Developing a two stage stochastic programming model of the price and lead-time decision problem in the multi-class make-to-order firm (original) (raw)
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European Journal of Operational Research, 2014
In this research, we integrate the issues related to operations and marketing strategy of firms characterized by large product variety, short lead times, and demand variability in an assemble-to-order environment. The operations decisions are the inventory level of components and semi-finished goods, and configuration of semi-finished goods. The marketing decisions are the products price and a lead time guarantee which is uniform for all products. We develop an integrated mathematical model that captures trade-offs related to inventory of semi-finished goods, inventory of components, outsourcing costs, and customer demand based on guaranteed lead time and price.The mathematical model is a two-stage, stochastic, integer, and non-linear programming problem. In the first stage, prior to demand realization, the operation and marketing decisions are determined. In the second stage, inventory is allocated to meet the demand. The objective is to maximize the expected profit per-unit time. The computational results on the test problems provide managerial insights for firms faced with the conflicting needs of offering: (i) low prices, (ii) guaranteed and short lead time, and (iii) a large product variety by leveraging operations decisions. We also develop a solution procedure to solve large instances of the problem based on an accelerated version of the Generalized Benders' Decomposition (GBD) method. The accelerating mechanism involves search intensification and diversification around solutions which improve the upper bound. The suggested GBD method gives a better solution and a tighter lower bound in a given time period than the conventional GBD implementation and the non-linear branch-and-bound method.
Dynamic Pricing and Lead-Time Policies for Make-to-Order Systems
Decision Sciences, 2002
Make-to-order firms use different approaches for managing their lead-times and pricing in the face of changing market conditions. A particular firm's approach may be largely dictated by environmental constraints. For example, it makes little sense to carefully manage lead-time if its effect on demand is muted, as it can be in situations where leadtime is difficult for the market to gauge or requires investment to estimate. Similarly, it can be impractical to change capacity and price. However, environmental constraints are likely to become less of an issue in the future with the expanding e-business infrastructure, and this trend raises questions into how to manage effectively the marketing mix of price and lead-time in a more "friction-free'' setting.
Pricing and scheduling decisions with leadtime flexibility
European Journal of Operational Research, 2006
This paper studies a problem faced by a manufacturer who has the ability to set prices to influence demand, reject orders, and set leadtimes or due-dates for accepted orders. We present decision models that integrate pricing and production decisions for the cases where the manufacturer charges the same price or different prices to different customers. Through numerical analyses, we present insights regarding the benefits of price customization, leadtime, and inventory flexibilities, in various demand environments.
International Journal of Production Economics, 2005
In this paper, we focus on a firm selling a single make-to-stock product to price-sensitive end customers. We develop an integrated operations-marketing model that can help determine the relevant profit-maximizing decision variable values for two pricing policies that the firm might follow-price as a decision variable, which is advocated by academicians, and mark-up pricing, used by most practitioners. We first consider an EOQ-based model with price and order quantity as independent decision variables. We then develop an analogous model where price is a mark-up over operating costs per unit, and order quantity becomes the sole decision variable. We are able to ascertain the optimal decision variable values for each model for log-linear and linear demand functions. We prove that for such profitmaximizing models, the optimal batch size is not necessarily monotone increasing in set-up cost. Interestingly, our numerical/analytical evidence suggests that from a profit perspective it is better for managers to be aggressive on price rather than reducing price too much, especially for highly price-sensitive and non-linear demand. Moreover, we establish that, in general, the profit penalty for not including inventory costs in determining the optimal batch size, or ignoring the batch size optimization issue in a mark-up price model is not significant. Only when the set-up cost is quite high and/or the firm faces non-linear demand from highly price-sensitive end consumers does it become crucial for managers to determine the ''exact'' optimal batch size and base the mark-up price on the entire unit operating cost, not only the unit (variable) production cost.
