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In practice, the demand for a fresh product depends on how fresh it is, therefore, it is important to take expiration date into consideration as it is a key to determine the freshness level of any perishable items. Furthermore, based on marketing and economic theory, selling price plays a crucial role in influencing the demand. Also, a higher inventory level may enhance the profit as it encourages consumers to buy more. Since the demand for fresh product declines over time, markdown policy is offered after some time to increase the demand and profit while reducing the inventory. For this demand function, it may be profitable to maintain a high stock level and the zero ending inventory is relaxed to non-zero ending inventory. Salvage value is incorporated into the deteriorating units. Using differential equations, we propose an economic order quantity model which demand dependent on freshness-expiration date, price and inventory level under markdown policy. We also demonstrate the relationship between markdown time and the annual total profit. Numerical example and sensitivity analysis are used to illustrate the effectiveness of the model.

Inventory level has a significant impact on the goodwill of products to customers, which seldom becomes the focus of previous studies. In this paper, joint dynamic pricing, advertising, and production decision-making problem is investigated, where the demand rate depends on sales price and goodwill. The inventory and backlog as well as advertisement are considered as goodwill-building factors. The optimal dynamic pricing, advertising, and production policies are derived by using Pontryagin’s maximum principle. Numerical examples are provided to demonstrate the obtained results, and sensitivity analysis of main system parameters is carried out to obtain some managerial insights. We find that when the initial goodwill is relatively high, the firm’s profit first decreases and then increases with respect to the impact intensity of inventory on goodwill; otherwise, the firm always benefits from a higher impact intensity of inventory on goodwill. Furthermore, the optimal production and advertising policies are complementary caused by the feature of inventory-dependent goodwill.

This paper studies a single-period inventory-pricing problem with two substitutable products, which is very important in the area of Operations Management but has received little attention. The proposed problem focuses on determining the optimal price of the existing product and the inventory level of the new product. Inspired by practice, the problem considers various pricing strategies for the existing product as well as the cross elasticity of demand between existing and new products. A mathematical model has been developed for different pricing strategies to maximize the expected profit. It has been proven that the objective function is concave and there exists the unique optimal solution. Different sets of computational examples are conducted to show that the optimal pricing and inventory strategy generated by the model can increase profits.

This study examines the joint optimization of pricing and ordering decisions for a loss-averse newsvendor with reference dependence. We explore the effects of reference dependence and loss aversion from various aspects. We find that demand type, reference point type and cost setting heavily affect the optimal decisions. For multiplicative demand, reference dependence leads to ordering less. Whether to further raise the price depends on the cost setting. For additive demand, selling fewer (cheaper) is the best in the fixed-amount (fixed-ratio) cost setting. Compared with a deterministic reference point, stochastic reference point has a lower price and a higher inventory level.

The impact of strategic consumers' disappointment aversion preference on retailer's inventory decision and profit when the retailer adopts quantity commitment strategy is studied in this paper. By comparing with the situation without quantity commitment, we analyze the effectiveness of this strategy. Through analytical analysis, we have the following conclusions. First, the optimal inventory level with quantity commitment is lower than that without quantity commitment, and both of them have positive correlations with the level of consumers' disappointment aversion. That is, consumers' disappointment aversion can mitigate the negative impact of their strategic behavior on the retailer's profit. Second, when other parameters are fixed and consumers' disappointment aversion level is below a certain threshold, the quantity commitment strategy is effective. However, when the cost is high, or consumer's valuation is low, or the salvage price is low, and at the same time if consumers' disappointment aversion level is high, then quantity commitment strategy can be ineffective. Finally, there are corresponding parameter intervals, when other parameters are fixed, the retailer's profit increment (when it is effective) by adopting quantity commitment strategy is positively related to consumers' valuation and salvage price of the product, and negatively related to the product cost. All our conclusions are illustrated in detail by numerical examples.

We consider a firm that faces the following pricing and leadtime disclosure decision. Either, (1) offer the same price to all arriving customers and disclose no leadtime information, in which case customers know only an expected leadtime, or, (2) vary the price dynamically based on the current inventory status, and disclose leadtime information dynamically. The second option allows the firm to offer a price discount for a long leadtime, and to offer a short leadtime when it has a large inventory. In order to determine which pricing and leadtime disclosure policy attains higher maximum profit, we formulate and solve a Markov decision problem for each policy and compare the two solutions. The comparison suggests that, typically, there is a critical inventory level, above which static pricing and no leadtime disclosure yields higher profit, and, below that level, dynamic pricing and leadtime disclosure yields a higher profit. We also identify certain situations where the static policy leads to profits at least as large as those under the dynamic policy, for any state, and we examine the price differences between the two policies. Finally, the structure of the solution is similar to the situation where the system manager can pause the production process, except that now this extra lever partly mitigates the superiority of the static policy.

