Optimal inventory and pricing policies for remanufacturable leased products

In this paper we consider a company which leases new products and also sells remanufactured versions of the new product that become available at the end of their lease periods. When the amount of end-of-lease items in stock is not sufficient to meet the demand for remanufactured products, the firm may purchase additional cores from a third-party supplier. We develop a dynamic programming formulation for determining the optimal price of remanufactured products, and optimal payment structure for the leased products. Our objective is to maximize the discounted system-wide profit over a finite horizon. The profit function consists of revenues that are obtained from remanufactured product sales and leasing, remanufacturing and manufacturing costs, inventory holding and shortage costs. We consider a consumer choice based demand model for mapping a potential customer into one of the product segments (a remanufactured product customer or a customer for a leased product with a particular lease period) for a given price/lease payment vector. We explore several properties of the discounted profit function and provide insight on the behavior of pricing and inventory policies. We also investigate the effect of key product characteristics such as deterioration in age, cost of shortage in remanufacturable product inventory, and key market characteristics such as relative willingness-to-pay for buying a remanufactured product and relative willingness-to-pay for leasing a new product on optimal pricing policies through a computational study.     

Consolidating distribution centers can reduce lost sales

In many industries, products are sold out of inventory. When inventory shortages are possible, expected product sales will fall short of expected product demand. We find that this shortfall is proportional to the standard deviation of demand. As we show, this implies that consolidating retailer units – which leads to a lower standard deviation for the aggregate demand – can increase sales.     

Optimal policies in hybrid manufacturing/remanufacturing systems with product substitution

In hybrid control systems for simultaneous remanufacturing of used products and manufacturing of new ones, the two operations are not directly interconnected if remanufactured items are downgraded and have to be sold in markets different from those for new products. Sometimes a connection between these markets is given by a downward substitution property which allows the producer to offer a new item instead of a remanufactured one in case of a shortage of a remanufactured product. Thus, shortage costs can be avoided, but a loss in profit due to sale of a high-graded product at the price of a low-graded one has to be accepted. For a single-period problem with stochastic returns of used products and stochastic demands of serviceable ones, it is shown how the manufacturing and remanufacturing decisions have been coordinated in order to maximize the total expected profit. It turns out that under strictly proportional costs and revenues a medium-simple ‘order-up-to policy’ with two parameters and two parameter functions is optimal. However, optimal policies in situations where manufacturing leadtimes exceed leadtimes for remanufacturing turn out to be different from those in the opposite leadtime case. The research presented combines methods for policy analysis in stochastic manufacturing/remanufacturing problems and in stochastic inventory control problems with substitutable products.     

Selecting make-to-stock and postponement policies for different products in a chemical plant: A case study using discrete event simulation

We present a guideline for selecting the inventory management policy for a specialty chemical plant that produces products with limited shelf life, by producing multiple grades of bulk chemical and packaging them into a large variety of bottles. The policy for each product was selected based on a cost-benefit analysis, using the multiple objectives of maximizing the on time order fulfillment, minimizing the production (cleaning and shelf life expiration) and inventory costs. To generate realistic cost estimates, we developed a discrete event simulation model that included demand variability, planning and scheduling policies, and operational details. We evaluated three different policies: make-to-stock (MTS), postponement, and combined MTS/postponement. We also evaluated different storage media and optimized the number of storage units for products selected for postponement. A combined MTS/postponement policy, in which postponement is applied to products with low to medium demand and high expiration provided lowest costs without significantly impacting the customer on time order fulfillment. For all other products, a MTS policy is applied to maximize order fulfillment on time, reduce cleaning costs and to reduce number of storage units.     

Unimodality of price-setting newsvendor's objective function with multiplicative demand and its applications

We present a general solution framework for the price-setting newsvendor problem with a multiplicative stochastic demand. Under mild assumptions, such as increasing price elasticity on the mean demand function and increasing generalized failure rate on the distribution of the random factor, we first prove that both the profit function with respect to price and its derived function with respect to order quantity are quasi-concave. Three applications are then studied under our solution framework: (1) We consider a wholesale price only contract by which a manufacturer sets a wholesale price and a newsvendor determines an order quantity and the retail price, and show that the manufacturer's profit function is unimodal with respect to retailing price or stocking factor under certain conditions. (2) We consider a newsvendor problem in which the demand depends on both the retail price and the level of sales effort, and the cost exerting the sales effort is proportional to the order quantity; we prove that there exists a unique pair of price and sales-effort levels that maximize the total profit. This result is established under a set of mild assumptions on the demand and cost functions. (3) We identify a property in the single-period profit function that satisfies Condition 1 of Huh and Janakiraman (2008), which in turn guarantees the optimality of (s, S) policy for an infinite stationary dynamic inventory-price control system with lost sales and fixed order costs. Finally, the unimodality of the newsvendor problem with a general stochastic and price-sensitive demand is studied.     

