Case:
“FIRST SMILE” AND ITS MANUFACTURERS:
ASSIGNMENT OF NEW KIDS STORES AND
PRODUCTION SCHEDULING OF KIDS
PRODUCTS
This case was written by Tanja Mlinar, Assistant Professor of Management at
IESEG School of Management (LEM-CNRS). This case is intended to be used as the
basis for class discussion rather than to illustrate either effective or ineffective
handling of a management situation.
Copyright © 2017, IESEG School of Management (LEM-CNRS), Paris, France. No
part of this publication may be copied, stored, transmitted, reproduced or distributed
in any form or medium whatsoever without the permission of the copyright owner.
Specialized
stores
1. The company “FIRST SMILE” is a retailer of large variety of products for children. The
products are classified into five categories: clothes, shoes, toys, furniture, and strollers. Due
to the previous success in the market during the last three years, the company has decided
to expand its business by opening new stores at different locations. Upon the detailed study,
the company has decided to open new specialized stores in which customers can find variety
of products from a specific product category. Five different locations are chosen where these
stores can be opened: The 1st, the 7th, the 8th, the 14th and the 15th arrondissement of Paris.
In order to provide full assortment of products in Paris, only one specialized store can be
open at a location, and all specialized stores should be opened. The expected annual profits
in 10.000 euros generated by opening specialized stores at different locations are provided
in Table 1. For instance, if the specialized store for clothes is opened in the 1st
arrondissement of Paris, the expected profit generated is 150.000 EUR per year.
Clothes
Shoes
Toys
Furniture
Strollers
Paris 1 arr.
Paris 7 arr.
Location
Paris 8 arr.
15
21
18
20
19
20
22
16
20
18
19
24
20
14
18
Paris 14
arr.
24
26
14
15
16
Paris 15
arr.
22
22
21
18
19
Table 1. The expected annual profits (in 10.000 EUR).
A. The company hires your team to help them to decide at which location to open each
specialized store (i.e. which product category should be offered at each location) in
order to maximize the total expected annual profit. Provide the optimal assignment
and the optimal total expected annual profit that the company can generate.
B. The top management has decided to follow your proposition (your solution of
Question A). However, the management has also decided to open one more store
that will sell the following product categories: clothes, shoes, and toys. The top
management aims to open the store in the 2nd arrondissement of Paris. Thus, in
addition to the total expected annual profit that you calculated, the company would
gain 260.000 euros more.
The company has chosen to open the mixed store in the 2nd arrondissement of Paris
because its expected annual profit is the highest. In other words, if the mixed store
is opened in any of the 5 initial locations, the expected annual profit would be lower
than 260.000EUR (see Table 2B). The top management has also considered the
possibility to open a specialized store in the 2nd arrondissement of Paris but they
estimated that the expected annual profit generated by any specialized store in the
2nd arr. would be lower than if the mixed store is opened there (see Table 2A).
Your task is to examine and to discuss whether the solution suggested by the top
management is the optimal. The data provided in Tables 1 and 2 should be taken
into account in your analysis. Note that, the constraints imposed by the company
remain the same: only one type of store can be assigned to one location, and all
types of store should be opened. Compare the solutions you obtained (the
assignment of each store to each location and the total expected annual profit) with
the solutions obtained for Question A?
A.
Children clothes
Children shoes
Toys
Furniture
Strollers
New Location:
Paris 2 arr.
24
25
14
19
17
B.
Paris 1 arr.
Paris 7 arr.
Paris 8 arr.
Paris 14 arr.
Paris 15 arr.
Mixed store
( clothes, shoes, and toys)
22
22
25
20
20
Table 2. The expected annual profits (in 10.000 EUR) of each specialized store in the new
location (A); and the expected annual profits (in 10.000 EUR) of the mixed store at the different
locations (B).
2. The retailer “First Smile” has ordered several types of shoes from the well-known shoe’s
manufacturer “Mr. Geppetto”. Each order has its code represented as follows “Shoes
XXYZWW”, where XX represents the age of the child in years, Y represents the color (for
instance, R-red, B-blue, Y-yellow, P-pink), Z represent the gender (G- girl, B-boy) and WW
represents the model of the shoe. The date when the order for a specific type of shoes is
placed, the size of order (in processing times in days) and the date when the products are
expected to be delivered at latest are given in Table 3. Note that “First Smile” expects
products to be delivered by the end of the order’s due date at latest. For instance, Shoes
15RG45 can be delivered at latest by the end of Friday of week 48.
Different models of shoes are processed at the manufacturer’s plant by using a single
production machine. The production of the orders is scheduled to start at earliest on Tuesday
Morning of week 43, 2016 (October 25). The manufacturer produces 7 days a week.
