Optimal Replenishment Policy Research Articles

ECONOMIC ORDER QUANTITY (EOQ) MODEL: WEIBULL AMELIORATING ITEMS WITH CONSTANT DEMAND RATE

In this study, we investigate the behavior of inventory items having the potential of incurring significant increase in their utilities or values while in stock in accordance to the Weibull distribution law. The amelioration of an inventory occurs when it remains in stock but depletes as a result of constant demand rate. The Weibull amelioration function plays the role of depicting the amelioration state of an inventory whereas the constant demand function describes the different possible stages of market demand. We describe the application of simple, yet analytical, approach for successful derivation and analyses of the underlying inventory system. We furthermore, analyze the model while providing, for the model, the necessary but sufficient and optimal replenishment policy. We use numerical results and examples to better illustrate the solution and successfully carryout the sensitivity analysis and the evaluation of the model.

Analyzing how inflation affects non-instantly decaying goods with demand linked to ads and selling price in a dual-warehouse setup

This study explores inventory management strategies specifically designed for non-instantaneous deteriorating goods under inflationary conditions, utilizing a dual-warehouse system—one owned and the other rented with limited storage capacity. We examine the effects of advertising frequency and product selling price on demand rates, taking into account the gradual decline in customer patience, which leads to partial backlogging of shortages. The primary objective is to determine optimal replenishment policies for retailers that effectively minimize total costs per unit time. In real life, managing oil inventory is crucial for industries where factors like gradual deterioration, demand fluctuations due to advertising and pricing, and sensitivity to inflation require sophisticated inventory models to optimize replenishment policies and minimize costs. To validate our proposed inventory model, we provide a numerical. A sensitivity study using MATLAB R2024a software highlights the impact of parameter changes, providing significant information for decision-makers across various industries.

Managing Replenishment and Clearance of Perishables: Last-In, First-Out (LIFO) Issuing Policy and Age-Sensitive Demand

In supermarkets, customers choose the unit(s) they purchase, which leads to inventory being sold in a last-in, first-out (LIFO) order for perishable products. Furthermore, for such products, 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. Despite the widespread occurrence of LIFO-based inventory systems, few studies have analyzed them. In this study, we contribute by developing insights on joint replenishment and clearance policy for a perishable product with a general, finite lifetime using a periodic review model such that the inventory is sold in a LIFO order and demand is age-dependent. The model seeks to optimize two decisions every period: how much of fresh inventory to order and how much of existing inventory to clear. A 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 clearance policy for all but the oldest inventory is a multiindex policy such that between any pair of adjacent indexes, either no inventory is cleared or all the inventory is cleared till the lower index. For the oldest inventory, we show that the optimal policy may have multiple forms depending on how sensitive demand is to inventory’s age. This is a notable result in inventory theory since parameters usually affect only the policy value(s) and not the policy structure. Since the optimal policy has a complex structure in general, which makes it difficult to compute, we develop an efficient heuristic to compute the replenishment and clearance quantities. The heuristic underperforms the optimal policy by [Formula: see text]0.92% on average.

Enhancing supply chain efficiency through blockchain technology: A centralized multidistributor and multi-retailer approach

Blockchain technology has emerged as a transformative solution for supply chain management, offering a myriad of benefits to the industry. This paper explores the potential benefits of incorporating blockchain technology into supply chain management to enhance security and trustworthiness. We present a centralized supply chain system comprising a single manufacturer, multiple distributors, and multiple retailers. Geographical divisions have been assumed among distributors, each catering to a specific area with its own set of retailers. Mathematical expressions are developed to determine the optimal replenishment policies for the manufacturer, distributors, and retailers. Numerical examples are provided to illustrate the results, and sensitivity analysis is conducted to assess the model's responsiveness to parameter variations. Finally, managerial insights are discussed, shedding light on the implications and advantages of the proposed blockchainbased supply chain management system.

