CN107644351A - Two-echelon supply-chain coordination approach based on quantity discount under the conditions of information symmetrical - Google Patents
Two-echelon supply-chain coordination approach based on quantity discount under the conditions of information symmetrical Download PDFInfo
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Abstract
The embodiment of the present invention provides the two-echelon supply-chain coordination approach based on quantity discount under the conditions of a kind of information symmetrical, under the conditions of two-level supply chain information symmetrical, when retailer's amount of purchase is above standard amount of purchase, certain price rebate is given by manufacturer, by establishing the respective standard purchase price decision model of two-level supply chain before coordinating and standard production decision model, and solve and obtain minimum cost and maximum profit, as the criterion subsequently coordinated.Again by establishing the mathematical modeling coordinated, and judge whether to meet mutual cooperation condition based on cooperation necessary condition, and application Nash Equilibrium Solution solves the optimal discount rate of acquisition, amount of purchase, output.Enable two-level supply chain to obtain more excellent market efficiency, help to maintain the long-term cooperative relationship of both sides.
Description
Technical field
The present invention relates to areas of information technology, in particular to being based on quantity discount contract under the conditions of a kind of information symmetrical
Two-echelon supply-chain coordination approach about.
Background technology
Under normal circumstances, in the two-echelon supply-chain being made up of retailer and manufacturer, have between retailer and manufacturer
Different decision objectives, when formulating decision-making, only consider number one, and ignore the interests or whole system of other member enterprises
Interests when, often reduce supply chain entirety profit, make system disequilibrium.And all decision-makings in system are by same
When individual decision-maker determines, system entirety profit can reach maximum, so as to realize optimum state.
At present in the research to two-echelon supply-chain coordination problem, the overwhelming majority is built upon monocycle or Continuous Demands
On the basis of, and what is be directed to is all single coordination contract.And much demand that is predictable or being known a priori by all is in reality
Discrete, such as make-to-order production.In addition, different contracts, to the trade-off effect of supply chain under multicycle discrete demand environment
May be different.Supply chain, which reaches coordination, then to be needed to meet two conditions：(1) coordinate after retailer gross profit and manufacturer it is total
Profit is more than respective profit before coordination；(2) after system reaches coordination, the respective profit of retailer and manufacturer keep it is stable or
Person is lifted, that is, needs to reach Nash Equilibrium.Only when both these conditions are met, supply chain is just really achieved coordination, retail
Cooperative relationship steady in a long-term could be established between business and manufacturer.
Therefore, under information symmetrical and multicycle discrete type conditions of demand, how supply chain constract is designed, reaches supply chain
It is subject matter to be solved to the trade-off effect of supply chain to coordinating and analyzing different contracts.
Quantity discount refers to that, for the different amount of purchase of retailer, manufacturer provides certain price to retailer and rolled over
Button.Rational quantity discount can promote retailer and manufacturer to work closely, and reduce the transaction cost of both sides, improve and supply
Answer catenary system totality profit.Quantity discount is main, and what is considered herein is full Board Lot discounted policy.In supply chain constract
In the coordination system, quantity discount is to coordinate one of two-echelon supply chain most efficient method.
Quantity discount problem to supply chain is studied, under based on hypothesis of the batch to batch, and single retail
In the supply chain of business and single supplier composition, it is proposed that the optimal quantity discount of system optimal and supplier.Two-stage supplies
Answering the change of quantity discount two ways and demand in chain can have an impact to Quantity Discount.How two-stage is optimized
Amount of purchase, output and the discount rate of supply chain are into being that Coordination Model needs the major issue that solves.
The content of the invention
In view of this, the purpose of the embodiment of the present invention is based on quantity discount under the conditions of being to provide a kind of information symmetrical
Two-echelon supply-chain coordination approach, to solve the problems, such as the amount of purchase, output and the discount rate that how to obtain optimization.