A multi-level and multi-node supply chain multi-agent simulation model is established based on the two maximum inventory level replenishment strategies, which consider the superior shipments. The e...

Price is an important factor affecting demand rate based on economic and marketing theory. In addition, today's health-conscious consumers prefer a product further from its expiration date because it is fresher and can be stored longer. Furthermore, a large display of goods in a supermarket induces customers to buy more due to its visibility, variety, and seasonality. As a result, we develop a joint pricing and lot-sizing model for retailers selling perishable products in which the demand depends on not only the selling price and reference price but also the product freshness linked to expiration date and displayed stock level. We then formulate the problem as a deterministic model in which the retailer determines the optimal selling prices and ending inventory levels to maximize the discounted total profit. Furthermore, we discuss the retailer's optimal decisions under two scenarios of demand behavior: loss neutrality and loss aversion. Our theoretical analysis shows that the optimal pricing and ending inventory level strategies are both monotonic in time, and the equilibrium of the system is unique for these two scenarios of demand behavior. Finally, a set of structural properties and sensitivity analysis is also developed to characterize the impacts of model parameters on the optimal decisions.

Numerous empirical studies show that advertising effort can stimulate demand in both current and future periods, and there is an interaction between pricing, advertising and ordering decisions. How do these decisions interact with each other and what is the effect of advertising on pricing and ordering decisions? To understand this interaction, we consider a newsvendor-type firm that sells a perishable product in a stable market and dynamically determines the joint ordering, pricing and advertising strategies. The problem is modeled as an infinite horizon newsvendor problem with an advertising carryover effect and price-sensitive demand. We characterize the optimal pricing, advertising and inventory strategies and their comparative statics, and consider how this policy differs from the traditional approach without the advertising effect. We show that the optimal effective advertising level is monotonically increasing with the effective advertising level in the previous period, and hence the optimal strategies (advertising, pricing, inventory level) globally converge to the steady states in the long run. We numerically show that the optimal policy can reap significant profit, which underscores the importance of the advertising-driven ordering and pricing strategies.

Pooling is a best practice in inventory management for economic objectives. In this paper we investigate whether pooling stays advantageous if environmental sustainability is considered in addition to the economic performance, i.e. we analyze whether pooling could have a negative impact on the environment and evaluate the resulting trade-off between economic and environmental performance. Within the newsvendor framework we consider three pooling models: pooling via centralized ordering, physical centralization including inventory allocation to the retailers with priority allocation, and transshipments. In addition, we include environmental constraints based on carbon emissions covering all manufacturing and logistics operations of the product.We characterize the optimal policy of the pooling models with emission constraints, make a detailed comparison between the models and compare them to the decentralized (i.e. no pooling) case. Using copulas to model the joint distribution of dependent demands we prove that the profit decreases with increasing demand dependence. Further, if the environmental constraint is binding, optimal inventory level and emissions decrease with increasing demand dependence and pooling harms the environment compared to the case of no pooling. Additionally, we numerically evaluate the impact of copulas and characterize when the economic and environmental performance of pooling can be balanced.

We investigate how firms make plant location and inventory level decisions to serve global markets. In our analysis, we consider not only differences in wages, transportation costs, and subsidies across countries but also exchange rate changes and competition between firms. We show that the degree of risk exposure of firms and the benefit of relocating plants to the final consumption market play a critical role in firms’ plant location decisions, especially when the global economy is highly uncertain. We provide conditions under which a firm relocates its plant from one country to another, and empirically validate the results. We then investigate how a firm manages inventory when its plant is located in a foreign country. We model and show that firm’s inventory level depends on currency exchange rates and transportation costs when the firm imports products. We empirically confirm the predictions of the theory by using a unique firm-level dataset drawn from Korean firms.

This paper deals with a single item deteriorating production inventory model with price sensitive demand. Items deteriorate at a constant rate. The rate of production is finite and controlled by modern technology, capital investment and number of labors. Demand is adjusted by flexibility of inventory level and this flexibility is introduced through the determination of optimal production stopping time, number of labors and unit selling price of the product. The total profit is determined by trading of selling price, production cost, deterioration cost and holding cost. The paper aims to maximize total profit per unit time in a production cycle. A real coded genetic algorithm is proposed to find out maximum total profit per unit time and to determine optimal production stopping time, number of labors and unit selling price of the product. Finally, a sensitivity analysis is performed to indicate the effects of the parameters on total profit, unit selling price, number of labors and optimal production stopping time.

