Suncoast Office, a Goal Programming Problem

Suncoast Office, a Goal Programming Problem, Solution, Analysis, Sensitivity Analysis, and Report

Source book: Anderson, Sweeney, Williams “An Introduction to Management Science” Prepared by: Parisay with some changes

Problem Statement:

Management of Suncoast Office Supplies establishes monthly goals, or quotas, for the types of customers contacted. For the next 4 weeks, Suncoast's customer contact strategy calls for the sales force, which consists of four salespeople, to make 200 contacts with customers who have previously purchased supplies from the firm. In addition, the strategy calls for 120 contacts of new customers. The purpose of this latter goal is to ensure that the sales force is continuing to investigate new sources of sales.

Making allowances for travel and waiting time, as well as for demonstration and direct sales time, Suncoast has allocated 2 hours of sales force effort to each contact of a previous customer. New customer contacts tend to take longer and require 3 hours per contact. Normally, each salesperson works 40 hours per week, or 160 hours over the 4- week planning horizon; under a normal work schedule, the four salespeople will have 4(160)=640 hours of sales force time available for customer contacts.

Management is willing to use some overtime, if needed, but is also willing to accept a solution that uses less than the scheduled 640 hours available. However, management wants overtime of at most 40 hours and underutilization of the work force limited to at most 30 hours over the 4-week period. Thus, from an overtime perspective, management’s goal is to use no more than 640+40=680 hours of sales force time, and from a labor utilization perspective, management’s goal is to use at least 640-30=610 hours of sales force time.

In addition to the customer contact goals, Suncoast has established a goal regarding sales volume. Based on past experience, Suncoast estimates that each previous customer contacted will generate $250 of sales and each new customer contacted will generate $125 of sales. Management would like to generate sales of at least $70,000 for the next month.

Given Suncoast’s small sales force and the short time frame involved, management has decided that the overtime goal and the labor utilization goal are both priority level 1 goals. Management also concluded that the $70,000 sales goal should be a priority level 2 goal and that the two customer contact goals should be priority level 3 goals.

1 Problem Summary:

Customer Min number of Contact hr / Sales $ / contacts required customer customer Previous 200 2 250 New 120 3 125 At most 680 At least $70,000 hours per month At least 610 hours

Priority level 1 goals: Goal 1: Do not use any more than 680 hours of sales force time. Goal 2: Do not use any less than 610 hours of sales force time. Priority level 2 goal: Goal 3: Generate sales revenues of at least $70,000. Priority level 3 goals: Goal 4: Call on at least 200 previous customers. Goal 5: Call on at least 120 new customers.

Formulation:

X1: the number of previous customers contacted in 4-weeks X2: the number of new customers contacted in 4-weeks

Over time Under utilization Sales goal Pervious contacts New contacts

  Over time and under utilization Z1  P1 (S1 )  P1 (S 2 )  Sales Z 2  P2 (S3 ) Number of contacts   Z 3  P3 (S 4 )  P3 (S5 )

2 Input to WinQSB software:

3 Output from WinQSB:

4 Summary of solution:

X1 = 250, X2 = 60 Z1 = 0, Z2 = 0, Z3 = 60

Analysis of output:

 X1 = 250 >>> It means that we will contact 250 previous customers. That is the minimum of 200 previous customers is fulfilled and exceeded by 50, which is - desirable. It results in S 4 = 0.  X2 = 60 >>> It means that we will contact 60 new customers. That is the minimum of 120 new customers is not fulfilled and it is behind by 60, which is - not desirable. It resulted in S 5 = 60. Because of this value we ended up having Z3 = 60.  Z1 = 0 >>> This is related to total time and indicates there is no undesirable situation. Plug in the values of X1 and X2 into the time constraint we will have: 2X1 + 3X2 = 2(250) + 3(60) = 680. This results in using all 40 hours of possible overtime, which is no problem. As well as being above under utilization, this is no problem either.  Z2 = 0 >>> This is related to total sales and indicates there is no undesirable situation. Plug in the values of X1 and X2 into sales constraint we will have: 250X1 + 125X2 = 250(250) + 125(60) = 70000.

Report

Based on the given information we need to contact 250 previous customers and 60 new customers. It will result in total sales of $70,000. We need 680 hours of agents, this mean we will use 40 hours of overtime.

5 Sensitivity analysis

Input for reordered goals scenario 1:

Partial output for reordered goals scenario 1:

6 Input for reordered goals scenario 2:

Partial output for reordered goals scenario 2:

7 Sensitivity Analysis Summary for a Goal Programming Problem

(Details are in file called “Suncoast Example on Goal Programming Sensitivity Analysis” on Class Notes web page.)

. Priorities . . Optimal Solution . Second Deviation Highest Highest Lowest X1 X2 Z1 Z2 Z3 . S1+, S2- S3- S4-, S5- 250 60 0 0 60 S3- S1+, S2- S4-, S5- 250 60 0 0 60 S4-, S5- S1+, S2- S3- 200 120 0 80 5000

Prepared: April 2005, updated September 2009