The two-echelon supply-chain based on quantity discount is coordinated under the conditions of present pre-ferred embodiments provide information symmetrical
Method, the coordination approach comprise the following steps:
S1, criterion is turned to retailer's cost minimization, the standard purchase price decision model of retailer before coordinating is established, obtains
Obtaining object function is：
In formula, CrFor the totle drilling cost of retailer；T is supply chain total cycle；qtFor in the amount of purchase of t cycle retailers, qt≥
0, t=1,2 ..., T；For in the ordering cost of t cycle retailers；For the unit stock of t cycle retailers into
This；ωtFor in the wholesale price of t cycle products；dtFor in the demand of t cycle customers；
Wherein,For in the quantity in stock of t cycle retailers,
In formula,
Further, using manufacturer's profit maximization as criterion, the production decision model of manufacturer before coordinating is established, is obtained
Obtaining object function is：
In formula, T is supply chain total cycle；qtFor in the amount of purchase of t cycle retailers, qt>=0, t=1,2 ..., T；πmFor
The gross profit of manufacturer；Used to produce payment for initiation in t cycle manufacturers；To be given birth in the unit of t cycle manufacturers
Produce cost；For in the unit inventory cost of t cycle manufacturers；ωtFor in the wholesale price of t cycle products；ytFor in t
Cycle manufacturer output, yt>=0, t=1,2 ..., T；
Wherein,For in the quantity in stock of t cycle manufacturers,
In formula,
S2, based on the procurement decisions model of retailer before coordination, applied dynamic programming Algorithm for Solving t cycles retailer is most
Small totle drilling cost, represent as follows：
Wherein, RC1(t) minimum total cost of the retailer in cycle 1 to cycle t is represented；
Further, based on the production decision model before coordination in manufacture, applied dynamic programming Algorithm for Solving t cycle manufacturers
Maximum gross profit, represent it is as follows：
Wherein, MP1(t) the maximum gross profit of the manufacturer in cycle 1 to cycle t is represented；
S3, based on amount of purchase and discount rate, the coordination mathematical modeling of retailer and manufacturer is established respectively,
The coordination mathematical modeling of retailer is expressed as：
The coordination mathematical modeling of manufacturer is expressed as：
And
Wherein, q+For retailer's standard purchase price amount,rtFor t cycle retailer procurement price discounts
Rate；
S4, it is non-negative with each cycle retailer amount of purchase and manufacturer's output, and zero after SC collaboration
Sell business minimum cost be less than coordinate before, after coordination the maximum profit of supplier be more than coordinate before be cooperation necessary condition, solution
Verify whether coordinate scheme be present, cooperation necessary condition is expressed as：
RC1(r ', q ') represents the minimum cost of retailer after being coordinated, MP1(r ', y ') represents to manufacture after being coordinated
The maximum profit of business；
And it is met the buying vector and production vector of cooperation necessary condition；
S5, using Nash Equilibrium Solution, solve optimal discount rate, amount of purchase, output (r*, q*, y*), Nash Equilibrium Solution
It is expressed as：
Optimal discount rate, amount of purchase, output (r*, q*, y*), it is respectively：
The present invention is under the conditions of two-level supply chain information symmetrical, the manufacturer when retailer's amount of purchase is above standard amount of purchase
Certain price rebate is given, by establishing the respective standard purchase price decision model of two-level supply chain and standard production before coordinating
Decision model, and solve and obtain minimum cost and maximum profit, as the criterion subsequently coordinated.Coordinated again by establishing
Mathematical modeling, and judge whether to meet mutual cooperation condition based on cooperation necessary condition, and application Nash Equilibrium Solution is solved and obtained
Optimal discount rate, amount of purchase, output.Enable two-level supply chain to obtain more excellent market efficiency, help to remain double
The long-term cooperative relationship of side.
Brief description of the drawings
In order to illustrate the technical solution of the embodiments of the present invention more clearly, below by embodiment it is required use it is attached
Figure is briefly described, it will be appreciated that the following drawings illustrate only certain embodiments of the present invention, therefore be not construed as pair
The restriction of scope, for those of ordinary skill in the art, on the premise of not paying creative work, can also be according to this
A little accompanying drawings obtain other related accompanying drawings.
