reductions accompanied by partial protection of the group O inventory will not result in significant shortages, a practical strategy was developed for establishing optimal target inventory levels for a hospital on an empirical basis. These target levels can serve as a guide for subsequent blood ordering. A step-by-step approach for analyzing a hospital blood inventory control program is then suggested, accompanied by an action plan for implementing change which incorporates the experimentally-derived blood ordering strategy. Adherence to this plan should result in a low outdate rate, a reduction in unnecessary cross-matching, and greater availability of blood for those patients with a legitimate need for it.

Target inventory levels for a hospital blood bank or a decentralized regional blood banking system.

For any blood type, there is a complex interaction among the optimal inventory level, daily demand level, the transfusion to crossmatch ratio, the crossmatch release period and the age of arriving units that determine the shortage and outdate rate. The blood bank administrator should establish optimal target inventory levels based on a simple equation (decision rule) relating these factors. Evaluation of this rule indicates that its implementation can lead to a very low shortage rate and a reasonable low outdate rate if the blood bank administrator makes efforts to control the crossmatch release period and the average transfusion to crossmatch ratio.