Order-up-to Research Articles

Correction to deep reinforcement learning‐based ordering mechanism for performance optimization in multi‐echelon supply chains

AbstractThis paper addresses and acknowledges the valuable feedback provided by Dr. Deniz Preil in response to the recent study conducted by Kurian et al which investigates the application of proximal policy optimization (PPO) to determine dynamic ordering policies within multi‐echelon supply chains. The first comment raised by Dr. Preil motivated an examination of the training and evaluation procedures in Experiments 2, 3, and 4. The Experiments 2 and 3 were reworked to address this, allowing the seed to vary for every training iteration, resulting in refined outcomes while there was no need of reworking of Experiment 4. The second comment focused on the benchmarking strategies involving the 1‐1 policy and the order‐up‐to (OUT) policy, clarifying the distinctions between the two policies and justifying the use of the 1‐1 policy for benchmarking in Experiment 4. The implementation of the widely accepted OUT policy was explained, highlighting the meaningful rationale behind its use. These discussions aim to enhance the methodology employed by Kurian et al and strengthen the implications of the findings within the domain of supply chain ordering management.

On the equivalence of the proportional and damped trend order-up-to policies: An eigenvalue analysis

We investigate the equivalence of the order-up-to (OUT) replenishment policy with damped trend forecasting (OUT-DT) to the proportional OUT (POUT) policy via an eigenvalue (zero-pole) analysis. We show when the damped trend forecasting parameters are selected from a specific region of the parameter space, the Bullwhip Avoidance(BA) region, the OUT-DT policy potentially possesses some desirable characteristics. Under an independent and identically distributed (i.i.d.) random demand (the simplest random demand) we show the OUT-DT policy: (a) can eliminate the bullwhip effect, (b) has the same dynamic response as the POUT policy (because of the superposition principle, this holds true for all demands, not just i.i.d. demands), (c) forecasting parameters can be set so as to minimize the sum of the inventory and order variances, and (d) has a similar order and inventory variance as the POUT policy when non-linear constraints are present. We investigate the case when the forecasting parameters are selected from the BA region and correlated demand with one auto-regressive term, one integrated term, and two moving average terms, ARIMA(1,1,2), is present. We reveal the effect of finite lead times on the bullwhip effect (order variance) using an approach based on the order of the eigenvalues (the zeros and poles). We reveal either: (a) the bullwhip effect is always present and always increasing in the lead time or (b) a smoothing effect can be present with short lead times (and the order variance may even be decreasing in the lead time) but the bullwhip effect may return with long lead times.

Taxonomical Classification of soils of Asvaru Sub-watershed, Hunsur Taluk, Mysuru District

Soil characterization and classification is crucial to all soil studies, as it is an important tool for understanding the nature of soil along with successful transfer of research results from one study area to another. The proper understanding of the nature and properties of soil and their management based on their potential and problems is important for increasing crop production to the optimum level. For understanding the problems and potentials, detailed soil survey plays an important role which provides adequate information in terms of land form, slope, land use as well as characteristics of soils (viz., texture, depth, structure, stoniness, drainage, acidity, salinity etc.) which can be utilized for the planning and development. The purpose of the study is to classify the soils of Asavru sub-watershed in Mysuru district to categorize the soils into different soil order upto family level of Soil taxonomy Classification and enhance the productivity and profitability of the area. The detailed soil survey was carried out in Asvaru sub-watershed. Seventy two profiles were studied for its different morphology, physical and chemical properties. The subwatershed area was grouped into 75 mapping units consisting of 16 soil series. The soils were shallow to very deep with texture varying from sandy loam to sandy clay. The structure was sub-angular blocky in all profiles with friable consistency. Soil reaction varied from moderately acidic to moderately alkaline and non saline in +2 + + + nature. Exchangeable cations followed the pattern of Ca >Mg >Na >K . The soil series identified in the sub-watershed area were classified under different soil orders (Alfisols and Inceptisols) upto family level according to revision of Soil Taxonomy. Major proportion of the soils of the sub-watershed belonged to Alfisols (Pedons1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12 and 15) and Inceptisols (Pedon5, 13 and 16).