Optimal policy for an inventory system with retailer's hybrid payment strategy and supplier's price discount facility under a supply chain management

Suppliers often offer item-wise price discounts and trade credit to their retailers after receiving an initial payment for the supplied product. This discount is proportional to the total payment done already against the total cost accrued by the retailer. The supplier may also decide to allow the retailer to prepay a random part of the purchasing cost at any random time within the duration that an advance payment is allowed. In order to encourage the customers to increase their orders, the retailer, in turn, offers a trade-credit for a partial amount of the sale price to the customers. In this paper, we focus on the optimal replenishment policies of a retailer that could maximize the retailer's average profit when (s)he is confronted with the supplier's trade offers of credit and price-discount under a two-layer supply chain management in a stochastic environment. We have obtained some theoretical results from the optimum cycle time and optimum order quantity of the proposed model and numerically analysed with a suitable example to demonstrate the real-life applicability of the model. The extended study proposes for maximum average profit, the retailer borrow half amount of purchasing cost from financial support and has to pay at the starting of the advance payment period. Finally, sensitivity analyses are made on the significant parameters in order to gain some managerial insights.

Optimal robust inventory management with volume flexibility: Matching capacity and demand with the lookahead peak‐shaving policy

We study inventory control with volume flexibility: A firm can replenish using period‐dependent base capacity at regular sourcing costs and access additional supply at a premium. The optimal replenishment policy is characterized by two period‐dependent base‐stock levels but determining their values is not trivial, especially for nonstationary and correlated demand. We propose the Lookahead Peak‐Shaving policy that anticipates and peak shaves orders from future peak‐demand periods to the current period, thereby matching capacity and demand. Peak shaving anticipates future order peaks and partially shifts them forward. This contrasts with conventional smoothing, which recovers the inventory deficit resulting from demand peaks by increasing later orders. Our contribution is threefold. First, we use a novel iterative approach to prove the robust optimality of the Lookahead Peak‐Shaving policy. Second, we provide explicit expressions of the period‐dependent base‐stock levels and analyze the amount of peak shaving. Finally, we demonstrate how our policy outperforms other heuristics in stochastic systems. Most cost savings occur when demand is nonstationary and negatively correlated, and base capacities fluctuate around the mean demand. Our insights apply to several practical settings, including production systems with overtime, sourcing from multiple capacitated suppliers, or transportation planning with a spot market. Applying our model to data from a manufacturer reduces inventory and sourcing costs by 6.7%, compared to the manufacturer's policy without peak shaving.

Determining the Optimal Replenishment Policy in an Integrated Vendor–Buyer with Multiple Delivery Policy

Determining the Optimal Replenishment Policy in an Integrated Vendor–Buyer with Multiple Delivery Policy

An inventory model with permissible delay in payment and different interest rate charges

Adopting the permissible delay method by suppliers offers ample opportunity to overcome the burden of holding costs from retailers. This compensates retailers against the competitive situation as an alternative to price discounts. We present an inventory model for a finite time horizon for deteriorating items. The model focuses on an optimal replenishment policy to maximize profit through inventory control by considering two different interest rate charges. The implementation is possible by the proposed mathematical model for a ramp-type demand with a permissible delay of payment approach. We compare two scenarios: with and without permissible delay in payment. The computational algorithm, numerical examples, theorems, Hessian matrix, and graphs confirm the effectiveness of the inventory model proposed in this study. Sensitivity analysis is used to find risk-compensate opportunities in a peculiar situation.

Optimal replenishment and transshipment management with two locations

AbstractWe study the problem of optimally managing an inventory system with backorders over a finite time horizon where the objective is minimization of expected total discounted costs. The system consists of two locations each stocking the same product. At the beginning of each time period decisions are made about replenishment at each location and about any quantity to transship between the locations before demand is observed. Leveraging the L♮‐convexity of the problem's cost function; we characterize the optimal replenishment and transshipment policy for this system. More specifically, we show the optimal policy can be described using switching curves monotone in the system state. We also discuss two extensions. For a lost‐sales model, we establish L♮‐convexity and apply it to characterize the optimal policy, simplifying the analysis found in previous work. In the other extension, we investigate the optimal policy for a partial transshipment problem where only one location orders from the external supply source and then transships to the other location.

