On the Algorithms of the Grid- Based EMMIL E-Marketplace Model Dr. Lívia Kacsukné Bruckner International Business School Inst. of Information Systems and Logistics Gábor Hermann MTA SZTAKI

1. Combined negotiation with trading partners and logistics service providers EMMIL E-commerce model to integrate logistics 2. Choosing trading partners and 3PLs

Auction Algorithm for buyer-oriented marketplaces 1.The buyer issues an RFP identifying the requirements 2. Sellers bid offering products. 3. The marketplace engine forwards the bids to the 3PLs who place their bids for logistics services. 4. The marketplace engine aggregates the offers from seller and 3PLs and forwards the best one to the buyer 5. The cycle is continued until the lowest accumulated cost is achieved.

Q i k Purchased quantity of product i. from seller k. P i k Unit-price of product i. at seller k. as a step function of quantity Δ k Discount given as a step function after the total purchase cost at seller k. x j l є {0,1} decision variable x j l =1  offer j. of 3PL l. is selected as winner The original Objective Function

Simplified Objective Function to minimize:  j = 1     i = 1   j = 1   i = 1  P j,i Q j,i +VjVj Q j,i +F j *  i = 1    Q j,i  i = 1    Q j,i  if then  i = 1    Q j,i  i = 1    Q j,i  else

Great trick to obtain linear equations  j = 1   i = 1  t * F j *y j,t +  t = 1 C (V j + P j,i )Q j,t,i Where C is the upper limit for  i = 1    QiQi  and the value of the help variable y j,t must be 0 or 1 The constraints to solve the linear programming problem will be set so that Qj,t,i will be 0 if yj,t is 0

The bad consequence is the big number of variables to solve the linear programing problem: Q j,t,i instead of Q j,i and the additional y j,t

Haw to avoid combinatorical explosion? Idea: Diminish the number of sellers (Dimension j in Q j,t,i ) Solution: Investigate only a limited number of “Best Sellers” (U), selected by the heuristic criteria “Every goods a delivered by the same seller”. Make the calculation parallel for S < U sellers in U S = U! /((U-S)!*S!) cases GRID must be used to exploit parallel computing capacity

Implementation Preparation, constructing the combinations Call the LP_Solver Call the LP_Solver (i) Collect and compare the results 1 2 USUS

Pilot Implementation using the P- GRADE Portal Solution details:

Project 1.: Test the existing EMMIL model on the P-Grade portal for the following scenarios: Enhance the basic version with capacity (upper) limits for products at suppliers. This involves the following: Add an array to the data structure that contains the capacity limits Integer Limits[k,i] (k=1..M, i=1,..N) Change the generator program Fill up the Limits table putting a normal distribution noise to the required quantities Change the prefilter program to cope with quantity limits Pass the relevant limits to the PS jobs Publish all data that has been generated, in a nice customized format. Change the PS job program Facilitate receiving the limits from the input file Generate additional conditions for the solvers to take quantity limits into consideration. Call the solver only if the selected sellers together have enough of all products otherwise generate the relevant error code. Enhance the collector program to handle errors properly. Test your solution. Compare the execution times with different granularities. Document your work.

Project 2.: Test the existing EMMIL model on the P-Grade portal for the following scenarios: Enhance the basic version with an extra feature to allow discounts on combination delivery from different suppliers. This involves the following: Change the user interface to allow entering combinations of seller indexes and discount percentages. Add an array to the data structure to store it. Integer Combination discounts[s1, s2,,..percentage] Change the generator program Change the prefilter program and make sure that the combination where discount is specified will be passed to the PS jobs. Pass the combination discounts table to the PS jobs Publish all data that has been generated, in a nice customized format. Change the PS job program Facilitate receiving the discounts from the input file Check if there is a discount for the current seller combination and change the fix cost of the transportation when generate the input for the solver. Test your solution. Compare the execution times with different granularities.

Project 3.: Test the existing EMMIL model on the P-Grade portal for the following scenarios: Modify the basic version and create a benchmark application where optimization is done only for prices, transportation costs are added after the best solution is found. This involves the following: Change the generator program Change the prefilter program to find candidates for best prices only Publish all data that has been generated, in a nice customized format. Change the PS jobs Modify the data that is passed to the solver excluding data about transportation Change the collector program After finding the best allocation calculate the total cot by adding transportation costs to the purchase cost Test your solution in parallel with the basic solution using the same data and publish the comparison of the results.