Heuristics for sourcing from multiple suppliers with alternative quantity discounts

In this paper, we analyze the impact of supplier pricing schemes and supplier capacity limitations on the optimal sourcing policy for a single firm. We consider the situation where the total quantity to be procured for a single period is known by the firm and communicated to the supplier set. In response to this communication, each supplier quotes a price and a capacity limit in terms of a maximum quantity that can be supplied to the buyer. Based on this information, the buyer makes a quantity allocation decision among the suppliers and corresponding to this decision is the choice of a subset of suppliers who will receive an order. Based on industry observations, a variety of supplier pricing schemes from the constituent group of suppliers are analyzed, including linear discounts, incremental units discounts, and all units discounts. Given the complexity of the optimization problem for certain types of pricing schemes, heuristic solution methodologies are developed to identify a quantity allocation decision for the firm. Through an extensive computational comparison, we find that these heuristics generate near-optimal solutions very quickly. Data from a major office products retailer is used to illustrate the resulting sourcing strategies given different pricing schemes and capacity limitations of suppliers in this industry. We find for the case of capacity constrained suppliers, the optimal quantity allocations for two complex pricing schemes (linear discount, and incremental units discount) are such that at most one selected supplier will receive an order quantity that is less than its capacity.     

A scenario-based stochastic model for supplier selection in global context with multiple buyers,currency fluctuation uncertainties,and price discounts

Suppliers network in the global context under price discounts and uncertain fluctuations of currency exchange rates have become critical in today’s world economy. We study the problem of suppliers’ selection in the presence of uncertain fluctuations of currency exchange rates and price discounts. We specifically consider a buyer with multiple sites sourcing a product from heterogeneous suppliers and address both the supplier selection and purchased quantity decision. Suppliers are located worldwide and pricing is offered in suppliers’ local currencies. Exchange rates from the local currencies of suppliers to the standard currency of the buyer are subject to uncertain fluctuations overtime. In addition, suppliers offer discounts as a function of the total quantity bought by the different customer’ sites over the time horizon irrespective of the quantity purchased by each site.     

Modeling a stochastic multi-objective supplier quota allocation problem with price-dependent ordering

One of the interesting subjects in supply chain management is supply management, which generally relates to the activities regarding suppliers such as empowerment, evaluation, partnerships and so on. A major objective of supplier evaluation involves buyers determining the optimal quota allocated to each supplier when placing an order. In this paper, we propose a multi-objective model in which purchasing cost, rejected units, and late delivered units are minimized, while the obtained total score from the supplier evaluation process is maximized. We assume that the buyer obtains multiple products from a number of predetermined suppliers. The buyer faces a stochastic demand with a probability distribution of Poisson regarding each product type. A major assumption is that the supplier prices are linearly dependent on the order size of each product. Since demand is stochastic, the buyer may incur holding and stockout costs in addition to the regular purchasing cost. We use the well-known L-1 metric method to solve the supplier evaluation problem by utilizing two meta-heuristic algorithms to solve the corresponding mathematical problems.     

Multi-period supplier selection under price uncertainty

We consider a problem faced by a procurement manager who needs to purchase a large volume of multiple items over multiple periods from multiple suppliers that provide base prices and discounts. Discounts are contingent on meeting various conditions on total volume or spend, and some are tied to future realizations of random events that can be mutually verified. We formulate a scenario-based multi-stage stochastic optimization model that allows us to consider random events such as a drop in price because of the most favoured customer clauses, a price change in the spot market or a new discount offer. We propose certainty-equivalent heuristics and evaluate the regret of using them. We use our model for three bidding events of a large manufacturing company. The results show that considering most favored customer clauses in supplier offers may create substantial savings that may surpass the savings from regular discount offers.     

Sourcing under incomplete information and negative capacity-cost correlation

We study a sourcing problem where a buyer reserves capacity from a set of suppliers. The suppliers have finite capacity and their unit production cost is a decreasing function of their capacity, implying scale economies. The capacity of each supplier and therefore the cost is his private information. The buyer and other suppliers only know the probability distribution of the supplier’s capacity. The buyer’s demand is random and she has to decide how much capacity to reserve in advance from a subset of suppliers and how much to source from marketplace. In this study we determine the buyer’s optimum reservation quantity and the size of the supply base. We find the presence of such capacity cost correlation leads to supply base reduction.     

