Optimal Replenishment Research Articles

Joint optimisation of replenishment policies on a downstream multi-echelon, multi-product pharmaceutical supply chain with lost sales, stochastic demands and storage capacity constraints: centralised vs. decentralised structure

This paper presents a methodology to identify the near optimal replenishment policies of a downstream pharmaceutical supply chain operating under two different structures (decentralised vs. centralised). We consider a stochastic demand as well as specific constraints related to pharmaceutical supply chain such as limited storage capacity, required service level and order frequency. To compare the performance of both structures an iterative procedure based on Monte Carlo simulation has been developed. The effectiveness and efficiency of the proposed framework are illustrated by using a real case of a university hospital. Detailed analyses of the numerical experiments show that centralised structure results not only in cost savings but also ameliorate the quality of care service.

An Algebraic Decision Support Model for Inventory Coordination in the Generalized n-Stage Non-Serial Supply Chain with Fixed and Linear Backorders Costs

This paper extends and generalizes former inventory models that apply algebraic methods to derive optimal supply chain inventory decisions. In particular this paper considers the problem of coordinating production-inventory decisions in an integrated n-stage supply chain system with linear and fixed backorder costs. This supply chain system assumes information symmetry which implies that all partners share their operational information. First, a mathematical model for the supply chain system total cost is formulated under the integer multipliers coordination mechanism. Then, a recursive algebraic algorithm to derive the optimal inventory replenishment decisions is developed. The applicability of the proposed algorithm is demonstrated using two different numerical examples. Results from the numerical examples indicate that adopting the integer multiplier mechanism will reduce the overall total system cost as compared to using the common cycle time mechanism.

WITHDRAWN: A fuzzy EOQ inventory model with advance payment and various fuzzy numbers

Abstract Normally, human based industrial decision making involves both quantitative and qualitative input factors such as ordering cost, setup cost, etc. Thus, the practitioners should be careful in accounting flexibility in the input factors to tackle the uncertainties that always fit the real situation. This study considers an optimization inventory system with advance payment in a fuzzy situation by employing four types of fuzzy numbers that are triangular, trapezoidal, pentagonal and Hexagonal. Fuzziness is established by allowing the cost components imprecise and vague to certain extent. There are two inventory models proposed in this paper. Initially crisp modelsare developed with fuzzy total inventory cost along crisp optimal replenishment cycle T. Next the fuzzy model is also formulated with fuzzy total inventory cost and fuzzy optimal replenishment cycle T. Graded mean integration method is employed to defuzzify the total inventory cost and the extension of the Lagrangian method is used to determine the optimal replenishment cycle T. Our aim is to minimize the total cost in the proposed inventory model. Numerical examples have been given in order to show the applicability of the proposed model.

Studying the effect of stochastic breakdowns, overtime, and rework on inventory replenishment decision

This study investigates the effect of stochastic breakdowns, overtime, and rework on the inventory replenishment decision. The overtime capacity and inevitable situations during the manufacturing process, such as the production of imperfect items and random breakdowns, are often considered in advance by production manager to smoothen fabrication schedules, maintain the desired quality, and reduce the impact from undesirable interruptions. This study builds a model to characterize these real features of a manufacturing process and derive the total relevant expenses of the system. Although a closed-form solution is unobtainable, a recursive algorithm is proposed to help find the optimal runtime for the batch fabrication plan. A numerical illustration shows how the proposed procedure and algorithm function. It also demonstrates the ability of the proposed model to reveal diverse crucial information regarding the individual and combined influences of deviations in overtime factors, the mean-time-to-failure, and rework- related variables, on the optimal replenishment runtime, total operating expenses, and different cost contributors. The research results will facilitate better decision-making aimed at increasing the competitive advantages of a manufacturing firm.

