Optimal sourcing from alternative capacitated suppliers with general cost structures

doi:10.1016/j.omega.2015.03.011

Omega

Volume 58, January 2016, Pages 26-32

https://doi.org/10.1016/j.omega.2015.03.011 Get rights and content

Highlights

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We solve the sourcing problem under general cost structures and stochastic demand.
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We provide an exact pseudo-polynomial algorithm.
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Procurement quantity might decrease when there are additional suppliers.
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Our model allows for introducing supplier restrictions and multi-period sourcing.

Abstract

Most manufacturers or retailers must procure items or services necessary for their businesses, in an environment that typically includes a number of competing suppliers with varying cost structures, price schemes, and capacities. In this paper, we consider the sourcing problem in which the buyer determines the sources that should be utilized and to what extent, in turn, dictating the total quantity available for the buyer to sell/utilize, subject to stochastic demand/requirement. Our approach advocates not to determine the quantity to be sourced a priori. We allow for capacitated sources and any cost structure in which fixed costs and quantity discounts are special cases. Some simpler versions of this problem are shown to be NP-hard in the literature. By proving that the order of the sources is irrelevant for the optimal solution, we devise a dynamic programming model with pseudo-polynomial complexity to solve the multiple supplier sourcing problem to optimality. We propose two extensions: one limits the number of suppliers, and the other allows multi-period sourcing.

Section snippets

Introduction and related literature

Consider a manufacturer or retailer who procures (or, ‘sources’) a certain product or service, to use directly or indirectly in meeting the stochastic demand that she faces. Considering the manufacturing environment as an example, the product that is to be procured (or, the ‘item’) can be supplied by a finite number of capacitated external suppliers, and the manufacturer must decide which of the sources to utilize and to what extent. One could prefix the procurement quantity based on inventory-

Modeling approach

In this section, we analyze the procurement problem in a single-period setting, under a given set of alternative capacitated suppliers, with corresponding general procurement cost functions. The procured quantity also dictates the stock quantity, subject to stochastic demand. There are two decisions in such an environment: which sources should be utilized and in what quantities? The relevant parameters in determining those quantities are not only procurement costs and supplier capacities, but

Numerical study

We conducted a numerical study to investigate (i) the effect of problem parameters on the optimal solution (3.1 Effects of demand variability and cost parameters, 3.2 Effects of flexibility) and (ii) the performance of the sequential approach (Section 3.3). We considered the following setting: the demand has a Gamma distribution with coefficient of variation (CV) values of 0.5, 1, 1.5, and with expected values, $E [W]$ , of 20, 40, 50, and 60. Demand is assumed to be discrete in this section for

Extensions

In what follows, we model two important extensions of the basic model. We note that the properties that hold in Theorem 1 also hold in these extensions, which we do not show for brevity.

Conclusions

In this paper, we consider the sourcing decisions of a retailer or a manufacturer for a particular product or service. There are basically two decisions: determining the quantity to be procured and selecting the suppliers to procure from. In this study, we develop a unified approach that combines these two decisions. We allow for stochastic demand and capacitated production facilities. Our modeling approach is capable of handling sourcing problems in a wide range of environments, as we do not

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Cited by (14)

