Replenishment Period Research Articles

Water-Filling Characteristics and Water Source of Weakly Rich Water and Weakly Conducting Water Aquifers in the Changxing Formation after Mining Damage

The escalation of mining activities in the karst regions of Guizhou Province has heightened the occurrence of water-inrush incidents in deep coal mines. This study focused on water-inrush phenomena within the Xinhua mining area of Jinsha County, Guizhou Province, aiming to investigate the sources of these incidents. The findings indicated that the overlying limestone of the Changxing Formation in the coal seam served as a vulnerable aquifer under certain conditions, leading to water inrushes. The analysis of the spatiotemporal distribution patterns of water-inrush incidents at the working face indicated that previous mining operations damaged the shallow Changxing Formation limestone, resulting in the accumulation of goaf water and the formation of numerous mining-induced fractures. These fractures served as rapid conduits for water inrushes from both atmospheric precipitation and underground sources at the deep working face. The examination of surface water and mine water quality demonstrated that both exhibited similar characteristics, predominantly featuring bicarbonate, sulfate, and sodium compositions. Investigation into the relationship between mine water inflow and atmospheric precipitation established that atmospheric precipitation influenced the mine water supply cycle, with a replenishment period of ~10 months during the operational phase of the Jinyuan Coal Mine and about one month post-closure. The fractures induced by mining activities within the Changxing Formation limestone facilitated water flow, with atmospheric precipitation serving as the primary water source for the mine. This study offered a valuable scientific foundation for addressing water-related damage resulting from atmospheric precipitation in mines susceptible to water inrushes under analogous hydrogeological conditions.

257 Estimating bone mineral replenishment following phosphorus deficiency in growing pigs

Abstract Available phosphorus (avP) is essential for bone health and strength in growing pigs. Our objective was to evaluate growth performance and replenishment of bone mineral in avP deficient pigs when fed diets adequate in avP. Over a 42-d test period, mixed sex pigs [n = 48; initial body weight (BW) = 13.1 ± 0.7 kg], were randomly assigned to one of three dietary treatments consisting of two experimental periods. In period 1(28 d), 8 pens/trt (2 pigs/pen) were fed diets formulated to 0.36, 0.17 and 0.08% avP and at a total calcium to avP ratio of 2.91, 3.15 or 6.40, respectively, representing adequate, marginally deficient, or deficient avP. In period 2 (14 d), marginally deficient and deficient pigs were then fed diets formulated to be above requirement at 0.54% avP and a 2.19 Ca:avP, while the adequate pigs staying on the same period 1 diet (n = 8 pens/trt). Pig BW and pen feed disappearance were recorded during each phase to calculate average daily gain (ADG), average daily feed intake (ADFI) and feed efficiency gain to feed (G:F). At the end of each period, 1 pig per pen was removed to assess whole body, femur, and 3rd metatarsal bone mineral content (BMC) and bone mineral density (BMD) via dual-energy X-ray absorptiometry (DXA). All data were analyzed with pen as the experimental unit and the fixed effect of diet within each period. At the end of period 1, adequate avP and marginally deficient fed pigs were heavier than the deficient avP fed pigs (41.9 and 41.2 vs 33.4 kg, respectively, P < 0.001). Consequently, ADG and ADFI were significantly reduced as avP decreased (P < 0.001). Compared with the adequate avP pigs, whole body BMD was reduced by 22% and 65% in marginal and deficient avP pigs (P < 0.001), respectively. At the end of period 2, adequate, marginal, and deficient avP pigs weighed 53.4, 53.2 vs 43.1 kg (P < 0.001), respectively. Within period 2, ADG, ADFI, and G:F did not differ. However, adequate avP fed pigs continued to have a greater body BMD compared with marginal and deficient avP pigs (0.928, 0.850, and 0.732 g/cm2; P < 0.001), respectively. Whole body BMD and BMC increased from period 1 to peiod 2, resulting in period 2 whole body BMC accretion rates of 2.31, 23.28, and 9.30 g/d (P < 0.007) for deficient, marginal, and adequate diets, respectively. In conclusion, pigs fed marginally deficient avP diets reduced body BMD while pigs fed deficient avP diets reduced body BMD and performance. Following this period of deficiency, marginal deficient avP pigs recovered growth and BMC within 14 d when fed increased dietary avP. However, compared with adequate avP fed pigs, the deficient pigs only partially recovered BMC and BW within the 14-d replenishment period.