Optimal Inventory Level Control and Replenishment Plan for Retailers

In vendor managed inventory (VMI) operations, it is necessary for both the suppliers and the customers to reach an agreement on the maximal and minimal inventory level. In practice, in VMI, inventory levels are decided manually by planning personnel, based on their experience and past operating records. From a system optimization point of view, the determination of the upper and lower inventory levels in storage areas is complicated, necessitating analysis of many factors. Consequently, it may not be possible to obtain the best planning results, to determine and maintain the optimum levels of inventory. In this study, we utilize network flow techniques to build a replenishment model to deal with the upper-and-lower inventory level control problem, with the objective of minimizing the total cost in short-term operations, subject to inventory level control and other operating constraints. The model is formulated as an integer network flow problem with side constraints and is characterized as NP-hard in terms of optimization. To efficiently and effectively solve the large-scale problems that occur in the real world, a solution algorithm is also developed. Finally, numerical tests are conducted using real data from a major retail company in northern Taiwan. The results demonstrate the usefulness of the proposed model and solution algorithm for replenishment planning in actual practice.

Optimal Replenishment Policy for Deteriorating Products in a Newsboy Problem with Multiple Just-in-Time Deliveries

Product deterioration is a common phenomenon and is overlooked in most contemporary research on the newsboy problem. In this study, we have considered product deterioration in a production–inventory newsboy model based on multiple just-in-time (JIT) deliveries. This model is solved by a classical optimization technique for the manufacturer production size, wholesale price, replenishment plan, and retailer order policy using a distribution-free approach. Moreover, in order to improve business and entice more customers, a return policy and a post-sale warranty policy is adopted in the model. Theoretical development and numerical examples are provided to demonstrate the validity of this approach.

Inventory renewal for a perishable product: Economies of scale and age‐dependent demand

AbstractWe consider a finite‐horizon, periodic‐review system for a perishable product at a retailer that faces stochastic, age‐dependent demand and loses excess demand, if any. For this system, we build three models that capture two sources of unfilled demand, insufficient inventory and inappropriate age, and penalize them at different rates. The models are characterized by increasing replenishment flexibility, and the goal of each model is to identify when to place an order and the quantity whenever an order is placed. In the first model, reorder intervals are equal. In the second model, reorder intervals can vary across orders. In the third model, reorder intervals continue to remain flexible but the retailer can also partially salvage her inventory whenever she has excess inventory. Using the models, we explore the effect of lost‐sales penalties on the structure of the optimal value function. We find that the inventory‐related cost in a period may lack convexity if the ratio of penalties for stockout and high age is below a threshold, which percolates to the value function as well. We also identify properties of the optimal replenishment policy for the three models. Finally, we conduct numerical experiments to identify the marginal value added by the flexibility in reorder intervals and the option to partially salvage inventory as a function of model parameters.

An accurate and reliable mathematical analytic solution procedure for the EOQ model with non-instantaneous receipt under supplier credits

Recently, Huang and Hsu (J Oper Res Soc Jpn 50:1–13, 2007) investigated the retailer’s optimal replenishment policy with non-instantaneous receipt under trade credit and cash discount. Basically, their inventory model is correct and interesting. However, they ignored explorations of interrelations of functional behaviors of the annual total cost to locate the optimal solutions so much so that the accuracy and reliability of the process of the proof of their solution procedure are questionable. The main purpose of this paper is to provide accurate and reliable mathematical analytic solution procedures to improve the findings in the aforementioned work of Huang and Hsu (J Oper Res Soc Jpn 50:1–13, 2007). Some related recent works on the subject-matter of this investigation are also cited with a view to providing incentive and motivation for making further advances along the lines of the supply chain management and associated inventory problems which we have discussed in this article.

Incorporating outsourcing, stochastic failure, and scrap into batch fabrication planning

In batch production planning, managers must consider the unforeseeable circumstances in the fabrication process and resources available to meet demand on time and determine the optimal replenishment policy. To address these concerns, this study examines a hybrid fabrication system incorporating outsourcing, stochastic machine failures, and random scraps. The objective is to decide the optimal uptime that minimizes the overall system expenses. Assumptions in this study include a partial outsourcing plan associated with a higher unit cost, random scrap, and stochastic breakdown under an abort/resume policy, wherein repair of a machine begins immediately after a breakdown, and the production of the interrupted batch resumes as soon as it is completed. A precise model is developed to explore this specific problem. Mathematical derivations, optimization methodology, and a recursive algorithm are used to derive the optimal replenishment policy. The applicability of the results is illustrated by a numerical example. To facilitate managerial decision making, it reveals the individual and/or combined impact of outsourcing, scrap, and machine failure on (i) the optimal policy; (ii) the system’s different cost contributors; (iii) total system expenses; (iv) machine utilization; and (v) other key parameters of the problem.