Fig. 1 is the two-echelon supply-chain based on quantity discount under the conditions of the information symmetrical that present pre-ferred embodiments provide
The flow chart of coordination approach.
Embodiment
Below in conjunction with accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Ground describes, it is clear that described embodiment is only part of the embodiment of the present invention, rather than whole embodiments.Therefore, with
Under the detailed descriptions of embodiments of the invention to providing in the accompanying drawings be not intended to limit the scope of claimed invention,
But it is merely representative of the selected embodiment of the present invention.Based on embodiments of the invention, those skilled in the art are not making wound
The every other embodiment that the property made is obtained on the premise of working, belongs to the scope of protection of the invention.
Two-echelon supply-chain coordination approach based on quantity discount under the conditions of information symmetrical, the coordination approach include with
Lower step:
S1, criterion is turned to retailer's cost minimization, the standard purchase price decision model of retailer before coordinating is established, obtains
Obtaining object function is：
In formula, CrFor the totle drilling cost of retailer；T is supply chain total cycle；qtFor in the amount of purchase of t cycle retailers, qt≥
0, t=1,2 ..., T；For in the ordering cost of t cycle retailers；For the unit stock of t cycle retailers into
This；ωtFor in the wholesale price of t cycle products；dtFor in the demand of t cycle customers；
Wherein,For in the quantity in stock of t cycle retailers,
In formula,
Retailer has irreplaceable status in production marketing, and the procurement strategy of retailer directly influences manufacturer
Production strategy.Retailer can be formulated the demand status of product as point-of-sale terminal according to the cost structure and customer of itself
Optimal procurement strategy.Therefore, based on retailer's cost minimization, procurement decisions model is established, is more preferably tallied with the actual situation, and marked
Quasi- procurement decisions model considers the influence factors such as supply chain total cycle, purchase cost, inventory cost, has high excellent of reliability
Point.
Further, using manufacturer's profit maximization as criterion, the production decision model of manufacturer before coordinating is established, is obtained
Obtaining object function is：
In formula, T is supply chain total cycle；qtFor in the amount of purchase of t cycle retailers, qt>=0, t=1,2 ..., T；πmFor
The gross profit of manufacturer；Used to produce payment for initiation in t cycle manufacturers；To be given birth in the unit of t cycle manufacturers
Produce cost；For in the unit inventory cost of t cycle manufacturers；ωtFor in the wholesale price of t cycle products；ytFor at t weeks
Phase manufacturer output, yt>=0, t=1,2 ..., T；
Wherein,For in the quantity in stock of t cycle manufacturers,
In formula,
S2, based on the procurement decisions model of retailer before coordination, applied dynamic programming Algorithm for Solving t cycles retailer is most
Small totle drilling cost, represent as follows：
Wherein, RC1(t) minimum total cost of the retailer in cycle 1 to cycle t is represented；
Further, based on the production decision model before coordination in manufacture, applied dynamic programming Algorithm for Solving t cycle manufacturers
Maximum gross profit, represent it is as follows：
Wherein, MP1(t) the maximum gross profit of the manufacturer in cycle 1 to cycle t is represented.
Step S1 and S2 is by establishing the respective standard purchase price decision model of two-level supply chain and standard production before coordinating
Decision model, and solve and obtain minimum cost and maximum profit, as the criterion subsequently coordinated.
S3, based on amount of purchase and discount rate, the coordination mathematical modeling of retailer and manufacturer is established respectively,
The coordination mathematical modeling of retailer is expressed as：
The coordination mathematical modeling of manufacturer is expressed as：
And
Wherein, q+For retailer's standard purchase price amount,rtFor t cycle retailer procurement price discounts
Rate；
S4, it is non-negative with each cycle retailer amount of purchase and manufacturer's output, and zero after SC collaboration
Sell business minimum cost be less than coordinate before, after coordination the maximum profit of supplier be more than coordinate before be cooperation necessary condition, solution
Verify whether coordinate scheme be present, cooperation necessary condition is expressed as：
RC1(r ', q ') represents the minimum cost of retailer after being coordinated, MP1(r ', y ') represents to manufacture after being coordinated
The maximum profit of business；
And it is met the buying vector and production vector of cooperation necessary condition；
S5, using Nash Equilibrium Solution, solve optimal discount rate, amount of purchase, output (r*, q*, y*), Nash Equilibrium Solution
It is expressed as：
Optimal discount rate, amount of purchase, output (r*, q*, y*), it is respectively：
When retailer's amount of purchase is above standard amount of purchase, certain price rebate is given by manufacturer, and step S3, S4, S5 lead to
Cross the mathematical modeling established and coordinated, and judge whether to meet mutual cooperation condition based on cooperation necessary condition, and application receive it is assorted equal
Weighing apparatus solution, which solves, obtains optimal discount rate, amount of purchase, output.Two-level supply chain is enabled to obtain more excellent market efficiency,
Contribute to the long-term cooperative relationship of maintenance both sides.