Trade credit financing is widely accepted as an inevitable strategy to increase profitability in inventory management. We assume that the supplier offers the retailer a fully permissible delay of M periods if the retailer orders more than or equal to a predetermined order quantity w. We revisit an economic order quantity model for instantaneous deteriorating commodities with inventory level dependent demand rate in a supply chain environment by allowing shortages which are partially backlogged. This model also incorporates aspects such as complete and no backlogging. The necessary and sufficient conditions for the existence and uniqueness of this model using the lemmas are investigated. An effective algorithm is proposed to obtain the optimal replenishment policies of this model using SCILAB 5.5.0 to resolve the problem. Finally, we solve numerical examples to substantiate the theoretical results of the underlying model and obtain some managerial insights.

In the production process, the issue of quality is always ignored which results in defective production. These defective items can be removed from the lot through the inspection process which becomes essential for the system. Demand is considered as stock dependent. It is continuously declined to meet the customer’s demand which depends on the on-hand inventory up to the time t2. After that the inventory level declines by constant demand up to time t3. Thereafter, shortages occur and it accumulates at the rate \( \psi \left( {\tau - t} \right)\,till\,t = \tau \) when the next batch arrives. The whole cycle repeats itself after the cycle length τ. Further, it is assumed that payment will be made to the supplier for the goods immediately after receiving the consignment. Whereas, in practice, supplier does offer a certain fixed period to the retailer for settling the account. During this period, supplier charges no interest, but beyond this period interest is being charged. On the other hand, retailer can earn interest on the revenue generated during this period. Keeping this scenario in mind, an attempt has been made to formulate an inventory policy for the retailer dealing with imperfect quality items under permissible delay in payments. Results have been analyzed with the help of a numerical example and sensitivity analysis also carried out.

International audience; The weekly release of the U.S. inventory level by the DOE-EIA is known as the market mover in the U.S. oil futures market. We uncover suspicious trading patterns in the WTI futures markets in days when the inventory level is released that are higher than market forecasts: there are significantly more orders initiated by buyers in the two hours preceding the official release of the inventory level, with a drop in the average price of -0.25% ahead of the news release. This finding is consistent with informed trading. We also provide evidence of an asymmetric response of the oil price to oil-inventory news, and highlight an over-reaction that is partly compensated in the hours following the announcement.

This paper examines the sale of a finite number of items in a class of stochastic dynamic pricing and advertising models with time-dependent demand elasticities. We prove structural properties of the optimal expected profits with respect to time, inventory level, price impact, advertising impact and different model parameters, such as discount rate, marginal unit costs, and holding costs. We find that the value of an additional item (opportunity costs) is decreasing in the unit costs, the discount rate, the holding cost rate and the number of items left to sell. We also derive structural properties of optimal joint pricing and advertising strategies. This way, we obtain general qualitative insights in the complex interplay and the mutual dependence of optimal pricing and advertising decisions. Among other properties, we show that a higher advertising impact leads to higher optimal prices and lower advertising rates, which in turn implies a lower speed of sale. The results obtained help practitioners to respond to changes in market conditions by adjusting price and advertising accordingly. Our results allow speeding up numerical computations of decisions as the set of possible actions can be reduced significantly. Our analysis implies general results for pure pricing as well as pure advertising models with time-dependent demand elasticities. (C) 2016 Elsevier B.V. All rights reserved.

This paper deals with a production–inventory control model with partial backlogging, in which a reflected Brownian motion governs the inventory level variation. We consider a single storage facility with infinite capacity and assume that shortages are allowed and the total amount of stock-out is a mixture of backordering and lost sales. In addition, the production facility is controlled by a two-parameter (m, M) policy, which switches the production rate when the inventory level reaches the threshold values. The aim is to determine the optimal control parameters m and M by minimising the long-run total expected cost of the system. Some results are illustrated using numerical examples. A sensitivity analysis of the optimal solution with respect to major parameters is also carried out.

The inventory-staggering problem is a multi-item inventory problem in which replenishment cycles are scheduled or offset in order to minimize the maximum inventory level over a given planning horizon. We incorporate symmetry-breaking constraints in a mixed-integer programming model to determine optimal and near-optimal solutions. Local-search heuristics and evolutionary polishing heuristics are also presented to achieve effective and efficient solutions. We examine extensions of the problem that include a continuous-time framework as well as the effect of stochastic demand.

The assumption of the newsvendor being able to satisfy demand as long as on-hand inventory is positive does not hold for a non-homogenous product. Consumers who do not find a unit of the product which satisfies their secondary features preferences may not purchase the product even though the newsvendor has positive on-hand inventory. This is likely to occur late in the season as inventory level declines. We solve a newsvendor problem in which the probability of purchase by consumers is increasing in on-hand inventory for any inventory level below that which is needed to have a complete assortment. We identify the sufficient optimality condition for the order quantity. We show that, unlike the case of inventory-dependent demand models in the literature, the optimal order quantity may decrease due to the assortment effect. We investigate two types of pre-end of season discounts, immediate all-units and delayed, as ways to mitigate the late season assortment effect and show that in some cases, they can increase the newsvendor׳s profit and free up the shelf space for other products.