Configurable offers and winner determination in multi-attribute auctions

The theory of procurement auctions traditionally assumes that the offered quantity and quality is fixed prior to source selection. Multi-attribute reverse auctions allow negotiation over price and qualitative attributes such as color, weight, or delivery time. They promise higher market efficiency through a more effective information exchange of buyer’s preferences and supplier’s offerings. This paper focuses on a number of winner determination problems in multi-attribute auctions. Previous work assumes that multi-attribute bids are described as attribute value pairs and that the entire demand is purchased from a single supplier. Our contribution is twofold: First, we will analyze the winner determination problem in case of multiple sourcing. Second, we will extend the concept of multi-attribute auctions to allow for configurable offers. Configurable offers enable suppliers to specify multiple values and price markups for each attribute. In addition, suppliers can define configuration and discount rules in form of propositional logic statements. These extensions provide suppliers with more flexibility in the specification of their bids and allow for an efficient information exchange among market participants. We will present MIP formulations for the resulting allocation problems and an implementation.     

Impact of supply base heterogeneity in electronic markets

Internet based marketplaces have enabled industrial buyers to locate suppliers from geographically diverse locations. This has resulted in increased variations in certain supplier parameters such as capacity and cost among the participating suppliers. However, the impact of this increased heterogeneity on the procurement practices are not well understood. In this paper we consider three supplier parameters that can affect the price the buyer pays and the number of suppliers that the buyer will select for award of contract. These attributes are capacity, production cost and demand for supplier’s capacity. We show how these parameters impact the price that a supplier quotes. We also show how the buyer will determine the optimum number of suppliers using a reverse auction mechanism when he does not have perfect knowledge of the suppliers’ parameters. Our model suggests that buyers need to adjust some of the input parameters while procuring capacity from a heterogeneous supply base. For instance, buyers need to pre-qualify more suppliers if the supply base has greater heterogeneity.     

Optimal supplier choice with discounting

This paper investigates a model for pricing the demand for a set of goods when suppliers operate discount schedules based on total business value. We formulate the buyers's decision problem as a mixed binary integer program, which is a generalization of the capacitated facility location problem (CFLP). A branch and bound (BnB) procedure using Lagrangean relaxation and subgradient optimization is developed for solving large-scale problems that can arise when suppliers’ discount schedules contain multiple price breaks. Results of computer trials on specially adapted large benchmark instances of the CFLP confirm that a sub-gradient optimization procedure based on Shor and Zhurbenko's r-algorithm, which employs a space dilation in the direction of the difference between two successive subgradients, can be used efficiently for solving the dual problem at any node of the BnB tree.     

Compact bidding languages and supplier selection for markets with economies of scale and scope

Combinatorial auctions have been used in procurement markets with economies of scope. Preference elicitation is already a problem in single-unit combinatorial auctions, but it becomes prohibitive even for small instances of multi-unit combinatorial auctions, as suppliers cannot be expected to enumerate a sufficient number of bids that would allow an auctioneer to find the efficient allocation. Auction design for markets with economies of scale and scope are much less well understood. They require more compact and yet expressive bidding languages, and the supplier selection typically is a hard computational problem. In this paper, we propose a compact bidding language to express the characteristics of a supplier’s cost function in markets with economies of scale and scope. Bidders in these auctions can specify various discounts and markups on overall spend on all items or selected item sets, and specify complex conditions for these pricing rules. We propose an optimization formulation to solve the resulting supplier selection problem and provide an extensive experimental evaluation. We also discuss the impact of different language features on the computational effort, on total spend, and the knowledge representation of the bids. Interestingly, while in most settings volume discount bids can lead to significant cost savings, some types of volume discount bids can be worse than split-award auctions in simple settings.     

An assessment of the effect of mass customization on suppliers’ inventory levels in a JIT supply chain

In some industries, mass customization requires a supplier to provide an Original Equipment Manufacturer (OEM) with a wide range of variants of a given part. We consider an OEM-parts suppliers system for an automotive supply chain where parts are delivered to the assembly line several times a day in a just-in-time environment. Simulating varying assembly schedule and parts delivery schemes, we assess the effect of mass customization on the level of inventory the supplier needs for each variant in order to prevent stockouts. We find, among other things, that as the level of mass customization increases, there tends to be an increase in the level of inventory the supplier needs to maintain for each part variant in order to prevent stockouts. Theoretical support is provided for the phenomenon. The presented framework is also useful for evaluating the levels of mass customization that will enable the manufacturer meet customers’ requirements in a cost effective manner. Furthermore, the study confirms the superiority, in terms of inventory levels, of the min–max over the min–sum optimization framework.     