Impact of Ordering Decisions on Performance of a Supply Chain – An Experimental and Simulation Study

A supply chain consists of a network of organizations. Each organization in it acts as either customer or supplier to others. Ordering and replenishment decisions of each organization or stage contribute to supply chain performance. A simulation study and experimentation were conducted in this study to determine the impact of ordering decisions on supply chain performance. The ordering decisions at each stage are taken by intuition for experimentation and are taken by inventory policies for simulation. Under customer demand distribution information sharing, the performance of a supply chain is evaluated and compared between those two conditions. A supply chain role play game software package is used to evaluate supply chain performance by intuition, and simulation is used to evaluate different inventory policies. Fixed order policy, Order Up-to Level (OUL), Modified OUL (MOUL), (r, Q) and (r, S) inventory policies are considered in this study. The performance measures used are the total supply chain inventory per period, bullwhip effect and supply chain fill rate. Grey Relational Analysis (GRA) is used to identify the best method to take decisions in supply chain. Results show that supply chain performance is best under MOUL policy. Based on the results of this study, supply chain members are encouraged to identify the best inventory policy and use that rather than making decisions based on intuition.

Many-objective optimization of a three-echelon supply chain: A case study in the pharmaceutical industry

This paper proposes an order-up-to (OUT) replenishment policy integrated with inventory routing optimization, formulated as a three-echelon supply chain. The OUT policy is used for raw material purchasing and transportation from the suppliers to support warehouses. Inventory routing optimization is applied to transport the raw materials to the main warehouse when required, where manufacturing operations take place. The optimization problem is solved using a many-objective genetic algorithm. The proposed optimization framework can be applied to the pharmaceutical industry and to any other highly dynamic industry with large product portfolios. This paper presents a real-world case in the pharmaceutical industry from Hovione Farmaciência SA. The performance of the many-objective optimization is compared with a summed single-objective simplification, showing that while the total cost reduces by using single-objective optimization, the optimal scenarios offered by the many-objective optimization may provide additional insight to decision-makers and act as a decision support system, being more inline with the human–machine cooperation trends of the industry.

Order Batching and the Bullwhip Effect Reduction in a Cross‐Docking Strategy

AbstractThe purpose of this article is to analyze the effect of order batching on the bullwhip effect in a cross‐docking strategy. The model proposed uses simulation to analyze empirically the impact of order batching on the bullwhip effect in cross‐docking strategy compared to traditional warehousing. The study is based on a case study of a fast‐moving consumer goods company and a French retailer. In the model, a three‐stage supply chain composed of one supplier DC, one retailer DC, and 10 retailer stores is considered. The order‐up‐to (OUT) level policy is used to control inventory at each stage. The demand is forecasted using a simple moving average scheme. The empirical investigation shows that the use of cross‐docking leads to a bullwhip effect gain upstream in the supply chain in all cases and situations. Moreover, we show that there exists a high positive correlation between the physical volume of a product (measured by the number of items per pallet) and the bullwhip effect gain. Finally, the increase in lead time to the stores has little impact on the bullwhip effect gain upstream in the supply chain.

When bullwhip increases in the lead time: An eigenvalue analysis of ARMA demand

Problem definition. The impact of lead times on the bullwhip effect produced by the order-up-to (OUT) replenishment policy is studied. Practical relevance. Under general auto-regressive moving average (ARMA) demand, we investigate when the OUT policy possesses an always-increasing-in-the-lead-time bullwhip effect and when it does not. Methodology. A bullwhip measure based on the difference between the demand and order variance is combined with a novel analysis based on the eigenvalues and impulse response of the ARMA demand process. Contribution. We show a positive demand impulse response is a necessary and sufficient condition for an increasing in the lead time bullwhip effect. The ordering of zeros and poles (the eigenvalue ordering) of the z-transform transfer function of the demand process reveals when the demand impulse is positive. To provide further insight, we study ARMA(2,2) demand, which contains six different eigenvalue orderings. Two of these orderings satisfy a sufficient condition (positive demand eigenvalues in a particular order) for a positive impulse response. Two orderings satisfy the inverse of this sufficient condition and do not possess a positive impulse response. The final two orderings do not satisfy the sufficient condition, nor its inverse, but do contain positive impulse responses. Managerial implications. Our findings are important as reducing lead-times is often advocated as an improvement action to reduce the bullwhip effect. By identifying the demand characteristics that lead to a bullwhip effect that increases in the lead time we offer prescriptive advice on when, and when not, to invest in lead time reduction.