A behavioural study on the newsvendor problem without demand distribution knowledge or realized demands is conducted. We configure a censored-information scenario, where only sales data in history are provided. With laboratory experiments, we analyse participants ordering levels and ordering oscillations over time. It is observed that participants perform a significant learning process in the censored-information scenario. Moreover, we find that participants make orders by anchoring on the previous-period sales and adjusting to an adapted inventory level. On the basis of the observations, we propose an exponential-type learning (EXP) model to describe the behaviour of decision makers. Comparing with a chasing model that is popularly used in the full-information scenario, the EXP model is more recommended in the censored-information scenario.

This paper proposes a dynamic advertising model for deteriorating items, and the demand is influenced by goodwill and inventory level. The goodwill affected by advertising effort has a positive effect on demand while the inventory level has a negative effect on demand, which is named as inverse inventory sensitive demand effect. We assume that the deteriorating rate could be influenced by the inventory level and we determine the deteriorating rate formulation based on this assumption. The optimal advertising effort and inventory level are obtained by solving the optimization problem based on Pontryagin’s maximum principle. Furthermore, numerical studies are provided and some managerial insights are presented.

It is well documented that the demand for fresh produce, to a great extent, depends on how fresh it is and an increase in shelf space for displayed stocks may induce more purchase of the produce. However, relatively little attention has been paid to the effect of expiration date despite the fact that produce deteriorates over time and expiration dates are often an important factor in consumers’ purchase decision. In this paper, we propose an economic order quantity model in which we explicitly specify the demand for fresh produce to be a function of its freshness-expiration date and displayed volume. With the demand being freshness-and-stock dependent, it may be profitable to maintain high stock level at the end of the replenishment cycle. Hence, we relax the traditional assumption of zero ending inventory to non-zero ending inventory. Consequently, the objective here is to determine the optimal level of shelf space size, replenishment cycle time, and/or ending inventory level in an effort of maximizing the total annual profit. We found that the total annual profit is strictly pseudo-concave with regard to the three decision variables, which simplifies the search for the global solution to a local optimal. Numerical examples are then presented to highlight the theoretical implications and managerial insights.

Inventory control is very important so that the production can operate run well, one of the inventory controls is by using the EOQ method (Economic Order Quantity) on the purchase of raw materials. The purpose of the research is to optimize inventory costs in the manufacturing of Mell Toys home industry and to find out the total optimal of raw material orders. The method used in this study is a quantitative method. The data used in the study were obtained from interviews. Data will be calculated manually obtained from the company using the EOQ method approach. This research produces data using EOQ the number of orders for raw materials is 3885 kg, this is greater than the company’s purchasing policy but with the calculation of EOQ, the total inventory cost can be saved from Rp. 4.800.000 to Rp. 424.250,8671. So using EOQ in purchasing raw materials can optimize inventory costs in Mell Toys home-made doll industry.

The paper attempts to reconstruct what goes on inside the black box of the fixed proportions production function underlying the matrix of technical coefficients in the famous Leontief's input–output analysis. The approach is based on an idea that the conversion of inputs to outputs in industrial supply chains occurs in much the same manner as does the conversion of substrates into different molecules in enzyme-catalyzed biochemical reactions. A bottleneck principle is derived according to which at any moment the steady-state output of a multi-resource, one-product supply chain is completely controlled by a sole, most deficient, factor of production. This dramatic shrinkage of complexity is made possible owing to two key features of the input–output production units comprising the chain: saturated response of the output to the inventory level and weak buffer inventory leakage.

In this paper, we examine a real-world case related to the consumer product supply chain to analyze the value of supply chain coordination under the condition of moral hazard. Because of the characteristics of a buyback contract scheme employed in the supply chain, the supplier company’s sales department encourages retailers to order more inventory to meet their sales target, whereas retailers pay less attention to their inventory level and leftovers at the end of the season. This condition induces moral hazard problems in the operation of the supply chain, as suppliers suffer from huge returns of leftover inventory. This, in turn, is related to the obsolescence of returned inventory, even with penalty terms in the contract for the return of any leftovers. In this study, we show under the current buyback-based supply chain operation, the inventory levels of both the supplier and retailers exceed customer demand and develop vendor-managed inventory (VMI) system with base stock policy to remove any mismatch of supply and demand. A comparison of both systems shows that through the proper coordination of supply chain operations, both suppliers and retailers can gain additional benefits while providing proper services to end customers.