Simultaneous Optimization of Contingent and Advance Purchase Orders with Fixed Ordering Costs
2019, Omega (United Kingdom)
Citation Excerpt :
This paper also contributes to dual sourcing literature in that it examines simultaneous optimization of committed and contingent orders, and sheds light on the trade off between long-term decisions and short-term decisions in a multi-period inventory system. Some papers in the dual-sourcing literature (e.g., [12,18,34,35,20,24,31]) do consider different sources and modes, which are differentiated by their fixed and variable costs, delivery lead times, as well as constraints on the order sizes. However, these papers address only contingent orders and not committed orders.
We analyze a finite horizon periodic-review inventory model in the presence of advance purchase discount (APD). In addition to the opportunity to place a contingent order when required, the buyer can also commit to advance orders and receive discounts. Thus the buyer faces the following tradeoff: Contingent orders provide operational flexibility to respond to uncertain demands at a high purchase cost, whereas advance orders incur low purchase cost while sacrificing operational flexibility. We consider a simple and easy-to-implement APD scheme in which the buyer enjoys price discounts by committing at the outset to a fixed size of advanced order for each period along with contingent orders when required. We first show that for any given advance order size, an advance-order dependent (s, S) policy is optimal. We then find the advance order size together with the corresponding (s, S) policy that minimizes the buyer’s total cost.
Economic and environmental considerations in a stochastic inventory control model with order splitting under different delivery schedules among suppliers
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This study analyzes an integrated inventory control and delivery scheduling problem in a stochastic demand environment with economic and environmental considerations. In particular, we examine a bi-objective continuous review inventory control model with order splitting among multiple suppliers, where both expected costs and carbon emissions per unit time are minimized. For this problem, two different delivery scheduling policies are considered for the split orders: sequential splitting and sequential delivery. First, we formulate the problem under each delivery scheduling policy as bi-objective mixed-integer nonlinear models. Then, an adaptive ϵ-constraint algorithm and an evolutionary search algorithm are proposed to approximate the Pareto front of these models. A numerical study is conducted to compare the two approximation algorithms. Another numerical study demonstrates the effects of the demand variance on the expected costs and carbon emissions per unit time under each delivery scheduling policy. Finally, examples are presented to show how the tools provided in this study can be used to compare different scheduling policies. Our results show that the delivery policy and supplier selection both have strong effects on the economic and environmental performance, and also that a good approximation of the Pareto front is crucial to accurately compare delivery scheduling policies.
An integrated supplier selection and inventory problem with multi-sourcing and lateral transshipments
2017, Omega (United Kingdom)
Citation Excerpt :
Therefore, the algorithm resorts to solutions with more suppliers (or more expensive suppliers with higher capacity), and ultimately, increasing the overall cost. This observation is also evidenced in the literature in [45]. Within both Figs. 7(a) and (b), in scenario 1, decreasing unit cost improves the total cost in all networks, however, the largest improvement comes from the MS-LT network.
In this research, we consider the supplier selection problem of a firm offering a single product via multiple warehouses. The warehouses face stationary, stochastic demand and replenish their inventory via multiple suppliers, to be determined from a set of candidates, with varying price, capacity, quality, and disruption characteristics. Additionally, the warehouses may simultaneously replenish their inventory from other warehouses proactively. With these characteristics, the problem is a multi-sourcing, supplier selection, and inventory problem with lateral transshipments. Even though the benefits of multi-sourcing and lateral transshipments have been presented in the literature individually to mitigate risks associated with uncertain demand and disrupted supply, the intertwined sourcing and inventory decisions under these settings have not been investigated from a quantitative perspective. We develop a decomposition based heuristic algorithm, powered with simulation. While the decomposition based heuristic determines a solution with supplier selection and inventory decisions, the simulation model evaluates the objective function value corresponding to each generated solution. Experimental results show, contrary to the existing literature, inferior decisions may result when considering the selection of suppliers solely on unit and/or contractual costs. We also evaluate the impact of multi-sourcing with rare but long disruptions compared to frequent but short ones.
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^☆: This manuscript was processed by Associate Editor Geunes.

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Optimal sourcing from alternative capacitated suppliers with general cost structures☆

Highlights

Abstract

Section snippets

Introduction and related literature

Modeling approach

Numerical study

Extensions

Conclusions

International Journal of Production Economics

European Journal of Operational Research

Operations Research Letters

European Journal of Operational Research

European Journal of Operational Research

European Journal of Operational Research

International Journal of Production Economics

OMEGA-International Journal of Management Science

OMEGA-International Journal of Management Science

European Journal of Operational Research

Operations Research Letters

OMEGA-International Journal Of Management Science

International Journal of Production Economics

Supplier selection and order lot sizing modelinga review

Computers & Operations Research