The preferred embodiments of the present invention are the foregoing is only, are not intended to limit the invention, for the skill of this area
For art personnel, the present invention can have various modifications and variations.Within the spirit and principles of the invention, that is made any repaiies
Change, equivalent substitution, improvement etc., should be included in the scope of the protection.
Claims (1)
1. the two-echelon supply-chain coordination approach based on quantity discount under the conditions of information symmetrical, it is characterised in that the coordination
Method comprises the following steps:
S1, criterion is turned to retailer's cost minimization, establishes the standard purchase price decision model of retailer before coordinating, obtains mesh
Scalar functions are：
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In formula, CrFor the totle drilling cost of retailer；T is supply chain total cycle；qtFor in the amount of purchase of t cycle retailers, qt≥0,t
=1,2 ..., T；For in the ordering cost of t cycle retailers；For in the unit inventory cost of t cycle retailers；
ωtFor in the wholesale price of t cycle products；dtFor in the demand of t cycle customers；
Wherein,For in the quantity in stock of t cycle retailers,
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In formula,
Further, using manufacturer's profit maximization as criterion, the production decision model of manufacturer before coordinating is established, obtains mesh
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In formula, T is supply chain total cycle；qtFor in the amount of purchase of t cycle retailers, qt>=0, t=1,2 ..., T；πmFor manufacture
The gross profit of business；Used to produce payment for initiation in t cycle manufacturers；For the production of units of t cycle manufacturers into
This；For in the unit inventory cost of t cycle manufacturers；ωtFor in the wholesale price of t cycle products；ytFor in the t cycles
The output of manufacturer, yt>=0, t=1,2 ..., T；
Wherein,For in the quantity in stock of t cycle manufacturers,
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S2, based on the procurement decisions model of retailer before coordination, the minimum of applied dynamic programming Algorithm for Solving t cycle retailers is total
Cost, represent as follows：
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Wherein, RC1(t) minimum total cost of the retailer in cycle 1 to cycle t is represented；
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Big gross profit, represent as follows：
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Wherein, MP1(t) the maximum gross profit of the manufacturer in cycle 1 to cycle t is represented；
S3, based on amount of purchase and discount rate, the coordination mathematical modeling of retailer and manufacturer, the coordination number of retailer are established respectively
Model is learned to be expressed as：
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<mo>,</mo>
<msub>
<mi>q</mi>
<mi>t</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msubsup>
<mi>c</mi>
<mi>s</mi>
<mi>r</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<msubsup>
<mi>I</mi>
<mi>t</mi>
<mi>r</mi>
</msubsup>
<mo>&rsqb;</mo>
<mo>}</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
The coordination mathematical modeling of manufacturer is expressed as：
<mrow>
<msub>
<mi>F</mi>
<mn>4</mn>
</msub>
<mo>=</mo>
<msub>
<mi>Max&pi;</mi>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>,</mo>
<mi>y</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>M</mi>
<mi>a</mi>
<mi>x</mi>
<mo>{</mo>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>t</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>T</mi>
</msubsup>
<mo>&lsqb;</mo>
<msub>
<mi>c</mi>
<mi>t</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>r</mi>
<mi>t</mi>
</msub>
<mo>,</mo>
<msub>
<mi>q</mi>
<mi>t</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msubsup>
<mi>c</mi>
<mi>o</mi>
<mi>r</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msubsup>
<mi>c</mi>