PENETRATION OF BORROWED HYBRIDS INTO THE KAZAKH LANGUAGE

Nowadays the history of linguistics is characterized by an intensive period of replenishment of the Kazakh language with foreign terms. The introduction of considerable amount of international words of foreign background and their quick combination in the Kazakh language is explained by fast changes of public and academic life. Many borrowed words were introduced to Kazakh language by different ways and the reason for these were connected with scientific, economic, political and cultural ties. The examples of hybrid words in Kazakh language and their origin within the unique dialects are given in this article. The structure for creating hybrid words using English and Kazakh languages and their functional characteristics are presented in this article. Hybrid words are considered to be borrowed words. Loan words are words which came from other dialects and they refer to the process of speakers adopting words from a source language into their native language. The penetration of hybrid terminology into Kazakh language and the development of Anglo-Kazakh bilingualism is a result of this very «internationalism» of the English language. This leads to the creation of a new language situation, the study of which is very relevant nowadays. Keywords: hybrid, language, loan words, lexicology, neologism, foreign words, word-building, terminology.

Optimal ordering based on shortage scenarios under presence of a low-quality substitute and supply uncertainty

Global trade has shifted from short-distance supply chains within countries to long-distance supply chains between countries. As a result, delivery lead time has become a key operational factor, and uncertainty causes stock-outs, resulting in massive losses. An important solution for shortages is product substitutes, but they can affect the quality of the end products. Moreover, even when demand is expected and planned for, unexpected last-minute demand makes operational conditions challenging. This paper considers a single-period problem of replenishing a high-quality product under both lead time and demand-related uncertainty. Stock-outs during and at the end of the replenishment period can be handled only by providing a low-quality substitute product that requires repeated replacements, therefore affecting pending demand. We provide detailed modeling of possible stock-out scenarios and show that, in presence of these two types of uncertainty, the optimal order quantity of a high-quality product can be determined using an upper and lower threshold and a base stock level equal to anticipated (planned) demand over the replenishment period. In particular, we derive a closed-form solution for the optimal order quantity under general probability distributions of lead time and demand and explicit solutions for uniform distributions. We also show the conditions under which optimal order quantities can be insensitive to the cost of the high-quality product.

Dynamic pricing and replenishment policy under price, time, and service level-dependent demand and preservation investment

Time, price, and servicing are three important factors which affect the demand for any product. In a multi-period inventory model, different pricing in different periods may have a positive impact on demand. Offering discounts to customers during a shortage period is an efficient way to reduce lost sales. To address all these issues, a multi-period inventory model is developed and analyzed in this paper to obtain optimal pricing and replenishment periods where the market demand depends on price, time and service level provided by the retailer. The time horizon is fixed; the replenishment cycles are of equal length, but the shortage period may vary in different cycles. The retailer is allowed to charge different prices in different periods and provide discounts if someone places demand during a shortage period. Learning effects in holding and ordering costs are considered. Under a dynamic pricing framework, this study examines service improvement through learning and price discounts during shortages as an incentive for customers. It demonstrates that discounting indeed helps to produce more revenue when the back-order rate is low, and the service level is critical in generating demand when the stock-out period is lengthy, revealing a critical relationship between shortage periods and service level. A numerical experiment is performed to investigate the optimal policy in different situations and obtain some managerial insights.