A capacity reservation game for suppliers with multiple blocks of capacity

This paper studies a supplier competition model in which a buyer reserves capacity from a number of suppliers that each have multiple blocks of capacity (e.g., production or power plants). The suppliers each submit a bid that specifies a reservation price and an execution price for every block, and the buyer determines what blocks to reserve. This game involves both external competition between suppliers and internal competition between blocks from each supplier. We characterize the properties of pure-strategy Nash equilibria for the game. Such equilibria may not always exist, and we provide the conditions under which they do.     

A multiple replenishment contract with ARIMA demand processes

This paper is concerned with a multiple replenishment contract with a purchase price discount in a supply chain. The chain is composed of one supplier, one buyer and consumers for a product. The replenishment contract is based upon the well-known (s, Q) policy, but allows us to contract replenishments at a future time with a price discount. Owing to the larger forecast error of future demand, the buyer should keep a higher level of safety stock to provide the same level of service as the usual (s, Q) policy. However, the buyer can reduce his purchase cost by ordering a larger quantity at a discounted price. Hence, there exists a trade-off between the price discount and the inventory holding cost. For the ARIMA demand processes, we present a model for the contract and an algorithm to find the number of the future replenishments. Computational experiments show that the algorithm finds the global optimum solution very quickly.     

Design of contract parameters in a closed-loop supply chain

We study an extended joint economic lot size problem which incorporates the return flow of remanufacturable used products. The supply chain under consideration consists of a single supplier and a single buyer. The buyer orders a single product from the supplier, uses it for her own needs, and collects the remanufacturable items after use. The ordered items are shipped from the supplier to the buyer in the lot-for-lot fashion by a vehicle which also returns the collected used items from the buyer to the supplier for remanufacturing and subsequent service of the buyer’s demand in the next order cycle. For satisfying the total demand, the supplier manufactures new items or remanufactures used ones received from the buyer. For given demand, productivity, collection rate, disposal cost, setup cost, order cost, holding cost for serviceable and nonserviceable products at the supplier as well as the buyer the lot size (order size) for the supplier (buyer) has to be found which minimizes the total cost. Furthermore, we address a decentralised decision making of the parties under a two-part tariff and determine their equilibrium strategies within the Nash framework.     

Optimal solutions for the economic lot-sizing problem with multiple suppliers and cost structures

This paper considers a multi-supplier economic lot-sizing problem in which the retailer replenishes his inventory from several suppliers. Each supplier is characterized by one of three types of order cost structures: incremental quantity discount cost structure, multiple set-ups cost structure and all-unit quantity discount cost structure. The problem is challenging due to the mix of different cost structures. For all cases of the problem where each supplier is characterized by one of the first two cost structures, some optimality properties are proposed and optimal algorithms based on dynamic programming are designed. For the case where all suppliers are characterized by all-unit quantity discount cost structures, it is hard to design a polynomial time algorithm by the analyzed optimal properties. However, it is proved that one of its special cases can be solved in polynomial time.     

Price markdown scheme in a multi-echelon supply chain in a high-tech industry

This paper studies the price markdown scheme in a supply chain that consists of a supplier, a contract manufacturer (CM), and a buyer (retailer). The buyer subcontracts the production of the final product to the CM. The CM buys the components from the supplier and charges the buyer a service fee for the final product produced. The price markdown is made possible by the supplier with the development of new manufacturing technologies that reduce the production cost for the sourced component. Consequently, the buyer adjusts the retail price in order to possibly stimulate stronger demand that may benefit both the supplier and the buyer. Under this scenario, we identify the optimal discount pricing strategies, capacity reservation, and the stocking policies for the supplier and the buyer. We also investigate the optimal inventory decision for the CM to cope with the price discount by considering both demand and delivery uncertainties. Our results suggest that higher production cost accelerates the effects of higher price sensitivity on lowering the optimal capacity and stocking policies in the supply chain. The effect of mean demand error on the optimal prices is relatively marginal compared with that from price sensitivity. We also found that increasing the standard deviation of the random demand does not necessarily increase the stocking level as one would predict. The results show that delivery uncertainty plays an important role in the inventory carried beyond the price break. We discuss potential extensions for future research.     