Job
Orders placed
Shoes 15RG45
Shoes 15BB43
Friday, week 41
Monday, week 41
Processing times
(in days)
5
13
Delivery deadline
Shoes 13YG40
Shoes 16YB45
Tuesday, week 42
Thursday, week 41
10
22
Wednesday, Week 48
Friday, Week 49
Shoes 18PG43
Wednesday, week 42
20
Monday, Week 52
Friday, Week 48
Monday, Week 45
Table 3. The orders placed, processing times and delivery deadlines of the orders
A. Currently, “Mr. Geppetto” has been using the First-Come-First-Served sequencing
rule (FCFS). According to the production manager the main reason lies in the
simplicity in its implementation. Would you agree with his explanation? Discuss
benefits and drawbacks of the FCFS rule in manufacturing.
B. Which sequencing rules would you suggest to the production manager in order to
increase the utilization rate and the average flow time and which one to reduce the
average lateness? Compare the performance measures achieved by the suggested
rules with those achieved by the current rule. Discuss it.
C. What is the job sequence of FCFS and each sequencing rule suggested? Discuss how
you obtained the sequence.
D. Given that the late jobs can have a significant impact on the reputation of FIRST
SMILE and its manufacturer, what would you suggest to the manufacturer in order
to deliver all products on time?
3. The retailer “FIRST SMILE” orders different sweaters for babies of age 0-1 year from
“Miumies”, an apparel manufacturer. The orders are placed twice per year in January and in
June to be delivered in June and December, respectively. In January, “FIRST SMILE” placed
12 different orders. Each order is represented by the code “Sweater XXY-ZWW”, where XX
represents the age of babies in months, Y the color, Z the gender and WW the model.
“Miumies” produces sweaters on a flow shop consisting of two dedicated machines for
sewing and dying. Each product is firstly produced on the sewing machine and then on the
dying machine. The processing times (in days) of products ordered are presented in Table 4.
The production of the orders at “Miumies” is scheduled to start in February 1.
A. Determine the schedule that will minimize the makespan. Explain how you obtain
the schedule.
B. Draw a Gant chart for the given problem.
C. Determine the total processing time of all jobs on each machine, the idle time of
each machine, and the makespan in the flow-shop.
Job
Sweater 12B-B12
Sweater 09B-B12
Sweater 06B-B12
Sweater 03B-B12
Sweater 01B-B12
Sweater 12R-G12
Sweater 09R-G12
Sweater 06R-G12
Sweater 03R-G12
Sweater 01R-G12
Sweater 12P-G22
Sweater 12B-B22
Sewing
7
3
9
4
8
7
5
2
4
6
14
12
Dying
4
5
1
2
11
13
6
7
3
1
9
7
Table 4. Processing times (in days) of the baby sweaters
4. The retailer “FIRST SMILE” orders strollers from the stroller manufacturer “BABYWOO”.
“BABYWOO” produces five different types of baby strollers such as travel strollers (denoted
by P1), double strollers (denoted by P2), triple strollers (denoted by P3), jogging strollers
(denoted by P4), and luxury strollers (denoted by P5). “BABYWOO” possesses a job shop
consisting of four different single-machine workstations used for the production of strollers.
Workstation j={1,2,3,4} is denoted by WSj.
Different types of strollers require different operations in the job shop. The schematic
representation of the job shop with a sequence of each stroller type is presented in Figure 1.
The sequence of a job represents the order of operations according to which the job has to
be processed. The product sequences are represented by straight lines with arrows and
different colors in Figure 1. For example, the sequence of the travel strollers (P1), represented
by blue line in Figure 1, is as follows: firstly the job is processed by WS1, then by WS2 and
finally by WS4. Upon finishing the last operation at WS4, the production of P1 is finished and
the product exits the production system (i.e., the job shop).
Note that, in Figure 1, Pi (ptij) represents product type i={1,..,5} and its processing time ptij
(in days) at workstation j. For example, P2 (7) presented on the line with the arrow towards
WS2 denotes that the processing time of P2 at WS2 is 7 days.
Figure 1. Job shop for production of baby strollers
A. Determine the schedule at each workstation that will minimize the makespan by
using the local search heuristic in Lekin. Show the schedule in a Gant chart. Show
the solutions of the problem (the total makespan, the total flow time, and the flow
time of each product). How many days it will take to produce each product?
Determine the bottleneck.
B. Determine the schedule at each workstation that will minimize the total flow time by
using the local search heuristic in Lekin. Show the schedule in a Gant chart. Compare
the solutions obtained with the ones in Question A. Discuss it.
C. The weights of the five jobs are presented in the second column of Table 5. Given
the weights, determine the schedule at each station that will minimize the total
weighted flow time. Show the schedule in a Gant chart. Discuss how your solutions
change with respect to the solutions obtained in Question B.
D. Determine the schedule at each station that will minimize the total weighted
tardiness considering the weights, due dates, and release dates of the five jobs given
in Table 5. Show the solutions of the problem (the total makespan, the total flow
time, the total tardiness, the total weighted tardiness, the total weighted flow time,
the flow time and the weighted flow time of each job). Show the schedule in a Gant
chart. Which products will not be delivered on time and what is their tardiness? How
much will tardy jobs cost the company? Discuss it.
Jobs
P1
P2
P3
P4
P5
Weights
6
1
10
3
1
Due dates
40
30
40
25
17
Release dates
0
3
5
5
3
Table 5. Weights, due dates and release dates of the five types of strollers