This paper studies single-period ordering and markdown pricing policies for short lifecycle products (SLP) by considering differing customer price and time sensitivities. The SLP is assumed to have declining customer valuation (and price) over the selling season and multivariate demand, which is a function of the inventory level, price and time. Promotional markdown (in contrast to clearance markdown) becomes an indispensable part of a pricing policy in view of stock-dependent demand and isused as a mechanism for customer segmentation and price discrimination over time. To offer a realistic pricing, we consider the impact of highly price-sensitive customers who value the price of the product over its innovativeness and who act strategically by purchasing only during a‘sale’ at a markdown price. In this context, single-period inventory models are formulated to include markdown under two market scenarios, namely the homogenous market and thetwo-segment market – a price insensitive (PI) segment, and a price-sensitive (PS) segment. The assumption of non-overlapping segments is relaxed later, and PI customers are allowed to buy later on at a markdown price. The proposed profit-maximising models determine the optimal order size, initial price, markdown time, and price. The solution methods along with the optimality conditions are specified in detail. The results are discussed by using numerical examples, and model behavior with respect to parameters is presented along with the sensitivity analysis.The study reveals the benefits of market segmentation and markdown pricing which recognise high price-sensitive ‘bargain hunter’ customers and offers deeper discounts that yield greater profits. It also demonstrates the superiority of a markdown policy to a single pricing policy, and the benefits of considering the demand stimulating-effect of inventory.

© 2017 Springer Science+Business Media New YorkThis paper proposes a multiple order-up-to policy based inventory replenishment scheme to mitigate the bullwhip effect in a multi-stage supply chain scenario, where various transportation modes are available between the supply chain (SC) participants. The proposed policy is similar to the fixed order-up-to policy approach where replenishment decision ¿how much to order¿ is made periodically on the basis of the pre-decided order-up-to inventory level. In the proposed policy, optimal multiple order-up-to levels are assigned to each SC participants, which provides decision making reference point for deciding the transportation related order quantity. Subsequently, a mathematical model is established to define optimal multiple order-up-to levels for each SC participants that aims to maximize overall profit from the SC network. In parallel, the model ensures the control over supply chain pipeline inventory, high satisfaction of customer demand and enables timely utilization of available transportation modes. Findings from the various numerical datasets including stochastic customer demand and lead times validate that¿the proposed optimal multiple order-up-to policy based inventory replenishment scheme can be a viable alternative for mitigating the bullwhip effect and well-coordinated SC. Moreover, determining the multiple order-up-to levels is a NP hard combinatorial optimization problem. It is found that the implementation of new emerging optimization algorithm named bacterial foraging algorithm (BFA) has presented superior optimization performances. The robustness and applicability of the BFA algorithm are further validated statistically by employing the percentage heuristic gap and two-way ANOVA analysis.

This paper considers a problem of determining the optimal dynamic pricing strategy and replenishment cycle for non-instantaneous deteriorating items, where the consumer demand depends on the sales price and the quantity of the items displayed in the store. For the given replenishment cycle, we derive the optimal dynamic pricing strategy by applying Pontryagin׳s maximum principle, and then design an effective algorithm to obtain the optimal dynamic pricing strategy and replenishment cycle simultaneously. Numerical examples are provided to illustrate the effectiveness of the proposed methods and solution procedure. Furthermore, sensitivity analysis of the key system parameters is carried out and some interesting managerial insights are presented.

The authors consider in this paper an integrated forecasting production system of the tracking type. The demand rate during a certain period depends on the demand rate of the previous period. Also, the demand rate depends on the inventory level. Items on the shelves are subject to deterioration. Using a model predictive control approach, the authors obtain the optimal production rate, the optimal inventory level, the optimal demand rate, and the optimal objective function value, explicitly in terms of the system parameters. A numerical example is presented.

In today's health-conscience markets, the demand for fresh produce is growing constantly. Additionally, the demand for fresh produce also depends on how fresh it is and the size of its shelf space for displayed stocks which may attract more consumers to buy it. Furthermore, perishable or deteriorating items deteriorates over time and their expiration dates are often an important factor in consumers’ purchase decision. As a result, in this paper, we assume that the demand for fresh produce is a time-varying function of its freshness, displayed volume, and expiration date. With the demand being freshness-and-stock-dependent, it may be profitable to maintain high stock level at the end of the replenishment cycle. Hence, we relax the traditional assumption of zero ending inventory to non-zero ending inventory. Consequently, the proposed objective is to determine the optimal replenishment cycle time and ending inventory level in order to maximise the annual total profit. Then we prove that the annual t...

Companies have been using various methods to ensure their sustainability and to increase their profit. Demand estimation can be defined as a process that involves coming up with an estimate of the amount of end use demand for a product or service. Companies use demand estimation techniques for various reasons. One of the reasons that businesses use demand estimation is to determining the production amount in a certain period of time and accordingly keep the inventory level under control. An additional consideration is to assist with pricing. Decision maker's uses various techniques for demand estimation. One of the techniques is using the earlier period data and the other is utilizing the test markets which are similar to larger targeted markets. In this paper, we resort to Bayesian approach for demand estimation and utilized the textile products export data which belongs to years between 2002 and 2014. In Bayesian analysis the new information is combined with the previously available information. At this point the prior information (distribution) corresponds to the historical data or the subjective thought of the decision maker about the unknown parameter of the involved process. The performance of the following updates depends on the prior information therefore the determination of prior information is significant. In this research to obtain the future demand level for the previously mentioned data we utilize the conjugate prior families to obtain the posterior distribution.