Impact of delay in payment, shortage and inflation on an EOQ model with bivariate demand

The major challenge of inventory decision makers is to determine an inventory optimization strategy that ensures the right balance between keeping abundant on hand inventory to meet the demand of the customers and optimizing costs related to holding inventory. This article analyzes on providing a general deterministic inventory model in which the rate of demand is determined by price and time over the ordering cycle time. The traditional assumption of zero ending invento ry level is relaxed to a non-zero ending inventory level. Shortages are allowed which are partially backlogged. We develop models with partial backlogging and without backlogging. The aim is to maximize the profit per unit time, assuming delay in payment and inflation. An algorithm is proposed to find the optimal selling price, optimal stockout period, optimal replenishment cycle time and the optimal ending inventory level. All the possible special cases of these two models are also discussed. The numerical examples, graphical representation, and sensitivity analysis are given to illustrate the practical application of the proposed model.

Optimal replenishment decision for retailers with variable demand for deteriorating products under a trade-credit policy

In this study one obtained the optimal decision of a retailer for the replenishment rate with selling-price and credit-period dependent demand to maximize the profit. A time-varying deterioration rate was considered for those products. A credit-period was offered by the retailer to the end customer to settle the whole payments. The aim of the model was to obtain the maximum profit for the retailer based model. A solution methodology with an algorithm was used to obtain the global optimum profit. An illustrative numerical example was given to test the practical applicability of the model. Numerical study indicated that the profit was at a maximum when the permissible delay-period for payment offered by the suppliers was lies between the permissible delay-time, and the cycle time, offered by the retailer.

Discount pricing policy for deteriorating items under preservation technology cost and shortages

This paper presents an inventory model with a constant rate of deterioration of the product, and shortages are allowed at the end of the cycle. The stock-dependent and price-sensitive demand have been considered with a policy of providing price discount to uplift the market demand. Preservation technology is applied to preserve the items from deterioration. The objective of this model is to maximize the total profit function by finding the optimal replenishment time, the optimal preservation technology investment and the optimal quantity. Next, we have shown that the total profit is a concave function of the replenishment time and preservation technology cost. Discount in pricing may be offered at a time of festival, season breaks down, lockdown and clearance of stock, before introducing a new product with up-gradations, etc. Numerical examples and graphical analysis are provided to explain the model. The discount policy could help any business organizations for smooth running of the business and obtain respective optimal profit.

Optimal hybrid inventory replenishment runtime for a vendor- buyer coordinated system with breakdowns and rework/disposal of nonconforming items

Most multinational/transnational manufacturers that own internal supply chains and operate in turbulent world markets apply strategies related to product quality, low-cost, and timely delivery. This study aims to assist such firms with making accurate decisions to enable their competitive strategies and cope with the realities of limited capacity and unreliable equipment. We examine a vendor-buyer coordinated system featuring batch fabrication, outsourcing, quality reassurance, discontinuous deliveries, and an unreliable machine. The system outsources a portion of a lot to reduce manufacturing uptime, and the in-house fabrication system experiences undesirable defective items and Poisson distributed breakdowns. In each cycle, corrective action and rework/disposal of defective stocks are undertaken as these incidents occur, and upon receipt of outsourced products and when the entire batch is quality ensured, it makes multiple deliveries of the end products. Using modeling, formulation, derivation, and an optimization methodology, we obtain the problem’s cost function and justify its convexity. We then apply differential calculus and propose a recursive algorithm to derive the problem’s optimal replenishment runtime. A numerical illustration is offered to show the applicability of the result that reveals various important system characteristics/ capabilities, such as the distinct and combined influences of breakdowns, outsourcing, rework, scrap, and delivery-frequency factors on various system parameters, performance, and optimal runtime. The methods proposed here can facilitate managerial operations planning and strategic decision making in an intra-supply chain setting in practice.