Fusion classes of Non-Abelian Metabelian groups of order upto

Fusion classes of Non-Abelian Metabelian groups of order upto

Automorphisms of non-abelian metabelian groups of order upto 24

Automorphisms of non-abelian metabelian groups of order upto 24

Comparison of discrete time inventory systems with positive service time and lead time

This paper investigates two discrete time queueing inventory models with positive service time and lead time. Customers arrive according to a Bernoulli process and service time and lead time follow geometric distributions. The first model under discussion based on replenishment of order upto $S$ policy where as the second model is based on order placement by a fixed quantity $Q$, where $Q=S-s$, whenever the inventory level falls to $s$. We analyse this queueing systems using the matrix geometric method and derive an explicit expression for the stability condition. We obtain the steady-state behaviour of these systems and several system performance measures. The influence of various parameters on the systems performance measures and comparison on the cost analysis are also discussed through numerical example.

Inventory control models for spare parts in aviation logistics

Effective inventory management has a direct influence on monetary savings, high customer service level and product quality and thus plays an essential role in a company’s economic and strategic performance. Forecasting and inventory models for aviation logistics are essential in commercial aviation. The objective of this paper is to study the problem of identifying the optimal order quantity of aircraft spare parts and the demand periods using the Order-Up-To (OUT) inventory model in conjunction with the Negative Binomial Distribution (NBD) and the (s, S) inventory model with Revised Power Approximation Method. These models are compared and contrasted via a real-world paradigm. The analysis reveals that the OUT inventory model in conjunction with the Poisson distribution allows ordering the lowest order quantity. However, the (s, S) inventory model with the Revised Power Approximation outperforms it in terms of average total inventory costs.

Dynamic Multi-Product Procurement with Joint and Individual Setup Costs: Theory and Insights

In practice, it is common, especially for online retailers, to bundle different products together during procurement to save transportation and handling costs. It is important to understand and theorize how to manage dynamic procurement by taking advantage of joint ordering in the presence of joint and individual setup costs. We characterize the structure of optimal policy for a periodic review multi-product inventory system with multiple setup costs, including a joint setup cost and individual setup costs for each product. By proposing the notion of ($\mathcal K,\bm \eta$)-quasi-convexity, we show that an optimal procurement policy for such a system follows the so-called ($\sigma,\omega,\bm S$) policy when demands are stochastically increasing over time: order up to $\bm S$ for states in the region $\sigma$, do not order for states in the region $\omega$, and order certain quantities for states neither in $\sigma$ nor in $\omega$. We also obtain ordering monotonicity properties that characterize the structure of the optimal policy, and we provide some bounds for the parameters of the optimal policy. Our results can also accommodate inter-product demand correlation, such as customer choice for different products. Leveraging these operational insights, we propose three simple heuristic policies: the independent ($\bm s,\bm S$) policy, vector ($\bm s,\bm S$) policy and linear interpolation ($\bm s,\bm S$) policy. Extensive numerical experiments indicate that the linear interpolation ($\bm s, \bm S$) policy outperforms the other two heuristics, with the performance gap being less than 3.5% on average and only 0.5% in some cases. Finally, we show that how our results can be extended to systems with more complex setup cost functions, such as time-varying, set-based, and quantity-dependent setup costs.

Analysis of Variance Amplification and Service Level in a Supply Chain with Correlated Demand

The bullwhip effect reflects the variance amplification of demand as they are moving upstream in a supply chain, and leading to the distortion of demand information that hinders supply chain performance sustainability. Extensive research has been undertaken to model, measure, and analyze the bullwhip effect while assuming stationary independent and identically distributed (i.i.d) demand, employing the classical order-up-to (OUT) policy and allowing return orders. On the contrary, correlated demand where a period’s demand is related to previous periods’ demands is evident in several real-life situations, such as demand patterns that exhibit trends or seasonality. This paper assumes correlated demand and aims to investigate the order variance ratio (OVR), net stock amplification ratio (NSA), and average fill rate/service level (AFR). Moreover, the impact of correlated demand on the supply chain performance under various operational parameters, such as lead-time, forecasting parameter, and ordering policy parameters, is analyzed. A simulation modeling approach is adopted to analyze the response of a single-echelon supply chain model that restricts return orders and faces a first order autoregressive demand process AR(1). A generalized order-up-to policy that allows order smoothing through the proper tuning of its smoothing parameters is applied. The characterization results confirm that the correlated demand affects the three performance measures and interacts with the operating conditions. The results also indicate that the generalized OUT inventory policy should be adopted with the correlated demand, as its smoothing parameters can be adapted to utilize the demand characteristics such that OVR and NSA can be reduced without affecting the service level (AFR), implying sustainable supply chain operations. Furthermore, the results of a factorial design have confirmed that the ordering policy parameters and their interactions have the largest impact on the three performance measures. Based on the above characterization, the paper provides management with means to sustain good performance of a supply chain whenever a correlated demand pattern is realized through selecting the control parameters that decrease the bullwhip effect.