Distribution contracts to support optimal inventory holdings under demand uncertainty

When suppliers produce products for which demand is uncertain, they face a problem of inducing downstream distributors to stock inventory levels that the suppliers prefer. This paper considers a wide array of alternative supply contracts, each of which consists of a mixture of constant per-unit wholesale prices, buy-back arrangements, and post sale payments contingent on sales made, such as revenue sharing or buybacks. We show that linear supply contracts specifying any combination of two of these three instruments can implement the vertical integrated outcome for a monopoly, thereby generating the supplier's preferred inventory configuration and price distribution. We extend our results to differentiated product oligopoly, demonstrating that each supplier obtains its preferred inventory configuration and price distribution, given the choices of its rival. Distributors choose optimal inventories from the suppliers' standpoint, even if suppliers do not know the distribution of demand uncertainty, and, given the perfect competition among distributors, all profits in the supply chain are captured by suppliers. Thus, suppliers are able to deal with demand uncertainty with remarkably little information about demand, and without the need to control dealer actions in detail. In particular, suppliers need not specify either dealer inventories or resale prices, but instead encourage distributors to order based on information in their possession and to set prices that generate desirable resale price dispersion.     

Modelling consumer-directed substitution

We discuss the challenges and difficulties arising when approaching and modelling the consumer-directed substitution problem in quick response supply chains. Further, we propose heuristic solutions suited for large problems with complex uncertainty and dependency patterns. Despite the single-period newsvendor model we use, our substitution process is an approximation of the dynamic product choice. To ensure consistency with regard to the information used to establish substitution fractions and information available at the time of optimisation, substitution fraction estimation and inventory/assortment optimisation are discussed simultaneously. The decision-independent substitution preferences applied here do not require inventory or sales transaction data, but reflect understanding on the demand driver attributes. This approach, in turn, leads to increased robustness in assortment planning. Factual substitution is an outcome of the optimisation process, constrained by the available substitutes and unfulfilled demand.Despite being unable to fully describe the dependencies among the substitute choice possibilities, our substitution approach, together with the modelling process, allows handling the most important dependencies, such as negatively correlated substitute choice possibilities and positively/negatively correlated first and second choice possibilities.     

Product substitution in different weights and brands considering customer segmentation and panic buying behavior

Due to recent supply disruptions, there has been a rapid increase in panic buying. This study considers a wholesaler selling two brands of a product with multiple weights and produced by different manufacturers to multiple retailers. The products are substituted based on weight (same brand) and a competitor’s brand over two periods. In the first period (panic situation), the wholesaler attempts to retain the inventory to satisfy the retailer. In the second period (supply disruption), retailers are willing to accept the substitute products. The wholesaler segregates the retailers into high and low indexed customers, where the high indexed retailers (provide higher profit) order greater quantities than the low indexed retailers. The objective of this model is to determine the optimal numbers for ordering quantities and substitutions to maximize total profit. Moreover, supply disruption for both single and multiple brands is analyzed, along with the influence of different degrees of supply disruption and panic rate on decisions and profits. Finally, we compare the models with and without customer-segmented substitution and brand substitution. In addition, other model extensions are discussed, such as an increase in the price in the second period.     

Replenish-up-to inventory control policy with random replenishment intervals

The multi period inventory problems have been studied under two main assumptions. Continuous review assumption where an order can be made at any time depending on inventory position and periodic review assumption where an order can be initiated only at discrete time epochs. In this study, we analyze a multi period inventory problem that falls under neither of these two assumptions. In the case we consider, there are periodic replenishments but the replenishment intervals are taken to be i.i.d. random variables. This setting represents the real life cases where a supplier visits a retailer with random inter arrival times and the retailer replenishes his inventories based on a replenish-up-to-level inventory control policy. We also assume that only a certain fraction of unmet demand is backordered and the rest of it is lost.In this setting under general distribution between replenishment epochs, we show the concavity of the expected profit function and give the condition that must hold for the optimal replenish-up-to-level. We also present the specific solutions and analysis under two different distributions, namely, uniform and exponential distributions, together with some numerical examples.     