Replenishment policy for an economic production quantity model considering rework and multiple shipments

Determining the optimal replenishment lot size and shipment policy for a production setup has been of greater interest during the last few years. This paper derives the optimal replenishment lot size and shipment policy for an Economic Production Quantity (EPQ) model with rework of defective items. However, in a real life situation, multi-shipment policy is used in lieu of continuous issuing policy and generation of defective items is inevitable. The proposed research assume that all imperfect quality items are reworked to perfect quality items and then all perfect quality items are delivered to the customers. Mathematical modeling is used in this study and the long-run average production–inventory-delivery cost function is derived. Convexity of the cost function is proved by using the Hessian matrix equations. The closed-form optimal replenishment lot size and optimal number of shipments that minimize the long-run average costs for such an EPQ model are derived.

Identifying optimal magnesium replenishment points based on risk of severe hypomagnesemia in colorectal cancer patients treated with cetuximab or panitumumab.

Cetuximab and panitumumab are monoclonal antibodies that target the epidermal growth factor receptor (EGFR). Treatment with cetuximab and panitumumab commonly causes hypomagnesemia, and optimal management of this adverse effect remains unclear. Here, we evaluated the optimal magnesium replacement points based on the risk of severe hypomagnesemia in colorectal cancer patients who received cetuximab or panitumumab. We retrospectively evaluated 184 patients who received cetuximab or panitumumab for colorectal cancer at Ogaki Municipal Hospital (Ogaki, Japan) between January 2010 and December 2019. Univariate analyses were conducted to evaluate the relationship between patient baseline characteristics and development of hypomagnesemia following cetuximab or panitumumab treatment. Variables that were significantly associated with hypomagnesemia in the univariate analyses as well as previously reported risk factors were entered into a multivariate logistic regression model. The incidence of hypomagnesemia was associated with panitumumab treatment, pre-replenishment serum magnesium concentration, treatment duration, and treatment line. Severe hypomagnesemia post-cetuximab or panitumumab treatment was significantly associated with low baseline magnesium concentrations (< 1.8mg/dL; odds ratio 18.100, 95% confidence interval 1.570-210.000; p = 0.020) and low serum magnesium concentrations during treatment (< 1.1mg/dL; odds ratio 93.800, 95% confidence interval 3.510-2510.000; p = 0.007). To minimize the risk of severe hypomagnesemia during anti-EGFR treatment, magnesium replenishment should be initiated in patients with pre-replenishment concentrations of < 1.8mg/dL, preferably before reaching intra-treatment concentrations of < 1.1mg/dL.

Optimal Replenishment and Clearance Policy for a Perishable Product with LIFO Issuing Policy and Age-Dependent Demand

We study joint replenishment and clearance policy for a perishable product with a general, finite lifetime using a periodic review model over a finite horizon such that the inventory is sold in a last-in, first-out (LIFO) manner. Further, the demand for inventory may depend on its age since customers may choose to walk away if the freshest available inventory is too old for them. The model seeks to optimize two decisions every period: how much of fresh inventory to order and how much of existing inventory to clear. The key objective of the model is to understand the effect of age-dependence of demand on the optimal replenishment and clearance policy. We find that the optimal policy when demand depends on age may diverge substantially from the optimal policy when demand is independent of age, though there exists a sufficient condition under which the structure of the optimal policy becomes identical in both scenarios for all units newer than a threshold age. Further, we show that the structure of the optimal policy for the inventory with one-period remaining lifetime may both simplify and complicate in terms of the number of indexes compared to when demand is independent of age. For the same set of results, we streamline a few arguments for the existing results that are derived assuming demand is independent of age. Finally, we briefly discuss an extension in which clearance is not possible.