Cross-docking or traditional warehousing: what is the right distribution strategy for your product?

PurposeThe objective of this paper is to investigate the impact of products' characteristics on the performance of three distribution strategies: traditional warehousing (TW), cross-docking pick by line (XDPL) and cross-docking pick by store (XDPS).Design/methodology/approachBased on a case study of an FMCG “Fast Moving Consumer Goods” company and a major French retailer, we empirically analyse the impact of the products' characteristics on the performance of the three distribution strategies. We consider a three-echelon supply chain composed of one supplier DC, one retailer DC and multiple retailer stores. The inventory at each echelon is controlled according to an order-up-to (OUT) level policy. The demand is forecasted by means of a single exponential smoothing method. A sensitivity analysis is also conducted to analyse the impact of the supply chain parameters on the comparative performance of the strategies when the parameters' values deviate from the empirical base case.FindingsThe empirical investigation shows that the use of XDPL results leads to an increase in the supply chain total cost, whereas XDPS reduces the cost. Moreover, we show that for a service-level target, cross-docking strategies should be selected for products with low variability, high shelf space, low value and short lead-time. For an inventory reduction target, these strategies should be selected for products with high demand volume. We also propose a managerial framework for choosing the right strategy for each product.Originality/valueThis paper fills a gap in the literature by presenting empirical results based on a real business case of a multi-echelon supply chain. Both cost and service are used to evaluate the performance of the strategies.Research limitations/implicationsOur work has the limitation to ignore the transportation cost implications when selecting the right distribution strategy. Hence, including such cost in the analysis would constitute an interesting extension of this work. Moreover, our empirical analysis represents a practical rich context that makes the scope for transferability of findings learned from this article substantial. However, for the generalisability of the findings, larger datasets in the retail supply chain would be interesting to consider

Modeling and optimizing of variance amplification in supply chain using response surface methodology

Abstract Supply chains experience variance amplification in replenishment orders and inventory levels, leading to severe inefficiencies. Extensive studies are conducted while focusing mainly on the demand variance amplification (also known as bullwhip effect), but limited research is undertaken to optimize the variance amplification that considers both the orders and net stock variability. A single-echelon supply chain with a stationary demand process, a generalized periodic-review order-up-to (OUT) policy, and an exponential smoothing forecasting model are assumed. Hence, this paper seeks to optimize the best values of the exponential smoothing and OUT policy parameters that minimize the sum of demand and inventory variances. A hybrid approach that integrates simulation modeling and response surface methodology is proposed. The algorithm is iterative in nature, where at each iteration simulation runs are conducted to generate a response surface for the variance amplification, and a gradient search is applied to locate a new incumbent solution. Several experiments are conducted to demonstrate the applicability of the approach, and to validate its results with previous researches. The proposed RSM-Simulation based algorithm produces comparable results to existing methods and thus having a good potential to accommodate more supply chain complexities. It can be used to model and optimize nonlinear supply chains, supply chain with stochastic lead-time, supply chains with correlated demand, and supply chains with capacity constraints.

Avoiding the capacity cost trap: Three means of smoothing under cyclical production planning

Companies tend to set their master production schedule weekly, even when producing and shipping on a daily basis—the term for this is staggered deliveries. This practice is common even when there is no marginal cost of setting a new schedule. We argue that the practice is sound for companies that use the ubiquitous order-up-to (OUT) policy to control production of products with a significant capacity cost. Under these conditions, the length of the order cycle (time between schedule updates) has a damping effect on production, while a unit (daily) order cycle can cause significant capacity costs. We call this the capacity cost trap.Developing an analytical model based on industrial evidence, we derive capacity and inventory costs under the staggered OUT policy, showing that for this policy there is an optimal order cycle possibly greater than unity. To improve on this solution, we consider three approaches to smoothing: either levelling within the cycle, deferring excess production or idling to future cycles via a proportional OUT policy, or increasing the length of the cycle. By deriving exact cost expressions we compare these approaches, finding that smoothing by employing the proportional OUT policy is sufficient to avoid the capacity cost trap.