Inventory model for green products with payment strategy, selling price and green level dependent demand using teaching learning based optimization algorithm

There has been a lot of research on pricing and lot-sizing practices for different payment methods; however, the majority has focused on the buyer’s perspective. While accepting buyers’ credit conditions positively impacts sales, requesting advance payments from purchasers tends to have a negative effect. Additionally, requiring a down payment has been found to generate interest revenue for the supplier without introducing default risk. However, extending the credit period, along with offering delayed payment options, has the potential to increase sales volume, albeit with an elevated risk of defaults. Taking these payment schemes into account, this study investigates and compares the per-unit profit for sellers across three distinct payment methods: advance payment, cash payment, and credit payment. The consumption rate of the product varies non-linearly not only with the time duration of different payment options but also with the price and the level of greenness of the product. The utmost objective of this work is to determine the optimal duration associated with payment schemes, selling price, green level, and replenishment period to maximize the seller’s profit. The Teaching Learning Based Optimization Algorithm (TLBOA) is applied to address and solve three numerical examples, each corresponding to a distinct scenario of the considered payment schemes. Sensitivity analyses confirm that the seller’s profit is markedly influenced by the environmental sustainability level of the product. Furthermore, the seller’s profitability is more significantly affected by the selling price index compared to the indices of the payment scheme duration and the green level in the demand structure.

The newsvendor problem with GHG emissions from waste disposal under cap-and-trade regulation

We study a newsvendor problem with greenhouse gas (GHG) emissions at the disposal stage regulated by a cap-and-trade policy. We first consider a synchronous version of the problem where the replenishment period and the emission assessment period are the same. For this problem, we propose simple algorithms to derive the optimal quantity and cost for both continuous and discrete demand distributions. We show that ignoring the carbon tax may lead to large overcost, especially when the GHG quota is small. For a normally distributed demand, we also show that the demand standard deviation has a non-linear and non-monotonic effect on the order quantity. We then investigate an asynchronous version of the problem where replenishment decisions occur at a higher frequency than the quota allocation. We formulate this lot sizing problem as a Markov decision process and solve it with a dynamic programming algorithm whose complexity is assessed. Through a numerical experimentation and theoretical results, we demonstrate how and when the flexibility of the optimal dynamic replenishment decisions allows to reduce costs. When approaching the end of the time horizon, the uncertainty reduction allows the decision maker to adopt a riskier policy and order larger quantities.

Replenishment Impacts on Hydrogeochemistry and Water Quality in the Hutuo River Plain

To investigate the influence of the Hutuo River (North China) ecological water replenishment project on the hydrogeochemical processes of groundwater, 64 groundwater samples collected at different time intervals after four replenishment events, and four samples from the Middle Route of the South-to-North Water Diversion Project water, were analyzed for water chemistry. Hydrogeochemical methods such as the Piper diagram, chloride-alkalinity index, and ion correlation were employed to analyze the characteristics of groundwater chemical evolution through replenishment. The results demonstrated that the hydrochemical types of groundwater in the study area underwent significant changes during continuous replenishment in the Hutuo River region. During the initial replenishment period (October 2019), the dominant hydrochemical type of groundwater in the study area was Mg-Na-HCO3-SO4, whereas the dominant type in the Middle Route of the South-to-North Water Diversion Project water was Ca-Na-SO4-HCO3. As the replenishment continued, the hydrochemical types of groundwater in the study area evolved into Ca-Na-Mg-HCO3-SO4, Na-Ca-Mg-HCO3-SO4, and Ca-Na-Mg-SO4-HCO3. The groundwater experienced a dissolution of calcite, gypsum, nitratine, carbonate rocks, and gypsum, accompanied by dilution effects, resulting in reduced ion exchange as replenishment progressed. The input of the high quality Middle Route of South-to-North Water Diversion Project water effectively promoted groundwater quality improvement, leading to an overall decrease or stabilization of components other than Ca2+ in the groundwater. Water quality was assessed using the entropy water quality index, with indicators including Na+, SO42−, Cl−, pH, total dissolved solids, NO3−-N, NO2−-N, F−, Al, As, and Zn. The evaluation results showed that, except for one medium-quality water sample, the water quality of the other samples was suitable for drinking and domestic purposes during the early replenishment period. The Middle Route of the South-to-North Water Diversion Project exhibited excellent quality (Rank 1), and as replenishment progressed, all water samples demonstrated good quality by October 2020, with a gradual improvement.

