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Assembly Systems Project Planning Production for Multi-Product Assembly Systems with Bottleneck Resources Introduction A jet engine manufacturing firm produces a range of engine models for both commercial and military customers

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Assembly Systems Project

Planning Production for Multi-Product Assembly Systems

with Bottleneck Resources

Introduction

A jet engine manufacturing firm produces a range of engine models for both commercial and

military customers. While the end products are vastly different, their supply chains and

manufacturing lines share key resources. Limited capacity in forging, a manufacturing step

required for parts going into every single final product, are resulting in delays throughout the

product line, disgruntled customers, and internal disputes among product managers fighting to

prioritize their supplies. Adding forging capacity in the short to medium terms is not possible.

Not only is the equipment extremely expensive, it will take over a year to build and install. As a

result, the firm is looking for a short-term solution that makes the best of the capacity available.

A system-wide perspective is thus needed to schedule the various production steps throughout the

supply chain and streamline the process for on-time product delivery so as to minimize the costs

and rippling effects of the part supply shortages.

Product Information

Each end product is complex, composed of thousands of parts. The product structure is described

by its bill of materials (BOM), which is typically represented as a product tree diagram that

shows the components making up each subassembly at each level of the assembly process, along

with the number of units needed; see Figure 1. To explore the joint scheduling of production of

various products, managers have provided a simplified BOM containing the critical components

for their two most profitable products, which we will refer to as end items 1 and 2.

In addition, they have provided the weekly holding costs (H) and delay penalties (P) for each

part to guide the scheduling of production towards minimizing these costs.

Figure 2: Holding and delay penalty costs per week.

Committed Orders

Management is most concerned about their ability to deliver their outstanding orders for these

two products over the next 10 weeks. Delays carry a steep penalty per week of delay, as

described above, and can severely damage their hard-earned trust from their most valuable

customers. Committed orders over the next 10 weeks are collected in the table below:

Figure 3: End item demand for each week in the horizon.

In addition, there are orders of 20 units of part C to be delivered on week 3, 8 units of part D on

week 5, and 2 parts F on week 7.

Process Capacity

The forging process has been proven to be the bottleneck for the firm’s entire supply chain. All

the lower level parts {C, D, E, H, I} undergo this process, which is performed by a single

production line running 24 hours a day, 7 days a week. The production times R and required

change-over (setup) times S for each of these parts are as follows:

Part

Time

(mins)

C

D

E

H

I

R

30

30

30

30

60

S

120

120

120

120

120

Figure 4: Processing (R) and setup (S) times for the bottleneck process.

Assignment

The goal is to develop a practical tool that the firm can use to streamline the production at each

level of the supply chain with that of the bottleneck resource in order to optimize profits. The

following steps are suggested to systematically address all aspects of the problem.

1. Write an AMPL data file that captures the given information on the BOM and on

demand. [10 points]

2. Write and run an AMPL model to calculate all of the parts that will need to be produced

and when to satisfy those demands assuming zero lead times and no capacity

constraints. [15 points]

3. Assume now a lead time of one week for each step. Change your model to consider this.

Will your data file need to change as well? [15 points]

4. Change your model to incorporate the processing times and capacity constraints. Find the

lowest cost production schedule given the holding costs (H) and penalties (P) for each

part. [10 points]

5. Change your model to incorporate the setup times and solve again. [20 points] a) Solve

first assuming both X (production) and z (setup) are non-negative continuous

variables.

b) Solve requiring z to be binary variables.

c) Solve requiring in addition the production X to be integer.

d) Compare the production schedule, cost and solution time of the three solutions and

explain the differences.

Hint: You can calculate the CPU time taken by the AMPL solution process by adding the

command display _total_solve_time;

6. In exploring longer term solutions, management would like to understand the value

associated with increasing capacity by a factor of 2 or 3? What would you

recommend? [30 points]

Note: You are not required to use AMPL. You can use Python/Gurobi or any other language and

solver of your choice.