<mi>o</mi>
<mi>m</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msubsup>
<mi>c</mi>
<mi>p</mi>
<mi>m</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>y</mi>
<mi>t</mi>
</msub>
<mo>-</mo>
<msubsup>
<mi>c</mi>
<mi>s</mi>
<mi>m</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<msubsup>
<mi>I</mi>
<mi>t</mi>
<mi>m</mi>
</msubsup>
<mo>&rsqb;</mo>
<mo>}</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
And
Wherein, q+For retailer's standard purchase price amount,rtFor t cycle retailer procurement price discount rates；
S4, it is non-negative, and retailer after SC collaboration with each cycle retailer amount of purchase and manufacturer's output
Minimum cost be less than coordinate before, after coordination the maximum profit of supplier be more than coordinate before be cooperation necessary condition, solution verify
With the presence or absence of coordinate scheme, cooperation necessary condition is expressed as：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>RC</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msup>
<mi>r</mi>
<mo>&prime;</mo>
</msup>
<mo>,</mo>
<msup>
<mi>q</mi>
<mo>&prime;</mo>
</msup>
<mo>)</mo>
</mrow>
<mo><</mo>
<msub>
<mi>RC</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msup>
<mi>q</mi>
<mo>+</mo>
</msup>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>MP</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msup>
<mi>r</mi>
<mo>&prime;</mo>
</msup>
<mo>,</mo>
<msup>
<mi>y</mi>
<mo>&prime;</mo>
</msup>
<mo>)</mo>
</mrow>
<mo>></mo>
<msub>
<mi>MP</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msup>
<mi>y</mi>
<mo>+</mo>
</msup>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
RC1(r ', q ') represents the minimum cost of retailer after being coordinated, MP1(r ', y ') represents manufacturer after being coordinated
Maximum profit；
And it is met the buying vector and production vector of cooperation necessary condition；
S5, using Nash Equilibrium Solution, solve optimal discount rate, amount of purchase, output (r*, q*, y*), Nash Equilibrium Solution represents
For：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>RC</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msup>
<mi>r</mi>
<mo>*</mo>
</msup>
<mo>,</mo>
<msup>
<mi>q</mi>
<mo>*</mo>
</msup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>MinC</mi>
<mi>r</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>,</mo>
<mi>q</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>MP</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msup>
<mi>r</mi>
<mo>*</mo>
</msup>
<mo>,</mo>
<msup>
<mi>y</mi>
<mo>*</mo>
</msup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>Max&pi;</mi>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>,</mo>
<mi>y</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
Optimal discount rate, amount of purchase, output (r*, q*, y*), it is respectively：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>q</mi>
<mi>t</mi>
<mo>*</mo>
</msubsup>
<mo>=</mo>
<mo>{</mo>
<msubsup>
<mi>q</mi>
<mn>1</mn>
<mo>*</mo>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>q</mi>
<mn>2</mn>
<mo>*</mo>
</msubsup>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msubsup>
<mi>q</mi>
<mi>T</mi>
<mo>*</mo>
</msubsup>
<mo>}</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>y</mi>
<mi>t</mi>
<mo>*</mo>
</msubsup>
<mo>=</mo>
<mo>{</mo>
<msubsup>
<mi>y</mi>
<mn>1</mn>
<mo>*</mo>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>y</mi>
<mn>2</mn>
<mo>*</mo>
</msubsup>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msubsup>
<mi>y</mi>
<mi>T</mi>
<mo>*</mo>
</msubsup>
<mo>}</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>r</mi>
<mi>t</mi>
<mo>*</mo>
</msubsup>
<mo>=</mo>
<mo>{</mo>
<msubsup>
<mi>r</mi>
<mn>1</mn>
<mo>*</mo>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>r</mi>
<mn>2</mn>
<mo>*</mo>
</msubsup>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msubsup>
<mi>r</mi>
<mi>T</mi>
<mo>*</mo>
</msubsup>
<mo>}</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
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