Sustainable production model with stochastic machine breakdown using smart manufacturing under circular economy

<abstract> <p>Machine breakdown usually implies unexpected physical damage to machinery due to any reason which requires fixing or replacement to continue the process. This article presentsan investigation of a sustainable model with stochastic machine breakdown. To reduce the risk of disruption,a smart manufacturing system is used. Considering the environmental issues faced by people,the model is developed under a circular economy through end-of-life treatment to recapture the value of the product,labor and resources. The used buyback products are collected,out of which items in good condition are remanufactured and sold in another market while the rest are salvaged. As the production process is not perfectly reliable,the serviceable products go through an automated inspection process,and imperfect items are reworked. A mathematical model is developed for deterioration of items to analyze the optimal replenishment policies,and the results have been illustrated with numerical verification. Based on the analysis,some managerial insights have been provided for decision-makers.</p> </abstract>

Inventory Management with Advance Supply Contracts Across Multiple Replenishment Periods

In this paper, we study optimal procurement policies with advance contracting option over a finite multi-period horizon for a seasonal product. In this setting, each period is defined by the time between two consecutive inventory replenishment stages where demand is not stationary across periods. Demand for the product in each period is stochastic whose probabilistic distribution is a function of the market signal received right before the beginning of the selling season. The firm receives price discounts by making quantity contracts in advance of the selling season and thus, before the realization of the market signal. Replenishment costs vary across periods during the selling season. We investigate optimal combination of advance contracting and expedited replenishment policies using stochastic dynamic programming. Our research is primarily motivated by applications in the cruise line industry where contracts are made before the final number of bookings is realized and additional purchases can be made at ports of call with varying local prices. Our results show that optimal replenishment policies follow order-up-to policies and there is a unique advance contract amount that minimizes the expected costs over the planning horizon. We provide a numerical sensitivity analysis to investigate the effects of replenishment prices, demand volatility, and disparity between periods in terms of demand on the advance contract amount, replenishments from the spot markets, service levels, and the overall expected cost.

Optimal replenishment policy for non‐instantaneous deteriorating items with stochastic demand under advance sales discount and available capacity

This paper presents a two‐warehouse inventory model for non‐instantaneous deteriorating items with a price‐dependent stochastic demand under advance sales discount and available capacity. In this model, the retailer offers a price discount to customers if they can commit their orders prior to the sales period. It encourages the retailer to order a large quantity that can be stored in an owned warehouse and then in a rented warehouse if there are excess items. Shortages are allowed and partially backlogged. The objective of this paper is to simultaneously determine the optimal price discount, the optimal order quantity, and the optimal replenishment schedule in such a way that the expected total profit is maximized. Two theorems are proved in order to verify that the expected total profit function is concave and to identify that an optimal replenishment decision exists. We further propose an algorithm to find the optimal replenishment policy by the retailer. Finally, we use numerical examples to illustrate the results presented herein. Moreover, based upon the sensitivity analysis, some important managerial implications are also discussed.

Optimal Replenishment Policies and Trade Credit for Integrated Inventory Problems in Fuzzy Environment

In this highly volatile, uncertain, complex, and ambiguous (VUCA) environment, a fuzzy inventory optimization problem is a hot topic that received the most attention from both academicians and practitioners. In this paper, the authors have studied the integrated inventory problems under trade credit in fuzzy environments, where the demand rate and deterioration rate are taken here as triangular fuzzy numbers. Accordingly, three types of fuzzy programming models as fuzzy expected cost minimization model, fuzzy α-cost minimization model, and credibility maximization model are built according to different management goals. Since the problem is shown to be NP-hard, this research focuses on proposing a hybrid intelligent algorithm by integrating fuzzy simulation, neural network, and genetic algorithm for solving these models. Then, some numerical examples are presented to illustrate the benefits of the models and evaluate the efficiency of the algorithms. The computational experiments show that the trade credit strategy has a positive impact on improving the supply chain’s performance and reducing its total cost. In addition, the maximum relative error of the objective values is less than 1%, which implies that the hybrid intelligent algorithm is robust to the parameter settings and effective in solving our models. Finally, the practical implications are discussed and useful managerial insights are given.