This paper considers the comparison of two $$\left( {s,S} \right)$$ production inventory systems with retrials of unsatisfied customers. The time for producing and adding each item to the inventory is exponentially distributed with rate $$\beta$$ . However, a production rate $$\alpha \beta$$ higher than $$\beta$$ is used at the beginning of the production. The higher production rate will reduce customers’ loss when inventory level approaches zero. The demand from customers is according to a Poisson process. Service times are exponentially distributed. Upon arrival, the customers enter into a buffer of finite capacity. An arriving customer, who finds the buffer full, moves to an orbit. They can retry from there and inter-retrial times are exponentially distributed. The two models differ in the capacity of the buffer. The aim is to find the minimum value of total cost by varying different parameters and compare the efficiency of the models. The optimum value of $$\alpha$$ corresponding to minimum total cost is an important evaluation. Matrix analytic method is used to find an algorithmic solution to the problem. We also provide several numerical or graphical illustrations.

In this paper we develop an inventory model, to determine the optimal ordering quantities, for a set of two substitutable deteriorating items. In this inventory model the inventory level of both items depleted due to demands and deterioration and when an item is out of stock, its demands are partially fulfilled by the other item and all unsatisfied demand is lost. Each substituted item incurs a cost of substitution and the demands and deterioration is considered to be deterministic and constant. Items are order jointly in each ordering cycle, to take the advantages of joint replenishment. The problem is formulated and a solution procedure is developed to determine the optimal ordering quantities that minimize the total inventory cost. We provide an extensive numerical and sensitivity analysis to illustrate the effect of different parameter on the model. The key observation on the basis of numerical analysis, there is substantial improvement in the optimal total cost of the inventory model with substitution over without substitution.

This study examines price discovery among the two most prominent price benchmarks in the market for crude oil, WTI sweet crude and Brent sweet crude. Using data on the most active futures contracts measured at the one-second frequency, we …nd that WTI maintains a dominant role in price discovery relative to Brent, with an estimated information share in excess of 80%, over a sample from 2007 through 2012. Our analysis is robust

We consider a continuous-review inventory system with perishable items and make-to-stock production facility. The customers are assumed to be generated by a finite number of sources. Each customer demands a single item. The life time of each item is assumed to be exponential. Customers demand is met from stock, if available, otherwise the customer enters into an orbit. The orbiting customer sends out signal to get his demand satisfied and the duration between two successive retrials is assumed to be distributed as exponential. In order to replenish stock, a production facility is switched on when the inventory level drops to s and items are produced one by one until the stock level reaches a maximum capacity S(> s). The production facility is dynamic in the sense that the rate, at which the item is produced, can be selected from a pre-fixed set of positive values. In other words, the successive production time is assumed to follow an exponential distribution whose parameter is chosen from a given set of positive values. The purpose of this paper is to investigate the optimal set of production rates that minimizes the total expected cost per unit time. We formulate this problem as a semi Markov decision problem. The stationary optimal policy is computed using linear programming algorithm and the results are illustrated numerically.

In this paper, we determine the order quantity and the prices for a perishable product with a multiple period lifetime. Demands for products of different ages are dependent on the prices of mutually “substitutable” products. The problem for a product with lifetime of two periods is first analyzed and the stochastic dynamic programming model is developed. Given the inventory level for the old product (product of age 2), the expected profit is a concave function of the order quantity, the price of the new product (product of age 1) and the discounted price of the old product (product of age 2). The computational results show that the total profit significantly increases when demand transfers between products of different ages are considered. For a product with lifetime of longer than two periods, a heuristic based on the optimal solution for a single period problem is proposed for a multiple period problem.

It is commonly seen that racks overflowing with large quantity of commodities, displayed in the market attracts more customers. This behavior of the customer suggests that demand varies in proportion with stock level. Also the inventory is subjected to deterioration which leads to some amount of loss to the firm.Taking all these points under consideration,a firm should seriously think of its pricing and ordering strategy, as the demand is highly influenced by the selling price and the inventory level of the commodity. This paper aims to develop an inventory model for finding the strategy for a firm that sells a seasonal item over a finite planning time. Keeping in mind the deterioration rate,the purpose of the paper is to develop a model which maximizes the firm’s expected profit by determining the optimal ordering quantity and price setting/changing strategy.