Joint determination of inventory replenishment and sales effort with uncertain market responses

An optimal joint operational and marketing decision is crucial for robust supply chain management. This paper addresses concurrent determination of inventory replenishment and sales effort decisions such as price, incentives to salesforce, and short-term promotions, or a combination of them. Market responses to sales efforts are typically highly uncertain, and demand in each period has its distribution dependent on the selected sales effort. In each period a replenishment order may be issued, which incurs both fixed and variable ordering costs, and at the same time the sales effort is also determined, the execution of which may incur costs. For such a model, the previously developed methods which are used for the joint inventory-pricing models become inadequate. A computational procedure for obtaining an optimal joint policy is addressed, and the conditions for the optimality of that policy are identified.     

Joint pricing and procurement of fashion products in the existence of clearance markets

This paper focuses on the joint pricing and procurement of fashion products in the existence of clearance markets. It is assumed that the expected regular season demand is a linear decreasing function of the price and the end of period excess inventory is sold at a known discounted price in a clearance market where the demand is a random variable that follows a general distribution. It is shown that the expected profit function is unimodal and the optimal procurement quantity and price can be found from the first order conditions. Existence of a clearance market increases the profit, price, and the procurement quantity. In order to prove this, the optimal procurement and pricing policy of a price-setting retailer who does not have a clearance market is provided. As opposed to the literature, it is shown that the expected profit function of this problem is unimodal as well. A numerical study demonstrating the magnitude of the increase in profit, procurement quantity, and price is reported.     

Integrated product specifications and productivity decision making in unreliable manufacturing systems

This paper considers joint production control and product specifications decision making in a failure prone manufacturing system. This is with the knowledge that tight process specifications, while leading to a product of more reliable quality and higher market value, are at the same time associated with higher levels of non-conforming parts, a higher rate of parts rejection and thus a lowering of overall plant productivity. The decision making is further complicated by the lack of reliability of the production process, which imposes that an adequate, also to be designed, level of inventory of finished parts be maintained. The overall optimal decision policy is defined here as one that maximizes the long term average per unit time profit of a combined measure of quality and quantity dependent sales revenue, minus inventory and backlog costs, in the presence of random plant failures and random repair durations. Policy optimization is achieved via a revisited model of the Bielecki–Kumar theory for Markovian machines and a simulation and experimental design based methodology for the more general cases.     

Introduction to design and analysis of production systems

In a two-party VMI channel, the vendor operates the basic stocking and delivery functions and makes inventory replenishment decisions while the retailer is responsible for customer acquisition and in-store services. This paper focuses on such retail channel and proposes an analytical model for the partners in supply channel to determine the inventory policy with the objective of optimizing system net profit. The model explicitly incorporates issues from both the vendor and the retailer in order to derive a policy for mutual benefits. To illustrate and obtain insights from the proposed solution procedure, we devise a set of numerical analyses based on various scenarios. Factors such as shelf-space-dependent demand, shelf-space capacity, demand pattern, logistics characteristics, and disparity between holding costs of the warehouse and the retail store are also investigated.     

Impact of loss aversion on the newsvendor game with product substitution

This paper studies a newsvendor game in which two substitutable products are sold by two different retailers (newsvendors) with loss-averse preferences. Each loss-averse retailer facing stochastic customer demand and deterministic substitution rate will make an order quantity decision to maximize his expected utility. Since product substitution causes two retailers to make decisions in a competitive environment, game theory is used to find the retailers' optimal order quantities. It is shown that under certain conditions, there exists a unique Nash equilibrium in the newsvendor game. Under a symmetry assumption, each retailer's equilibrium order quantity is decreasing in the loss aversion coefficient and increasing in the substitution rate. Further, if the effect of loss aversion on the order quantity is strong enough to dominate the effect of competition, the total inventory level of a decentralized supply chain will be lower than that of a centralized supply chain. Numerical experiments are conducted to illustrate our results.     

Production capacity planning for multiple products under uncertain demand conditions

This study chiefly deliberates issues regarding capacity allocation for multiple products. When producing multiple products, a manufacturer needs to allocate a favorable production quantity to each product under conditions of uncertain demand since the excess or shortage of a product will in turn cause the loss of profit. The proposed model and the corresponding algorithm in this study are used to find out the optimal capacity allocation under the given probability density function of specific demands and to effectively allocate limited capacity to multiple products with an aim to maximize profit. Finally, the numerical example suggests that the marginal profit, the inventory holding cost, the shortage cost, the loss of excess production, and market demands should be considered in an effort to discover an optimal capacity allocation with regard to multiple products.     