Optimal policies for finite horizon model with time-varying demand rate, non-instantaneous deterioration and backlogging

This paper is concerned with the problem of finding an optimal replenishment policy for a finite planning horizon inventory model with time-varying demand, non-instantaneous deteriorating items and backlogging. This is formulated as a problem of solving some mixed integer non-linear program whose optimal solution delivers the frequency of orders as well as the timing of orders. The phenomena of non-instantaneous deterioration introduce a non-smoothness in the objective function which makes direct application of existing results, in the literature, not possible to the present model. A complete mathematical analysis of the problem is undertaken to overcome the non-smoothness of the objective and derive the optimal inventory policy. Uniqueness of the policy is shown under some technical conditions. Numerical results are presented for illustration.

Strategic decisions in an imperfect quality and inspection scenario under two-stage credit financing with order overlapping approach

To sustain fierce competition prevailing in the market, customer satisfaction is one metric that any firm can profoundly rely on to measure its performance. In the proposed model, a tri-tier supply chain (manufacturer - wholesaler - retailer) is studied where the consignment received is unreliable due to imperfect items. With the focus on customer satisfaction, the consignment is first screened for defects where screening, realistically, is error prone. With the intent of not losing customers due to shortages, the demand during current screening period is fulfilled from the perfect items of the previous order cycle. In addition, for financial safety, the wholesaler who receives a full trade credit by the manufacturer in turn offers partial a trade credit to his/her subsequent retailer. Therefore, a valid assumption in such type of scenario is that the demand is credit period dependent. Considering all the above-mentioned factors, an optimal replenishment policy has been investigated which serves as a ready reckoner for the operations manager. An extensive numerical and sensitivity analysis has been performed to demonstrate the validity of the proposed framework and provide useful managerial insights.

Optimal replenishment, pricing and preservation technology investment policies for non-instantaneous deteriorating items under two-level trade credit policy

<p style='text-indent:20px;'>In the business world, both the supplier and the retailer accept the credit to make their business position strong, because the credit not only strengthens their business relationships but also increases the scale of their profits. In this paper, we consider an inventory model for non-instantaneous deteriorating items with price sensitive demand, time varying deterioration rate under two-level trade credit policy. Besides, to reduce deterioration rate, retailers invest some cost to prevent product degradation/decay, known as preservation technology, is also inserted. Consumption of such items within shelf life prevents to deterioration, which can be achieved by bulk sale. In order to stimulate the selling, trade-credit policy is also considered here. In the sequel, not only the supplier would offer fixed credit period to the retailer, but retailer also adopt the trade credit policy to the customers in order to promote the market competition. The retailer can accumulate revenue and interest after the customer pays for the amount of purchasing cost to the retailer until the end of the trade credit period offered by the supplier. The main objective is to determine the optimal replenishment, pricing and preservation technology investment strategies including whether or not invest in preservation technology and how much to invest in order to maximize the average profit of the system. It is proved that the optimal replenishment policy not only exists but is unique for any given selling price and preservation technology cost. An algorithm is presented to derive the optimal solutions of the model. Numerous theorems and lemmas have been inserted to obtain the optimal solution. Finally, numerical examples and managerial implications are incorporated to validate the proposed model.</p>

Optimal replenishment and preservation investment policy for hybrid demand with trade credit schemes