We investigate the feasibility of coordination mechanism for two possible disruption(s) situations.When the inventory-cost disruption level is larger than a certain threshold, both players achieve win-win.The inventory-subsidy contract for disruption(s) situation has its rationality and limitation.Both disruption situations have their own robust scales.Some counter-intuitive managerial insights can be observed in the robust scale. This paper introduces a game model of one manufacturer and one retailer with the demand depending on the amount of inventory displayed on the retailer's shelf. We study coordination mechanisms of the supply chain with the two kinds of disruptions. To coordinate the channel as well as make a profit, the manufacturer needs to augment the wholesale price lever by another, i.e., an inventory-holding cost subsidy to the retailer. We show that the inventory-subsidy contract for disruption(s) situation has its rationality and limitation: from the perspective of feasibility analysis, we find that when the disrupted amount of inventory-holding cost is larger than a certain threshold value, both players can achieve win-win by using inventory-subsidy contract. Otherwise, it may be ineffective. For two-factor disruptions, there are some mutual restraints between the disrupted inventory-holding cost and the disrupted demand when the coordination mechanism is used. We also find that both disruption situations have their own robust scales, in which the manufacturer should not change the original production plan but at the expense of providing a more attractive subsidy scheme to the retailer. Interestingly, some counter-intuitive managerial insights can be observed in robust scales. For example, the market demand increases with the displayed inventory level in the setting of the demand-stimulating inventory. However, the higher the demand, the less displayed inventory level will be in the robust scale.

We consider a make-to-stock system served by an unreliable machine that produces one type of product, which is sold to customers at one of two possible prices depending on the inventory level at the time when a customer arrives (i.e., the decision point). The system manager must determine the production level and selling price at each decision point. We first show that the optimal production and pricing policy is a threshold control, which is characterized by three threshold parameters under both the long-run discounted profit and long-run average profit criteria. We then establish the structural relationships among the three threshold parameters that production is off when inventory is above the threshold, and that the optimal selling price should be low when inventory is above the threshold under the scenario where the machine is down or up. Finally we provide some numerical examples to illustrate the analytical results and gain additional insights.

In this paper, we develop an inventory model under a stock-dependent demand rate and stock-dependent holding cost rate with relaxed terminal conditions. Shortages are allowed and partially backlogged in the model. The purpose of this study is to determine the optimal order quantity and the ending inventory level such that the total profit per unit time is maximized for the retailer. We first establish a proper model for a mathematical formulation. Then we develop several theoretical results and provide the decision-maker with an algorithm to determine the optimal solution. Finally, numerical examples are provided to illustrate the solution procedure, and a sensitivity analysis of the optimal solution with respect to major parameters is carried out.

We examine the relative merits of bank versus trade credit in a supply chain consisting of a manufacturer and a capital-constrained retailer. We show that trade credit is more effective than bank credit in mitigating double marginalization when production costs are relatively low, and that bank credit becomes more effective otherwise. The reason is as follows. Under bank financing, with limited liability the retailer carries the same inventory as if it faces no capital constraint. Under trade financing, the manufacturer shares the risk of low demand with the retailer, prompting the latter to stock a higher inventory than under bank financing. This higher inventory level mitigates (aggravates) double marginalization when the production costs are relatively low (high). This article thus provides a new explanation for trade credit, and also guides the manufacturer’s decision as to when to offer trade credit.

This study proposes a continuous production inventory model for deteriorating items with time and price-dependent demand under markdown policy for both fresh and deteriorated units. In this model, we have adopted the markdown policy to reduce the inventory and to increase the profit or rate of sale of an article, typically for clearance at the end of the season or to sell off obsolete merchandise at the end of its life. Completely deteriorated items are allowed to carry under markdown. Using the differential equations and under various cost considerations, expressions for total profit function, optimum inventory level and cycle length are obtained. All the expressions are illustrated with the help of a numerical example. Sensitivity analysis is carried out to demonstrate the effect of changing parameter values on the optimal solution of the system.

We study a scenario in which a firm designs the compensation contract for a salesperson who exerts unobservable effort to increase the level of uncertain demand and, jointly, the firm also decides the inventory level to be stocked. We use a newsvendor-type model in which actual sales depend on the realized demand but are limited by the inventory available, and unfulfilled demand cannot be observed. In this setup, under the optimal contract, the agent is paid a bonus for meeting a sales quota. Our key result is that it may be optimal for the firm to stock more than the first-best inventory level, because this enables the firm to obtain a more precise indicator of the salesperson's effort. The possibility of stockouts due to limited inventory also leads to several counterintuitive results, including the following: (i) relative to when stockouts are not considered, it may be optimal for the firm to pay a higher bonus even though limited inventory constrains sales; (ii) as inventory becomes more expensive, thereby forcing the firm to lower its inventory, the firm may nevertheless pay the agent a higher bonus; and (iii) if there is a lower probability that the agent's effort exertion leads to high demand, rather than lowering inventory due to the lower sales potential, the firm may increase inventory. This paper was accepted by J. Miguel Villas-Boas, marketing.

