Quantity-Flexibility

Procurement - flexibility relatively elastic (>1) Flexible Quantity, fixed Quantity, flexible orice. fixed orice... 

Commodity-related models focus on demand volatility and uncertainty in volumes and prices as with sales quantity flexibility. Several authors proposed models to handle demand uncertainty in general focusing on quantities (Cheng et al. 2003 Gupta/Maranas 2003 Cheng et al. 2004 Chen/Lee 2004). Uncertainty is reflected by demand quantity scenarios and/or probabilities. Proposed models maximize expected or robust profit. Process industry-specific models use simulation to address demand uncertainty and to determine optimal inventory levels (Jung et al. 2004). 

Since both spot price and quantity are modeled as variables, the resulting optimization problem of maximizing turnover is quadratic. In the following, we show how a linear approximation of the turnover function can be achieved (see also Habla 2006). This approach is based on the concavity property of the turnover function and the limited region of sales quantity flexibility to be considered. Approximation parameters are determined in a preprocessing phase based on the sales input and control data. The preprocessing is structured in two phases as shown in table 25 ... 

Muchofthe re search has assumedthateach agent in a supply chain is risk-neutral and his objective is to maximize (minimize) the expected profit (cost). Under this assumption, a supply chain is said to be coordinated when the summation of individual expectedprofits (costs) are maximized (minimized). A number of contractual forms have been studied recently under the risk-neutral assumption. These include the three popular contracts wholesale price (WP) contracts (Lariviere Porteus, 2001 Corbett et al., 2004), buy back (BB) contracts (Pasternack, 1985), and quantity flexibility (QF) contracts (Tsay, 1999 Cachon, 2003). 

Tsay, A. A. (1999). The quantity flexibility contract and supplier-customer incentives. Management Science, 45, 1339-1358. 

The chapter studies a supply chain consisting of one supplier and one retailer with satisficing objectives for each player. The authors examine the supply chain under three types of contracts wholesale price, buy back, and quantity flexibility contracts. They show that under the satisficing objectives, wholesale price contracts can coordinate the supply chain, whereas buy back contracts cannot. In addition, quantity flexibility contracts must degenerate into wholesale price contracts to coordinate the supply chain. The authors also discuss possible extensions to their model. 

Tsay, A.A., W.S. Lovejoy. 1999. Quantity Flexibility Contracts and Supply Chain Performance. Manufacturing and Service Operations Management 1(2), 89-111. 

The typical analytical approach is to study the source of inefficiency (often related to double marginalization), and various mechanisms for achieving channel coordination and/or Pareto improvement. Mechanisms so studied recently include resale price maintenance, full-line forcing, quantity discounts, manufacturer returns, quantity flexibility, sales rebates, revenue sharing, price protection, and markdown allowances. New studies continue to be produced at a prodigious rate by generalizing the basic framework, perhaps by adding retailer decision variables (e.g., some form of effort, in addition to retail price... 

Observation 4. None of the following contracts - returns, quantity-flexibility, penalty (all as described by Lariviere 1999), revenue sharing (as described by Cachon and Lariviere 2000), or quantity discount (as described by Jeuland and Shugan 1983) - can coordinate the supply chains in Models T or D. 

PRICING FOR COORDINATION In many instances, suitable pricing schemes can help coordinate the supply chain. A manufactmer can use lot-size-based quantity discounts to achieve coordination for commodity products if the manufacturer has large fixed costs associated with each lot (see Chapter 11 for a detailed discussion). For products for which a firm has market power, a manufacturer can use two-part tariffs and volume discounts to help achieve coordination (see Chapter 11 for a detailed discussion). Given demand uncertainty, manufactmers can use buyback, revenue-sharing, and quantity flexibility contracts to spur retailers to provide levels of... 

Assume that the manufacturer incurs a production cost of v per unit and charges a wholesale price of c from the retailer. The retailer, in turn, sells to customers for a price of p. The retailer salvages any leftover units for sr. The manufacturer salvages any leftover units for %. If retailer demand is normally distributed, with a mean of /r and a standard deviation of a, we can evaluate the impact of a quantity flexibility contract. If the retailer orders 0 units, the manufacturer is committed to supplying Q units. As a result, we assume that the manufacturer produces Q units. The retailer purchases q units if demand D is less than q, D units if demand D is between q and Q, and Q units if demand D is greater than Q. In the following formulas, Fs is the standard normal cumulative distribution function and fs is the standard normal density function discussed in Appendix 12A in Chapter 12. We thus obtain... 