A safe and sustainable environment has become a top priority for all kind of businesses. This research is to develop a sustainable model of frozen products for hybrid price-stock-dependent demand with preservation technology. Generally, the consumption rate is often affected by the price and stock levels for some types of consumer products. In this study, the demand of the product depends on the price and stock of the product as well, and the retailer invests in preservation technology to decrease the occurrence of deterioration of seasonal goods. This results in high demand of products, which encourage both the retailer and the consumer. A massive pile of items in the supermarket is typically found to lead the consumer to buy more creating high demand. The objective is to optimise the replenishment cycle and preservation technology investment cost with hybrid price-stock dependent demand, time-varying carrying cost, and trade-credit policy under shortages for dairy and frozen products. These factors will improve and encourage the purchaser's judgment to buy more products with the appropriate amount. The model is illustrated numerically and validated by sensitivity analysis.

Technical Note—A Permutation-Dependent Separability Approach for Capacitated Two-Echelon Inventory Systems

Analyzing Capacitated Two-Echelon Systems with Permutation-Dependent Separability Capacitated multiechelon systems are common in practice due to the escalating costs of labor and advanced manufacturing technology. However, identifying the optimal replenishment policies for such systems is a largely open area of research due to the intrinsic complexity, especially when there is an upstream bottleneck. In “A Permutation-Dependent Separability Approach for Capacitated Two-Echelon Inventory Systems”, Shen, Yu, and Huh propose a new approach, that is, permutation-dependent separability, to tackle a capacitated two-echelon system in which the capacity of upstream stage can be the bottleneck. They show that the value function for the capacitated two-echelon system in each period is permutation-dependent separable, and that for each echelon, a permutation-dependent echelon base stock policy is optimal. The authors also develop efficient solution procedures on how to obtain the optimal policy.

Design of multi-warehouse inventory model for an optimal replenishment policy using a Rain Optimization Algorithm

In most of the inventory management model, deterioration of item is considered as a common problem. In this study, non-instantaneous type of items are taken to examine a new decision making model of Optimal Replenishment Policy (ORP) scheme with multi-ware house multi-item model. This model is solved by a recent optimization algorithm named as Rain Optimization Algorithm (ROA) by considering different parameters like total cost, total delivery time and total investment on each item. Moreover, this research is developed with multi-warehouse model in which one is an own house and others are rented houses with restricted volume of storage. In particular period of time, deterioration of item is considered as constant and demand of items are assumed as stock independent. Shortage are allowed in the own warehouse model with backlogging. Major goal of this research is to discover retailers’ replenishment policy to obtain maximum total profit on each items with less total cost. Matlab tool is utilized to illustrate the proposed methodology as well as to solve the mathematical model. Footwear inventory management dataset engaged to evaluate the robustness of proposed methodology. Sensitivity and statistical analysis are made to examine the influence of different significant metrics on system decision variables and its outcomes are compared with different optimization algorithms.

Multiperiod Portfolio Procurement Problem With Option Contracts

A multiperiodic structure always underlies the procurement problem in practice. Option contracts are widely used to make a firm capable of responding flexibly to high demand uncertainty. However, so far, the impact of different option contracts on the multiperiod decisions and performance of a firm has been not discussed. Motivated by this problem, in this paper we analyze the multiperiod procurement problem within the framework of wholesale price, call, put, and bidirectional option contracts. Based on the dynamic programming theory, we characterize the structure of the firm's optimal replenishment policy for each period in four cases. We then develop a heuristic to approximate the corresponding policy parameters. Through system comparisons of four cases, we examine the value of option contracts for the firm and discuss the best option contract type for the firm. The results show that the firm will gain higher profits after the option contracts are introduced. Moreover, if the unit purchase and exercise costs of the bidirectional option are equal to those of the unilateral option, then bidirectional option contracts are preferred over unilateral option contracts. If the unit purchase cost of the bidirectional option is higher than that of the unilateral option, unilateral option contracts may be more profitable than bidirectional option contracts. Furthermore, if the unit backlogging cost is high and the unit inventory holding cost is low, call option contracts are better than put option contracts; if the unit backlogging cost is low and the unit inventory holding cost is high, then put option contracts work better than call option contracts.