A fluid model of dynamic pricing and inventory management for make-to-stock manufacturing systems
In this paper, we introduce a fluid model of dynamic pricing and inventory management for make-to-stock manufacturing systems. Instead of considering a traditional model that is based on how price affects demand, we consider a model that relies on how price and level of inventory affect the time a unit of product remains in inventory. Our motivation is based on the observation that in inventory systems, a unit of product incurs a delay before being sold. This delay depends on the unit price of the product, prices of competitors, and the level of inventory of this product. Moreover, delay data is not hard to acquire and is internally controlled and monitored by the manufacturer. It is interesting to notice that this delay is similar to travel times incurred in a transportation network. The model of this paper includes joint pricing, production and inventory decisions in a competitive, capacitated multi-product dynamic environment. In particular, in this paper we (i) introduce a model for dynamic pricing and inventory control that uses delay rather then demand data and establish connections with traditional demand models, (ii) study analytical properties of this model, (iii) establish conditions under which the model has a solution and finally, (iv) establish an algorithm that solves efficiently a discretized version of the model.
This paper explores the setup and order processing cost reduction in the single vendor and the single buyer integrated production inventory model. The mathematical model is derived to investigate the effects of the optimal decisions when capital investment strategies in setup and order processing cost reduction are adopted. This proposed model intends to derive the exact cost function for the entire supply chain including logarithmic investment functions and an efficient computational algorithm is constructed to find the best solution.
A ‡uid model of dynamic pricing and inventory management for make to stock manufacturing systems
2002
In this paper, we introduce a fluid model of dynamic pricing and inventory management for make-to-stock manufacturing systems. Instead of considering a traditional model that is based on how price affects demand, we consider a model that relies on how price and level of inventory affect the time a unit of product remains in inventory. Our motivation is based on the observation that in inventory systems, a unit of product incurs a delay before being sold. This delay depends on the unit price of the product, prices of competitors, and the level of inventory of this product. Moreover, delay data is not hard to acquire and is internally controlled and monitored by the manufacturer. It is interesting to notice that this delay is similar to travel times incurred in a transportation network. The model of this paper includes joint pricing, production and inventory decisions in a competitive, capacitated multi-product dynamic environment. In particular, in this paper we (i) introduce a model...
Journal of Industrial Engineering International, 2013
The integration of marketing and demand with logistics and inventories (supply side of companies) may cause multiple improvements; it can revolutionize the management of the revenue of rental companies, hotels, and airlines. In this paper, we develop a multi-objective pricing-inventory model for a retailer. Maximizing the retailer's profit and the service level are the objectives, and shortage is allowed. We present the model under stochastic lead time with uniform and exponential distributions. Since pricing is important and influences demand, the demand is considered as a general function of price. The multiple-objective optimization model is solved using the weighting method as well as the L-P metric method. Concerning the properties of a nonlinear model, a genetic algorithm is taken into account to find the optimal solutions for the selling price, lot size, and reorder point. Finally, numerical examples with sensitivity analysis regarding key parameters are provided.
Coordination mechanism for the supply chain with leadtime consideration and price-dependent demand
European Journal of Operational Research, 2010
We study a coordination contract for a supplier-retailer channel producing and selling a fashionable product exhibiting a stochastic price-dependent demand. The product's selling season is short, and the supply chain faces great demand uncertainty. We consider a scenario where the supplier reserves production capacity for the retailer in advance, and permits the retailer to place an order not exceeding the reserved capacity after a demand information update during a leadtime. We formulate a two-stage optimization problem in which the supplier decides the amount of capacity reservation in the first stage, and the retailer determines the order quantity and the retail price after observing the demand information in the second stage. We propose a three-parameter risk and profit sharing contract that coordinates the supply chain. The proposed contract is robust which permits any agreed-upon division of the supply chain profit between the channel members.
PRICING AND INVENTORY DECISIONS WITH UNCERTAIN SUPPLY AND STOCHASTIC DEMAND
We consider a retailer, facing uncertain supply and price-sensitive stochastic demand, who has to make stocking and pricing decisions for a given selling period. We also consider the case when the demand is price-sensitive deterministic and provide a unified framework for the model with additive errors. For both scenarios, we look at the case when the price is set before receiving the supply, called simultaneous pricing and the case when the price is set after receiving it, which is called postponed pricing. We develop a procedure for finding the optimal policy for the retailer with general distributions for the supply and the demand. To study the effect of supply uncertainty on expected profit, we conduct sensitivity analysis and develop results for both pricing scenarios and give insights. The results have important implications for a retailer in the supply chain, where a portion of the inventory may be lost due to variety of factors including mishandling and failure to meet quality standards. The findings shed light on the nature and role of prices and their relationship to supply and demand.