Synthesis and Applications of Hybrid Polymer Networks Based on Renewable Natural Macromolecules.

Macromolecules obtained from renewable natural sources are gaining increasing attention as components for a vast variety of sustainable polymer-based materials. Natural raw materials can facilitate continuous-flow production due to their year-round availability and short replenishment period. They also open new opportunities for chemists and biologists to design and create "bioreplacement" and "bioadvantaged" polymers, where complex structures produced by nature are being modified, upgraded, and utilized to create novel materials. Bio-based macromonomers are expected not only to compete with but to replace some petroleum-based analogs, as well. The development of novel sustainable materials is an ongoing and very dynamic process. There are multiple strategies for transforming natural macromolecules into sophisticated value-added products. Some methods include chemical modification of macromolecules, while others include blending several components into one new system. One of the most promising approaches for incorporating renewable macromolecules into new products is the synthesis of hybrid networks based on one or more natural components. Each one has unique characteristics, so its incorporation into a network brings new sustainable materials with properties that can be tuned according to their end-use. This article reviews the current state-of-the-art and future potential of renewable natural macromolecules as sustainable building blocks for the synthesis and use of hybrid polymer networks. The most recent advancements and applications that involve polymers, such as cellulose, chitin, alginic acid, gellan gum, lignin, and their derivatives, are discussed.

Machine learning based fuzzy inventory model for imperfect deteriorating products with demand forecast and partial backlogging under green investment technology

This article proposes a novel approach to managing inventory by incorporating machine learning techniques to handle imperfect deteriorating products under green investment technology. The shortages are permitted and partially backlogged. Due to uncertainty, deterioration rate and defective percentage in quantity in the received lot are considered fuzzy variables. This study aims to determine optimal ordering quantity and replenishment period to minimise the total average cost with carbon emission cost. Decision Tree Classifier algorithm is used to demand forecast seasonally. The total fuzzy cost functions defuzzify by applying sign distance approach method. A numerical example is taken to illustrate the proposed model. A comparative analysis has been studied between fixed demand and month-wise forecasted demand. The study highlights the importance of forecasted demand in the inventory system and establishes methodology to get direct month-wise forecasted demand. Finally, the sensitivity analysis performs to determine more sensitive parameters and provides managerial insights.

A new economic order quantity model for deteriorated items under the joint effects of stock dependent demand and inflation

In the present market scenario, it is seen that commodity is attracted by the stock of the items. Considering this fact in this present work, the demand for the item is considered as stock dependent in an inventory control system, where the items are deteriorating in nature. When the number of items in the stock increases, the number of deteriorations also increases. Also, this is important to know for a retailer that when an order will be placed and when the order will be received from the supplier. So, the lead time has an important role in the inventory control system in this stock-dependent demand inventory model. Also, it is seen that the market price of any item may increase gradually with time. Considering this phenomena, the inflation has been incorporated in this work. Here, the proposed model has been analyzed in a finite time horizon. From our analysis, the optimal profit has been calculated for optimal replenishment period of each cycle. Also, depending on the changes in the parameters such as demand, stock, and deterioration, the changes in optimal profit have been analyzed numerically and graphically in the numerical section and the effects of inflation also has been analyzed in this section. As the parameters associated with the system are not always deterministic, so uncertainty arises in the model. To remove this uncertainty, the model has been extended to a fuzzy model considering the q-fuzzy membership function. The fuzzy model has been defuzzified using the Center of Gravity (COG) method and fuzzy extension principle. Also, the fuzzy model has been analyzed by numerical illustration and some sensitivity analysis have been shown corresponding to different values of q and different membership values of the fuzzy parameters.