An exact algorithm for the Capacitated Total Quantity Discount Problem

In this paper we analyze the procurement problem of a company that needs to purchase a number of products from a set of suppliers to satisfy demand. The suppliers offer total quantity discounts and the company aims at selecting a set of suppliers so to satisfy product demand at minimum purchasing cost. The problem, known as Total Quantity Discount Problem (TQDP), is strongly NP-hard. We study different families of valid inequalities and provide a branch-and-cut approach to solve the capacitated variant of the problem (Capacitated TQDP) where the quantity available for a product from a supplier is limited. A hybrid algorithm, called HELP (Heuristic Enhancement from LP), is used to provide an initial feasible solution to the exact approach. HELP exploits information provided by the continuous relaxation problem to construct neighborhoods optimally searched through the solution of mixed integer subproblems. A streamlined version of the proposed exact method can optimally solve in a reasonable amount of time instances with up to 100 suppliers and 500 products, and largely outperforms an existing approach available in the literature and CPLEX 12.2 that frequently runs out of memory before completing the search.     

Multisourcing suppliers selection in service outsourcing

Multisourcing suppliers selection in service outsourcing involves selecting a supplier portfolio with a reasonable number of suppliers and better performance to cover aspiration levels of criteria. It is a specific weighted matching problem with new challenges. This paper proposes a decision method for solving this problem. In the proposed method, different formats of preference information, including numerical values, interval numbers and linguistic variables, are used to express alternative ratings. The technique for order preference by similarity to ideal solution is extended to aggregate the three formats of preference information. A bi-objective 0–1 linear programming model using the aggregated information is built to select a desired supplier portfolio, in which the objectives of minimization of suppliers number and maximization of supplier performance are involved. To solve this model, we transform it into an equivalent, and then an exact multi-objective branch-and-bound algorithm is developed to obtain Pareto-optimal solutions. In addition, a real case of an insurance company is used to illustrate the applicability of the proposed method.     

The optimal quantity discount that a supplier should offer

Quantity discounts are a useful mechanism for coordination. Here we investigate such discounts from the supplier's perspective, both from a non-cooperative game-theoretical approach and a joint decision model. Taking into account the price elasticity of demand, this analysis aids a sole supplier in establishing an all-unit quantity discount policy in light of the buyer's best reaction. The Stackelberg equilibrium and Pareto optimal solution set are derived for the non-cooperative and joint-decision cases, respectively. Our research indicates that channel efficiency can be improved significantly if the quantity discount decision is made jointly rather than non-cooperatively. Moreover, we extend our model in three directions: (1) the product is transported by a private fleet; (2) the buyer may choose to offer her customers a different percentage discount than that she obtained from the supplier; and (3) the case of heterogeneous buyers. Numerical case studies are employed throughout the paper to illustrate the practical applications of the models presented and the sensitivity to model parameters.     

Analyzing online B2B exchange markets: Asymmetric cost and incomplete information

This research applies the discriminating auction to analyze the online B2B exchange market in which a single buyer requests multiple items and several suppliers having equal capacity and asymmetric cost submit bids to compete for buyer demand. In the present model, we examine the impact of asymmetric cost and incomplete information on the participants in the market. Given the complete cost information, each supplier randomizes its price and the lower bound of the price range is determined by the highest marginal cost. In addition, the supplier with a lower marginal cost has a larger considered pricing space but ultimately has a smaller equilibrium one than others with higher marginal costs. When each supplier’s marginal cost is private information, the lowest possible price is determined by the number of suppliers and the buyer’s reservation price. Comparing these two market settings, we find whether IT is beneficial to buyers or suppliers depends on the scale of the bid process and the highest marginal cost. When the number of suppliers and the difference between the highest marginal cost and the buyer’s reservation price are sufficiently large, each supplier can gain a higher profit if the marginal costs are private information. On the contrary, when the highest marginal cost approaches the buyer’s reservation price, complete cost information benefits the suppliers.     

A mathematical model for a capacity reservation contract

It is common practice in many industries to use a replenishment contract with a mechanism of capacity reservation. In this paper, we focus on a multi-period capacity reservation contract practiced between a buyer, who buys a single type of product and sells it to end-customers, and two or more heterogeneous suppliers, who produce and replenish the product as agreed upon contractually.In this paper, a mathematical model including several key features of a real contract is developed for a single supplier situation from the buyer’s perspective. It is then extended to a multiple supplier model for a system in which there are several heterogeneous suppliers with different capacities and prices. A rolling-horizon implementation strategy is suggested for the efficient application of the models. Extensive computational experiments demonstrate that the model and strategy can produce cost effective contractual terms for the buyer within a few seconds.