This study is motivated by the paper of Chang et al. [International Journal of Production Economics 123 (2010) 62–68]. We extend their inventory model from two aspects. (1) The demand rate as multivariate function of price and level of inventory (2) Delay in payment is permissible. Under these assumptions, we first formulated a mathematical model and then some useful theoretical results have been derived to characterize the optimal solutions for non-zero and zero ending inventory system. Numerical examples are presented to illustrate the theoretical results. The sensitivity analysis of a suitable example is performed and some managerial insights are proposed. Our analysis revels that it is more beneficial to keep higher inventory level, hoping to stimulate more demand, even if it results in non-zero ending inventory.

Market segmentation has emerged as the primary means by which firms achieve optimal production policy. In this paper, we use market segmentation approach in multi-product inventory system with inventory-level-dependent demand. The objective is to make use of optimal control theory to solve the inventory-production problem and develop an optimal production policy that minimizes the total cost associated with inventory and production rate in segmented market. First, we consider a single production and inventory problem with multi-destination demand that vary from segment to segment. Further, we describe a single source production and multi destination inventory and demand problem under the assumption that firm may choose independently the inventory directed to each segment. The optimal control is applied to study and solve the proposed problem.

An effective inventory replenishment method implemented in the supply chain is one of the key success factors to achieve low inventory while maintaining high customer delivery performance. The Theory of Constraints (TOC) Supply Chain Replenishment System (TOC-SCRS) is one of the solutions to get this improvement in a multi-echelon supply chain. The TOC-SCRS is a replenishment method of the TOC supply chain solution. The TOC is a global managerial methodology that helps the manager to concentrate on the most critical issues. The TOC-SCRS is based on the following two strategies to decouple the bullwhip effect (or excess inventory in each node) and maintain the inventory availability to consumers (next nodes): (1) each node holds enough stock to cover demand during the time it takes to reliably replenish; (2) each node only needs to replenish what was sold. The TOC- SCRS is now being implemented by a growing number of companies. The performance reported by the implemented companies includes reduction of inventory level, lead-time and transportation costs and increasing forecast accuracy and customer service levels. However, the exploration of TOC-SCRS is lack in the literature. In this study, the concept and method of TOC-SCRS is first reviewed and modeled. A virtual supply chain case is secondly designed to show the behavior of the TOC-SCRS. A three factorial experiment, i.e., fluctuation of demand, time of replenishment and frequency of replenishment, is then presented to explore the feasibility and effectiveness of TOC-SCRS. A simulation model is designed to complete the experiment.

In this paper, we derive an economic production model having two-parameter Weibull distribution deterioration. In this model, we considered a demand rate that depends on price stock and indirectly on time. Shortage is allowed and partially backlogged. We assume that customer return is a factor of quantity sold, price, and inventory level. Time horizon is finite. Production is also dependent on demand. The goal of this production is to maximize the profit function. An illustrative example, sensitivity analysis, and a graphical representation are used to interpret the usefulness of this model.

In many manufacturing systems the production rate cannot be instantaneously adjusted in response to inventory updates. This article addresses such a system under price-dependent stochastic demand. The objective of the system is to choose a time-invariant production rate and time-dependent product price that maximize the expected profit. This manufacturing system is compared to a benchmark system where both production rate and product price are adjustable. It is shown that the expected inventory level does not necessarily increase when the manufacturer can handle stock spikes only by leveling the demand with the product price. Although the inability to adjust production rate under a high level of uncertainty is difficult to offset with dynamic pricing, the non-linear components of the production and inventory costs can make a difference. For example, by reducing the non-linear component of the production cost and increasing price volatility, the manufacturer may close the profit gap between the two systems...

The paper deals with (s,S) inventory models, where S is maximum inventory level, while s represents safety stock level. Whenever the inventory level falls to s level, an order M = S-s is placed assuming S>2s. The lead time (time between the placement of an order and delivery) has a stochastic character and if the customer's demand is placed at the time when the inventory level is zero, the demand is not satisfied and it goes to an orbit of unsatisfied customers. After a random amount of time these unsatisfied demands are reconsidered and satisfied provided that the inventory level is positive at the time. The paper illustrates application of the model to the selected parametre values s and S which minimize the total expected cost.

This paper introduces a novel approach to discuss an optimal inventory level of a retail product using a real option framework. We consider stochastic models for the evolution of the demand and unit price of the product over time. The profit structure of the retailer is represented by the payoff of the real option. An actuarial approach is then used to price the option. The retailer determines an optimal inventory level of the product with a view to maximizing the net expected profit. Numerical examples will be given to illustrate the practical implementation of the proposed approach and to investigate the impacts of changes in parameters on the optimal inventory level of the product.