Quantity Discounts: An Overview and Practical Guide for Buyers and Sellers

Munson, Charles L.; Jackson, Jonathan E.

doi:10.1561/0200000041

Cited by 10 publications

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“…The research area remains vibrant, with quality publications appearing every year in the operations-management field alone. A comprehensive overview of quantity discounts by [2] covers many of the papers published in the last 25 years.…”

Section: Introductionmentioning

confidence: 99%

“…σ α (q i , q −i )P(q N )q i = αP(q N )q i +(1−α)P(q i )q i ∑ j∈N [αP(q N )q j +(1−α)P(q j )q j ] P(q N )q N = (α i (c)+(1−α)c({i}))c(N) αc(N)+(1−α) ∑ j∈N c({j}) . Denote by f (q i ) = (α i (c) + (1 − α)c({i}))c(N) and g(q i ) = αc(N) + (1 − α) ∑ j∈N c({j}), thus σ α (q i , q −i )P(q N )q i = f (q i ) g(q i ) and ∂(σ α (q i ,q −i )P(q N )q i ) ∂q i = f (q i )g(q i )− f (q i )g (q i ) (g(q i )) 2 , with ∂(σ α (q i ,q −i )P(q N )q i ) ∂q i > 0 ⇔ f (q i )g(q i ) − f (q i )g (q i ) > 0 In addition, it is known that…”

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Cooperative Purchasing with General Discount: A Game Theoretical Approach

2022

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In some situations, sellers of certain commodities usually provide price discounts for large orders according to a decreasing unit price function. Buyers of such commodities can cooperate and form purchasing groups to benefit from these price discounts. A natural way to allocate the corresponding cost reductions is the equal price rule. We analyze this situation as a cooperative game. We show that when the decreasing unit price function is linear, the equal price rule coincides with the Shapley value and the nucleolus of the cooperative game. However, some buyers may argue that the equal price rule is not acceptable because it favors those who buy just a few units of the product. This can be more problematic when the decreasing unit price function is nonlinear: In that case, the equal price rule loses some of its good properties and it no longer matches the Shapley value or the nucleolus. Unlike the linear case, in this nonlinear case, the Shapley value and nucleolus do not assign the same price to all agents, so there are different price rules. However, they have a computability problem, as both are very laborious to calculate for a large number of agents. To find a suitable alternative, we first study the properties that a different price rule should have in this situation. Second, we propose a family of different price rules that hold those properties and are easy to calculate for a large number of agents. This family of different price rules provides buyers (companies, institutions, consumers, etc.) with an easy-to-implement method which ensures stability in cooperative purchasing.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%