We illustrate the impact of quantity flexibility on supply chain profits using Example 15-4 (see worksheet Examplel5-4). 

EXAMPLE 15-4 Impact of Risk Sharing Through Quantity Flexibility... 

We return to the music store in Example 15-1 with all data as specified. The retailer is charged 5 for each disc and has a retail price of 10. Assume that the supplier agrees to a quantity flexibility... 

Profits at Music Supply Chain Under Different Quantity Flexibility Contracts... 

In Table 15-5, we show the impact of different quantity flexibility contracts on profitability for the music supply chain when demand is normally distributed, with a mean of jx = 1,000 and a standard deviation of a- = 300 (see worksheet Examplel5-4 in spreadsheet Chapterl5-examples). We assume a wholesale price of c = 5 and a retail price of p = 10. All contracts considered are such that a = (3. The results in Table 15-5 are built in two steps. We first fix a and j8 (say a = j8 = 0.2). The next step is to identify the optimal order size for the retailer. This is done using Excel by selecting an order size that maximizes expected retailer profits given a and j8. For example, when a = j8 = 0.05 and c = 5, retailer profits are maximized for an order size of 0 = 1,017. For this order size, we obtain a supplier commitment to deliver up to g = (1 + 0 05) X 1,017 = 1,068 and a retailer commitment to buy at least q = ( - 0.05) X 1,017 = 966 discs. In our analysis, we assume that the supplier produces Q = 1,068 discs and sends the precise number (between 966 and 1,068) demanded by the retailer. Such a policy results in retailer profits of 4,038 and supplier profits of 4,006. 

From Table 15-5, observe that quantity flexibility contracts allow both the manufacturer and the retailer to increase their profits. Observe that as the manufacturer increases the wholesale price, it is optimal for it to offer greater quantity flexibihty to the retailer. 

Quantity flexibility contracts are common for components in the electronics and computer industries. In the previous discussion, we considered fairly simple quantity flexibility contracts. Benetton has used sophisticated quantity flexibility contracts with its retailers successfully to increase supply chain profits. We describe such a contract in the context of colored knit garments (see Heskett and Signorelli, 1984). 

Relative to buyback and revenue-sharing contracts, quantity flexibihty contracts have less information distortion. Consider the case with multiple retailers. With a buyback contract, the supply chain must produce based on the retailer orders that are placed well before actual demand arises. This leads to surplus inventory being disaggregated at each retailer. With a quantity flexibility contract, retailers specify only the range within which they will purchase, well before actual demand arises. If demand at various retailers is independent, the supplier does not need to... 

As with the other contracts discussed, quantity flexibility contracts result in lower retailer effort. In fact, any contract that gets retailers to provide a higher level of product availability by not making them fully responsible for overstocking will result in a lowering of retailer effort for a given level of inventory. 

Risk sharing in a supply chain increases profits for both the supplier and the retailer. Risk sharing mechanisms include buybacks, revenue sharing, and quantity flexibility. Quantity flexibility contracts result in lower information distortion than buyback or revenue-sharing contracts when a supplier sells to multiple buyers or the supplier has excess, flexible capacity. 

For a manufacturer that sells to many retailers, why does a quantity flexibility contract result in less information distortion than a buyback contract ... 

Benetton has entered into a quantity flexibility contract with a retailer for a seasonal product. If the retailer orders O units, Benetton is willing to provide up to another 35 percent if needed. Benetton s production cost is 20, and it charges the retailer a wholesale price of 36. The retailer prices to customers at 55 per unit. Any unsold units can be sold by the retailer at a salvage value of 25. Benetton can salvage only 10 per unit for its leftover inventory. The retailer forecasts demand to be normally distributed, with a mean of 4,000 and a standard deviation of 1,600. 

Consider a manufacturer selling DVDs to a retailer for 6 per DVD. The production cost of each DVD is 1 and the retailer prices each DVD at 10. Retail demand for DVDs is normally distributed, with a mean of 1,000 and standard deviation of 300. The manufacturer has offered the retailer a quantity flexibility contract with a = p = 0.2. The retailer places an order for 1,000 units. Assume that salvage value is zero for both the retailer and the manufacturer. 

Imagine that you have acquired both the retailer and manufacturer discussed in Exercise 7. Your interests now are in maximizing profitability for your new firm and in setting up an incentive system to make this happen. You have ehosen to keep the quantity flexibility contract in place to provide incentive to both your retailer and your manufacturer. 

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