Economic ordering policy for non‐instantaneous deteriorating items with price and advertisement dependent demand and permissible delay in payment under inflation

In recent years, offering credit period by the supplier to the retailer has become a usual strategy. Hence, in the present work, an inventory model for noninstantaneous deteriorating items is framed considering money inflation and time discounting, where a permissible delay period is offered by the supplier as an alternative to price discount. Further, the salvage value associated with deteriorated units is considered, and the shortages allowed are partially backlogged. Focus is made on obtaining the optimal replenishment policy by minimizing the total inventory cost. This is achieved by developing mathematical theorems that determines the existence and the uniqueness of the optimal solutions. Moreover, computational algorithm is designed and illustrated using numerical examples and analysis. Various managerial insights obtained from the analysis are also highlighted.

Reinvent Retail Supply Chain: Ship‐from‐Store‐to‐Store

Retailers such as Best Buy are reinventing their supply chains for the era of Omnichannel with new strategies like ship‐from‐store‐to‐store (SFSTS) where stores are also used as shipping points. Under the SFSTS practice, to fill the demand (offline and online) from a customer region, two or more nearby stores of the retailers’ frequently replenish from each other as well as from a distribution center (DC) to better prepare inventory before the demand arrives. We study how to best replenish the DC and multiple nearby stores under this new practice using a multi‐period inventory model with proactive transshipments. To the best of our knowledge, this study is the first to solve this model, and the characterized optimal replenishment policy is valuable especially as it differs significantly from the past relevant literature on single‐period models. In contrast, for the DC, although the procure‐up‐to policy is still optimal, the procure‐up‐to level is no longer constant but depends on all stores’ on‐hand inventory. For each store, the optimal policy no longer remains the same structure but changes with whether the DC procures inventory from the supplier. When the DC procures inventory, the stores’ optimal policy is no longer single‐threshold, but two‐threshold (order‐up‐to and ship‐down‐to); and these thresholds decrease in any other store’s on‐hand inventory. When the DC does not procure inventory, the stores ship between each other only when their inventories are imbalanced enough, and they ship until the benefit drops to just cover the shipping cost. Our results demonstrate that it is important to constantly track every store’s on‐hand inventory and it is much more complex to implement SFSTS with more nearby stores, despite the additional profit earned.

An Inventory Model based on Imperfect Production with Shortage Backorder

In this paper, we discussed about the imperfect items. In practice items may get damaged due to production or transportation conditions. Each lot receives some imperfect items. This model also considers the effects of business strategies such as optimal order size of raw materials, production rates and unit production costs, and idle time in different areas on the cooperation of marketing systems. The model can be used in industries such as textiles and footwear, chemicals, food. We develop an inventory model based on imperfect products and shortages. We consider demand is constant and continuous. Purpose of this study is not only to find the retailer`s optimal replenishment policies but also to minimize the total average cost. Finally, a numerical example is presented to illustrate the proposed model and sensitivity analysis of the optimal solution concerning parameters is carried out using the Mathematica 10.0 software.

Optimal replenishment and inventory financing strategy in a three-echelon supply chain under the variable demand and default risk

As supply chains span across one or more continents, an intermediate firm becomes an inevitable supply chain component. While seller-financing options (e.g. delay in payment), are well studied, researchers have rarely investigated them from the perspective of an intermediate firm in a supply chain. We construct a three-echelon supply chain that consists of a supplier, distributor, and retailer. In our model, the supplier and distributor may offer seller financing to their buyer, but only the distributor is subject to the buyer’s default risk. We consider a seller-financing supply chain wherein either all or none of the sellers premise delay in payment and a special case where the distributor may coordinate with the supplier or retailer. An algorithm solves optimal replenishment and delay-in-payment decisions. Numerical analyses illustrate managerial insights, which show that when the retailer’s default risk is high, the distributor’s best strategy is not to offer any delay-in-payment. When the distributor–retailer coordination can subsidise the retailer’s default risk, the distributor’s best strategy is coordination with the retailer and bargaining for more financial support from the supplier. In contrast, as the retailer’s default risk is inevitable, the distributor–supplier integration is the optimal supply chain financing strategy.