Driving mechanism of water replenishment on DOM composition and eutrophic status changes of lake in arid and semi-arid regions of loess area

Water replenishment can be a key factor in driving lake eutrophication status. In arid and semi-arid regions of China, water replenishment for a lake has been widely carried out for not only improving water environmental quality, but also maintaining ecological system function. However, it is still unclear in terms of mechanism by which water replenishment drives lake eutrophication status. In this study, fluorescence excitation-emission matrix spectroscopy (EEMs) combined with multiple statistical analysis models (including parallel factor analysis, correlation analysis, redundancy analysis, and partial least squares structural equation modeling) was utilized to reveal potential driving mechanism and causality between water replenishment, dissolved organic matter (DOM) fractions and eutrophic status of Lake Shahu in China. Based on variations of DOM fractions, fulvic-like substances could be accumulated during the replenishment period, while nutrients carried along the replenishment might conduce to increase microbial activities during the non-replenishment period. This should be contributed to an alteration of prominent component from fulvic-like substances to tyrosine-like substances during the replenishment period to non-replenishment period. According to partial least squares structural equation modeling, two potential indirect paths were finally revealed, i.e., water replenishment derived the eutrophic status of Lake Shahu: water replenishment → microbial activity → algae → eutrophication, and water replenishment → microbial activity → eutrophication. This supposed that the water replenishment should indirectly drive the algae and eutrophication of the lake by promoting the transformation of DOM fractions. In addition, natural conditions could indirectly contribute to the eutrophication of the lake through impacting the algae growth. These findings should be conducive to trace the alteration of DOM fractions in lakes by water replenishment and in recognizing potential driving mechanisms of water replenishment on eutrophication of lakes by changing DOM fractions. This could provide basic theoretical support for policymakers to regulate and treat the eutrophication of lakes.

Особенности распределения снежного покрова в насаждениях Рудного Алтая

The article presents the results of examining the formation and peculiarities of snow cover in fir plantations compared to open shrubland in the conditions of Southwestern Altai obtained during 2020-2021 snow period. The forest stand affects snow distribution and characteristics in fir woods by capturing snow with tree crowns, snow accumulation around crown perimeter and, as a result, leads to the formation of near-trunk snowdrifts, in their turn facilitating higher snow accumulation among trees and at forest edges. The maximum snow cover thickness in fir woods ranged from 80 cm (under crowns) to 150 cm (among trees and along forest edges). In the open (control) zone, snow distribution appeared more homogenous – from 126 to 135 cm. During the period of maximum snow accumulation, snow density in fir plantations ranged from 0.19 to 0.26 g/cm3; and, from 0.24 to 0.29 g/cm3 in the control zone. Snow cover humidity likewise demonstrated significant differences between fir plantations and control site, and amounted to 258.3±13.47 mm and 279.7±12.80 mm, respectively. Whereas in the control (overgrown) zone the complete snow cover melting ended in the second 10-day period of April, in fir woods it finished in the second 10-day period of May. The research findings suggest that fir plantations in river catchment areas boost winter precipitation retention and slow down its loss resulting in more uniform water transition into subsurface runoff and longer period of river water replenishment.

An Adaptive Web-Based Inventory Control System for Universities

Managing inventories is one of the major challenges that organizations such as tertiary institutions are facing. Most of the stocks kept in organizations are characterized by excessive inventory on hand, raw materials losing their quality, improper sourcing methods, poor personnel management skills, etc. There also exists a lack of accurate and timely information. In order to arrest these deficiencies, an adaptive web-based inventory control system was developed. The current inventory in the storage unit of Olusegun Agagu University of Science and Technology (OAUSTECH), Okitipupa was captured. Collection of data from the Procurement and Store Unit was done through interviews, observation of record books, and some printable data. The system was implemented using PHP, HTML files, BOOTSTRAP, and MySQL. The outcomes are the generation of timely alert messages and reports to management when the inventory level reaches an out-of-stock threshold, computation of various inventory analyses such as price levels, lead-time analysis, replenishment period demand analysis, vendors' delivery performance, and generation of low-cost stock recommender system.