A big data driven framework for demand-driven forecasting with effects of marketing-mix variables

This study aims to investigate the contributions of promotional marketing activities, historical demand and other factors to predict, and develop a big data-driven fuzzy classifier-based framework, also called “demand-driven forecasting,” that can shape, sense and respond to real customer demands. The availability of timely information about future customer needs is a key success factor for any business. For profit maximization, manufacturers want to sense demand signals and shape future demands using price, sales, promotion and others economic factors so that they can fulfil customer's orders immediately. However, most demand forecasting systems offer limited insight to manufacturers as they fail to capture contemporary market trends, product seasonality and the impact of forecasting on the magnitude of the bullwhip effect. This paper aims to improve the accuracy of demand forecasts. In order to achieve this, a back-propagation neural network-based model is trained by fuzzy inputs and compared with benchmark forecasting methods on a time series data, by using historical demand and sales data in combination with advertising effectiveness, expenditure, promotions, and marketing events data. A statistical analysis is conducted, and the experiments show that the method used in the proposed framework outperforms in optimality, efficiency and other statistical metrics. Finally, some invaluable insights for managers are presented to improve the forecast accuracy of fuzzy neural networks, develop marketing plans for products and discuss their implications in several fields.     

Economic lot-sizing and dynamic quantity competition

We study a problem of dynamic quantity competition in continuous time with two competing retailers facing different replenishment cost structures. Retailer 1 faces fixed ordering costs and variable procurement costs and all inventory kept in stock is subject to holding costs. Retailer 2 only faces variable procurement costs. Both retailers are allowed to change their sales quantities dynamically over time. Following the structure of the economic order quantity (EOQ) model, retailer 1 places replenishment orders in batches and retailer 2 follows a just-in-time (JIT) policy. The objective of both retailers is to maximize their individual average profit anticipating the competitor's replenishment and output decisions. The problem is solved by a two-stage hierarchical optimization approach using backwards induction. The second-stage model is a differential game in output quantities between the two retailers for a given cycle length. At the first stage, the replenishment policy is determined. We prove the existence of a unique optimal solution and derive an open-loop Nash equilibrium. We show that both retailers follow contrary output strategies over the order cycle. The EOQ retailer, driven by inventory holding costs, decreases his market share whereas the output of the JIT retailer increases. Moreover, depending on the cost structure, the EOQ retailer might partially be a monopolist. At the first stage, the EOQ retailer determines the cycle length, anticipating the optimal output trajectories at the second stage.     

Centralized and decentralized control polices for a two-stage stochastic supply chain with subcontracting

An analysis of control policies for a two-stage supply chain with subcontractors at each stage is presented when decisions at each stage concerning safety stocks, backorders, and subcontracting are made jointly or in a decentralized manner. The inventory/admission control policies considered are base stock, echelon base stock and partial backordering, and the objective is to maximize the mean profit rate of the system. The optimal control parameters are found by exhaustive search using Markov chains. From numerical examples it appears that the policies which manage jointly sales and production levels in each stage provide much higher overall (system) profits than decentralized policies, although the latter are individually more profitable for the second stage. In addition, partial backordering provides the system with an extra profit above those that result from the lost sales (no backordering) and complete backordering policies. Finally, a number of numerical results show the impact of variations in certain system parameters on the optimal control parameters and the corresponding profit.     

Ordering and pricing policies in a manufacturing and distribution supply chain for fashion products

In the paper, we develop a model of manufacturing and distribution supply chains that are operating to meet price-sensitive random demand for products with short life cycles such as fashion products. Two specific scenarios are considered. The manufacturer-controlled scenario is one where the distributor shares price-sensitive random demand with the manufacturer, and the manufacturer controls the supply chain stocking decisions and bears the risk of overstocking costs. The distributor-controlled scenario works in the opposite direction. Prevailing wisdom suggests that the manufacturer should control supply chain decisions (e.g., via vendor-managed inventory). Our results indicate that such an arrangement is against the interest of a distributor selling short life-cycle products. Furthermore, we find that the total supply chain profit is generally higher when the distributor controls the supply chain stocking decisions and bears the risk of overstocking costs.