Formulation and evaluation of Self-Poring osmotic tablet of diltiazem HCl for the treatment of hypertension

With emergence of new technology and concept, self-poring osmotic tablets were developed in order to reduce the complications and problems associated with micro drilling and laser drilling in osmotic tablet. This research describes a very simple and cheap method of developing self-poring osmotic tablet that deliver Diltiazem HCl in a controlled rate for prolonged duration. For this purpose 5 formulations of osmotictablets were prepared through wet granulation technique in which different concentration of sodium lauryl sulphate (SLS) were used as pore forming agent in coating solution. In tablet core also varied concentration of sorbitol as osmogens, guar gum and HPMC were encorporated, which forms gel like matrix through which drug releases at zero order. Through optimization out of 5 formulations, F3 (C2) formulation was selected as best. From result of invitro drug release study it was clear that more concentration of pore former and osmogens releases drug in short time while less concentration takes more time for drug release. Therefore, it is necessary to use SLS, polymer and osmogens in balance concentration for getting optimum control release at zero order upto 24 hrs. Self-poring Osmotic tablets hold promising potential for increasing drug efficacy and reducing dosing frequency with minimal side effects also provides an economic means of developing controlled release dosage forms.

Analysing the impact of different classical controller strategies on the dynamics performance of production-inventory systems using state space approach

PurposeThe purpose of this paper is to examine the impact of applying two classical controller strategies, including two proportional (P) controllers with two feedback loops and one proportional–integral–derivative (PID) controller with one feedback loop, on the order and inventory performance within a production-inventory control system.Design/methodology/approachThe simulation experiments of the dynamics behaviour of the production-inventory control system are conducted using a model based on control theory techniques. The Laplace transformation of an Order–Up–To (OUT) model is obtained using a state-space approach, and then the state-space representation is used to design and simulate a controlled model. The simulations of each model with two control configurations are tested by subjecting the system to a random retail sales pattern. The performance of inventory level is quantified by using the Integral of Absolute Error (IAE), whereas the bullwhip effect is measured by using the Variance ratio (Var).FindingsThe simulation results show that one PID controller with one feedback loop outperforms two P controllers with two feedback loops at reducing the bullwhip effect and regulating the inventory level.Originality/valueThe production-inventory control system is broken down into three components, namely: the forecasting mechanism, controller strategy and production-inventory process. A state-space approach is adopted to design and simulate the different controller strategy.

Revisiting rescheduling: MRP nervousness and the bullwhip effect

We study the material requirements planning (MRP) system nervousness problem from a dynamic, stochastic and economic perspective in a two-echelon supply chain under first-order auto-regressive demand. MRP nervousness is an effect where the future order forecasts, given to suppliers so that they may plan production and organise their affairs, exhibits extreme period-to-period variability. We develop a measure of nervousness that weights future forecast errors geometrically over time. Near-term forecast errors are weighted higher than distant forecast errors. Focusing on replenishment policies for high volume items, we investigate two methods of generating order call-offs and two methods of creating order forecasts. For order call-offs, we consider the traditional order-up-to (OUT) policy and the proportional OUT policy (POUT). For order forecasts, we study both minimum mean square error (MMSE) forecasts of the demand process and MMSE forecasts coupled with a procedure that accounts for the known future influence of the POUT policy. We show that when retailers use the POUT policy and account for its predictable future behaviour, they can reduce the bullwhip effect, supply chain inventory costs and the manufacturer’s MRP nervousness.

Vibration of a steam turbo-generator (TG) set during shutdown period

The steam turbo-generator (TG) sets in power plants during the shutdown period often operate at a very low speed with the aid of barring gear. This low speed is known as the barring speed and it is of the order upto 100RPM. The purpose is to float the rotor in the fluid bearings so that the rotor heavy self-weight should not cause any damage to the bearings. The barring speed also maintains uniformity of temperature across the complete rotor when cooling down from operating condition to normal condition. Operating at the barring speed is often considered as the machine is close to the stand still condition and may not be subjected to any harsh vibration problem. However the in-situ vibration measurement on a typical steam TG set during machine shutdown operating at the barring speed reveals that the machine is subjected to vibration which may have potential to propagate the existing damage further. The paper presents a typical industrial case study and observations.