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.

Optimization of the vendor's inventory model with multisupplier and multiretailer using fuzzy parameters

This paper explores the multi-item vendor's inventory (VI) model in which the vendor replenishes the products from various suppliers and satisfies the retailers' demand. Different types of products scrutinize this model under two cases. The first case considers the products are replenished in bulk and packed in small quantities by the vendor and sent to the retailers. The second case presumes that the vendor replenishes the packed items from the supplier and sent to retailers without the packaging process. The wastage of products during the packaging process occurs in the first case and the deterioration of items occurs in both cases. The unpredictable parameters such as the proportion of wastage products and the proportion of deteriorated products lead the model under fuzzy logic. The VI model and the Vendor's fuzzy inventory (VFI) are framed. VFI model is formulated by assuming the wastage rate and the deterioration rate as triangular fuzzy numbers (TFN) as well as trapezoidal fuzzy numbers. The defuzzification method of TFN and trapezoidal fuzzy numbers by the combination of Beta distribution and a uniform distribution is utilized in this paper. For both cases, the optimal ordering and purchasing period, the optimal retailer's replenishment period, and the optimal packaging period for case (i) is computed which minimizes the vendor's total cost. The computational example and sensitivity analysis are performed to flourish the study more effectively.

EFFECTIVENESS OF JUST-IN-TIME PRINCIPLE IN TODAY´S CIRCULAR ECONOMY AND ITS NEGATIVE EFFECT

In the context of circular economy, manufacturers aim to improve the quality of the environment and human life. With regard to the nature of their production, business entities within circular economy adopt the philosophy of the Just-In-Time method. This paper analyses the impact of this method on the current supplier-customer relations in the Czech Republic as well as the quality of fulfilment of its obligations. Moreover, it is evaluated whether the concept of Just-In-Time method is suitable for efficient functioning of this economy. Based on the data obtained, a comparison analysis of the research problem is performed. The level of meeting deadlines for supplies in the manufacturing process of a domestic business entity is examined. The analysis performed did not confirm the idea of combining speed with the adaptive response to change. In the Czech Republic, the Just-In-Time method is currently influenced by a number of negative factors, which significantly affect the current supplier-customer relations and the quality of fulfilment of their obligations. The key factors affecting the effectiveness of the Just-In-Time principle include the extension of the stock replenishment period and inaccurate logistics cooperation in the area of production planning.

Insight into temporal\u2013spatial variations of DOM fractions and tracing potential factors in a brackish-water lake using second derivative synchronous fluorescence spectroscopy and canonical correlation analysis

BackgroundInsight into temporal–spatial variations of dissolved organic matter (DOM) fractions were undertaken to trace potential factors toward a further understanding aquatic environment in Lake Shahu, a brackish-water lake in northwest China, using synchronous fluorescence spectroscopy (SFS) combined with principal component analysis (PCA), second derivative and canonical correlation analysis (CCA).ResultFive fluorescence peaks were extracted from SFS by PCA, including tyrosine-like fluorescence (TYLF), tryptophan-like fluorescence (TRLF), microbial humic-like fluorescence (MHLF), fulvic-like fluorescence (FLF), and humic-like fluorescence (HLF), whose relative contents were obtained by second derivative synchronous fluorescence spectroscopy. The increasing order of total fluorescence components contents was July (11,789.38 ± 12,752.61) < April (12,667.58 ± 15,246.91) < November (19,748.87 ± 17,192.13), which was attributed to tremendous enhancement in TYLF content from April (1615.56 ± 258.56) to November (5631.96 ± 634.82). The PLF (the sum of TYLF and TRLF) dominated the fluorescence components, whose proportion was 40.55, 37.09, or 46.91% in April, July, or November. DOM fractions in November were distinguished from April and July, which could be attributed to that water of the Yellow River was continuously loaded into the lake as water replenishment from April to September. From the replenishment period to non-replenishment, the contents of the five components gradually changed from low in the middle and high around the lake to high throughout entire lake. Based on the CCA results, the potential factors included TYLF, TRLF, MHLF, SD, and BOD5 in April, which were relative to organic matter pollution. The potential factors contained TYLF, TRLF, FLF, Chl-a, TP, CODCr, and DO in July, indicating the enrichment of TP lead algae and plants growth. The potential factors in November consisted of TYLF, TRLF, CODCr, SD, TN, and FLF, representing residue of the algae and plants have been deeply degraded.ConclusionThe replenishment of water led to enrichment of TP, resulting in growth of algae and plants, and was the key factor of water quality fluctuations. This work provided a workflow from perspective of DOM to reveal causes of water quality fluctuations in a brackish-water lake and may be applied to other types of waterbodies.

