DRY-CLEANING SCHEDULING Ratnam Jain (rj2333)Ponni Vel (pvv2001)Yeereina Wu(yw2394)

PROBLEM SETUP

Non-Homogeneous Poisson Arrival Process

1 day15 lbs

3 day5 lbs

2 day18 lbs

J1J2J3

1 Load: 40lbs, 1hr

w3 = $10/lb*15lbs= $150

w2= $4/lb*5lbs= $20

w1= $6/lb*18lbs= $108

1-day $10/lb

2-day $6/lb

3-day $4/lb

1. Simulation to generate instances of jobs characterized by rj,

turnaround-time, lbs of clothes

2. Compute a schedule using the same instance via the Dynamic

Programming and Approximation Algorithms

3. Compare costs, number of tardy jobs, and run times of algorithms

4. Incorporating research from dry-cleaner visits into model

5. Sensitivity Analysis by on pricing matrix, arrival process, and

machine capacity

ANALYSIS METHODOLOGY

TWO ALGORITHMS

Dynamic Programming● Solving a knapsack problem maximizing weight for jobs with a

common deadline● Each item selected will add its weight (lbs) to the load capacity

up to 40 lbs

Approximation Algorithm● Orders jobs with a common deadline in decreasing weight● Jobs added to a load by moving down the list and adding if its

weight (lbs) will fit in the load capacity

BASE CASE MODELSimulate 2 weeks and select 7 days worth of data from middle (to avoid edge effects) as described in the problem setup

Assumptions

● Customers bring in loads with average of 10 lbs● The machine is scheduled at the beginning of each day

BASE CASE MODEL RESULTS

DP schedules with lower cost and number of tardy jobs but takes a longer running time than Approximation Algorithm.

REALISTIC MODELBased on surveys of dry-cleaners around Columbia University, we developed a more realistic instance generation model by:

1. Using a price per garment system rather than a uniform pound-based arrival

2. Only offering 2 and 3 day turnarounds

Item 2-day Price 3-day Price Weight (lbs)

Shirts $4.25 $2.25 0.5

Coats $15.00 $13.00 2

Trousers $5.00 $3.00 1

Dresses $10.00 $8.00 1

Sweaters $5.50 $3.50 1.5

REALISTIC MODEL RESULTS

When compared to Approximation Algorithm, DP performs better with fewer tardy jobs and lower cost, but takes significantly longer running time.

NEW MODEL SENSITIVITY ANALYSIS

1. Arrival rates

2. Load of machines

3. Price structures

ARRIVAL RATE SENSITIVITY

As the number of jobs increases, DP progressively performs:● better than Approximation Algorithm in terms of Total Cost of Tardy

Jobs, Number of Tardy Jobs● worse than Approximation Algorithm in terms of Run Times

LOAD SIZE SENSITIVITY

As the load size increases, DP progressively performs:● better in terms of Total Cost of Tardy Jobs, Number of Tardy Jobs● worse in terms of Running Times

PRICING STRUCTURE SENSITIVITY

Base Case: Difference between 2-day and 3-day is $2

Changed Structure 1: Increasing cost of garments by different amounts

Changed Structure 2: Difference between 2-day and 3-day is $3

PRICING STRUCTURE SENSITIVITY

● Increasing all the prices in the matrix resulted in slightly higher costs for tardy jobs (yet fewer tardy jobs), but about the same runtimes

● Increasing the difference in the 2-day and 3-day turnaround price resulted in the same the cost of tardy jobs, number of tardy jobs, and running times

CONCLUSIONS● Beyond a threshold in the volume of customer arrivals, we see that the DP

scheduling method performs better than the approximation method in reducing costs as well as tardy jobs.

● While the DP has a significantly longer running time than the approximation algorithm, the absolute time taken to run the DP is < 1 minute maintaining practicality in actually implementing it.

● Sensitivity Results○ Purchasing a machine with larger capacity can minimize costs further in an

overloaded system but may not be feasible for space or environmental reasons○ To increase revenue, it is better to increase all prices rather than just the

2 or 3-day prices.○ If the arrival rate is more variable than modeled, higher costs will be

incurred by the shop as the current rate lies at the threshold of incurring more tardy jobs

FUTURE STEPS● Introduce more realistic factors to the model

○ Increased volume of jobs by closing shop on Sunday○ Research probabilities of arrival of different garments ○ Include more garment types○ Use a data-driven customer arrival process

● Modify the problem setup○ Increase the number of machines○ Consider the fixed-cost of running a machine○ Expand the model to be a Flow Shop to include other processes

involved in dry-cleaning such as ironing and steaming

THANK YOU

Any questions?