industrial engineering hw

IE413 HW2 Soln 1

♣ ♣ ♣ ♣ ♣ ♣ ♣♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ IE 413 Engineering OR I Homework #3 Solution

Due Tuesday, September 29, 2015 ♣ ♣ ♣ ♣ ♣ ♣♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣

1. “Mama’s Kitchen” serves from 5:30am each morning until 7:30pm in the afternoon. Tables are set and cleared by busers working 5-hour shifts beginning on the hour from 5am (shift #1) through 3pm (shift #11). Most are college students who hate to get up early in the morning, so Mama’s pays $12 per hour for the 5am, 6am, 7am and 8am shifts, and $9 per hour for the others. The manager seeks a minimum cost staffing plan that will have at least a minimum number of busers on duty each hour:

5am 6am 7am 8am 9am 10am 11am Noon #reqd 3 5 6 5 1 2 4 6

1pm 2pm 3pm 4pm 5pm 6pm 7pm #reqd 7 1 3 1 4 6 7

(a) Formulate a linear programming model (LP) for this problem. Be sure to define your

decision variables! (b) Provide LINDO input to solve the LP model provided in (a) (c) Provide LINGO input to solve the LP model provided in (a) (d) Use LINDO (or LINGO) to solve the problem, and describe the optimal solution

briefly in “plain English” 2. (Modification of Problem 3.5-2, page 87-88, of Hillier & Lieberman’s OR book, 10th edition) You are given the following data for a linear programming problem where the objective is to maximize the profit from allocating three resources to two nonnegative activities.

Contribution per unit = profit per unit of the activity

(a) Formulate a linear programming model for this problem. Be sure to define your

decision variables! (b) Use the graphical method to solve this model

IE413 HW2 Soln 2

(c) Use the simplex algorithm to solve this model (Show the initial and each succeeding tableau)

(d) Provide LINDO input to solve this model (e) Provide LINGO input to solve this model (f) Describe the optimal solution briefly in “plain English” 3. (Modification of Problem 3.4-10, page 85-86, of Hillier & Lieberman’s OR book, 10th edition) Eddie Smith is the director of the Computer Center for Johnson College. He now needs to schedule the staffing of the center. It is open from 8 A.M. until midnight. Eddie has monitored the usage of the center at various times of the day, and determined that the following number of computer consultants are required:

Two types of computer consultants can be hired: full-time and part-time. The full-time consultants work for 8 consecutive hours in any of the following shifts: morning (8 A.M.–4 P.M.), afternoon (noon–8 P.M.), and evening (4 P.M.–midnight). Full-time consultants are paid $40 per hour. Part-time consultants can be hired to work any of the four shifts listed in the above table. Part-time consultants are paid $30 per hour. An additional requirement is that during every time period, there must be at least 2 full-time consultants on duty for every part time consultant on duty. Eddie would like to determine how many full-time and how many part-time workers should work each shift to meet the above requirements at the minimum possible cost.

(a) Formulate an integer programming model for this problem. Be sure to define your

decision variables! (b) Use LINDO (or LINGO) to solve this model and describe the optimal solution briefly

in “plain English”