A resilient hybrid payment supply chain inventory model for post Covid-19 recovery

The present Covid-19 pandemic causes disruptions to markets and businesses in general, affecting the supply chain inventory system most significantly. This work investigates a hybrid payment inventory model considering inflation, cash discount, price-sensitive demand, and preservation technology investment for non-instantaneous deteriorating products. Due to the economic downturn, a hybrid payment scheme composed of multiple prepayments and a delay in payment is proposed to facilitate post Covid-19 recovery. The proposed model is one of the first models to consider a hybrid payment scheme in view of the Covid-19 pandemic, and to provide guidelines to retailers in planning the selling price, replenishment period, and preservation investment in view of the pandemic situation. The hybrid payment policy is suggested during the financial crisis to sustain orders from a retailer to the supplier and from the consumers to the retailer. During the supply disruptions, two cases for shortages and without shortages are studied. The nonlinear model is solved by Lingo 17 software. This study shows the effect of advance and delayed payments on the retailer’s total profit. It also shows that the total profit is extremely delicate to the inflation rate. The numerical examples illustrate the inventory model for different scenarios. Sensitivity analysis is carried out to provide managerial insights to management during post Covid-19 recovery.

Cyclic inventory routing with dynamic safety stocks under recurring non-stationary interdependent demands

We consider the Inventory Routing Problem (IRP) with one vendor replenishing the inventories of many retailers who face stochastic demands. To hedge against demand uncertainty, dynamic lot-sizing and safety stock planning are integrated using chance-constrained programming to adapt to the varying demand uncertainty across planning periods and allow for variable replenishment periods. We present a tactical approach towards obtaining cyclic delivery schedules that avoid given starting inventories and account for non-stationary interdependent demands. The assumption of independent, identically distributed (i.i.d.) demands often oversimplifies the stochasticity of the underlying demand time series by neglecting, among other things, seasonality and correlation. In IRPs, the evolution of the demand time series highly affects the consolidation of retailer replenishments in delivery routes. The problem is modeled as a mixed-integer linear program (MILP), including several real-world characteristics. To obtain solutions faster than by using MILP solvers, we propose a multi-start adaptive local search and an adaptive large neighborhood search (ALNS) heuristic. The influence of several problem parameters on the solutions is investigated. The benefit of an integrated planning of lot-sizing and routing over sequential planning is assessed. The results show that the proposed approach for cyclic delivery schedules allows a (de-)synchronization of retailer replenishments and their consolidation in vehicle routes while meeting real-world constraints in both routing and inventory management. Under non-stationary demands, it yields savings of 2.8% and 1.9% on average compared to given or zero starting inventories by setting initial inventories endogenously. The presented heuristics render near-optimal results. The ALNS deviates by only 0.6% from optimal on instances where cv=0, and by an average of 1.6% from optimal on all small-sized instances. On larger problems, it outperforms the other heuristics and obtains an average deviation from the best solution found of only 0.1%.